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Lorentz forces

http://weelookang.blogspot.sg/2010/11/ejs-open-source-lorentz-force-on.html

Lorentz force on a wire

This program simulates the force exerted by a magnetic field between two magnets on an electrical current trough a wire.

The wire is suspended on a spring and will oscillate when the battery (which is connected to the ends of the wire) is turned on and off, the angle of the wire with respect to the magnetic field is changed, or the poles of the magnets are switched.

new remixed version by lookang 20 Dec 2010

original version by Professor Francisco (Paco) Esquembre

Credits:

The Lorentz force on a wire model was created by Francisco (Paco) Esquembre, customized by Loo Kang Wee using the Easy Java Simulations (EJS) version 4.2 authoring and modeling tool. An applet version of this model is available on the NTNU website < http://www.phy.ntnu.edu.tw/ntnujava/ >.

You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP comPADRE collection <http://www.compadre.org/OSP/>.

Exercise Exercise by lookang

Introduction www.bk.psu.edu/faculty/gamberg/mag_lab.doc
A current-carrying wire in a magnetic field experiences a force. The magnitude and direction of this force F, depend on four variables:
the magnitude and direction of the current (I),
the strength and direction of the magnetic field (B)
the length of the wire expose to magnetic field is (L)
the angle between the current I and field B is (ϑ)
Advanced: The force can be described mathematically by the vector cross-product:
O level: Fleming’s Left Hand Rule predicts the using the left hand, F (thumb) B (index finger) I (middle finger)

image from National High Magnetic Field Laboratoryhttp://www.magnet.fsu.edu/education/tutorials/java/handrules/index.html

Advanced: F = I ^ B. L where ^ is the cross product
O level and A level: F = I . B. L.sin ϑ where ϑ is the angle between I and B

where
Force F is in newtons N
current I is in amperes A
length L in meters m
magnetic field B in teslas T

The direction of the force F is perpendicular to both the current I and the magnetic field B, and is predicted by the Advanced: right-hand cross-product rule.
O level and A level: Fleming’s Left Hand Rule

Engage:
a real live demo is the best.!!
a youtube video http://www.youtube.com/watch?v=_X8jKqZVwoI&feature=player_embedded
Engage 1: Would you believe that a wire can jump up even though it is not alive?
Engage 2: have you thought about how a direct current can cause a rotating motion which can be used to drive some simple toys (e.g Tamiya cars) ?
http://www.tamiya.com/english/products/42183trf502x/top.jpg

Explore
1. Explore the simulation, this simulation is designed with a wire supported by a spring in a system of magnetic fields in y direction.
2 The play button runs the simulation, click it again to pause and the reset button brings the simulation back to its original state.
3 by default values B, I, L, play the simulation. Notice that the wire is in its motionless in its previous state of motion. What is the physics principle simulatted here.
hint: newton's 1st law
4 reset the simulation.
5 using the default values(L = 1 m, ϑ = 90 deg), adjust the value of By =1 and Ix =1 play the simulation. what did you observe? explain the motion in terms of the influences of magnetic field (assume gravitational effect can be neglected, in this computer model gravity is not model)
6 explore the slider z. what do this slider control?
7 explore the slider vz. what does this slider control?
8 by leaving the cursor on the slider, tips will appear to give a description of the slider. you can try it the following sliders such as the drag coefficient b.
9 there are some value of time of simulation t and the checkbox graph for height vs time.
10 vary the simulation and get a sense of what it does.

11 reset the simulation
Mechanics
12 using the default values (By =0, Ix=0) set z = -0.6, vz=0, b=0). Observe the motion of the wire in the absence of magnetic field. Predict what you will see. Describe the motion of the wire. Explain why this it is so?
hint: select the checkbox to view the scientific graph of height vs t.
13 using the default values (By =0, Ix=0) set z = -0.6, vz=0, b=1). Observe the motion of the wire in the absence of magnetic field. Predict what you will see. Describe the motion of the wire. Explain why this it is so?
hint: select the checkbox to view the scientific graph of height vs t.
14 using the default values (By =0, Ix=0) set z = -0.6, vz=1, b=0). Observe the motion of the wire in the absence of magnetic field. Predict what you will see. Describe the motion of the wire. Explain why this it is so?
hint: select the checkbox to view the scientific graph of height vs t.
15 using the default values (By =0, Ix=0) set z = -0.6, vz=1, b=1). Observe the motion of the wire in the absence of magnetic field. Predict what you will see. Describe the motion of the wire. Explain why this it is so?
hint: select the checkbox to view the scientific graph of height vs t.
16 conduct more scientific inquiry into the simulation if need before the next part of the question.
Elaborate
17 explain the effects of b, the model used is drag force = b.v.

18 reset the simulation
Magnetic Force
Evaluate:
19 A scientist hypothesis "O level and A level: F = I . B. L. where ϑ =90 deg" play the simulation for different initial condition and design an experiment with tables of values to record systematically, determine whether the hypothesis is accurate.

20 what is the impact of the ϑ != 90 deg ?
21 Suggest a better hypothesis
22 This computer model does not build in gravity, suggest with reason(s) why you agree or disagree with this statement. You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: and in the OSP comPADRE collection

Have Fun! Lorentz force on a wire

Title and author:

Lorentz force on a wire
Logo

author image Francisco (Paco) Esquembre; lookang (This email address is being protected from spambots. You need JavaScript enabled to view it.)

Released under a

license.

Translations

Code	Language		Translator	Run

Credits

Francisco (Paco) Esquembre; lookang (This email address is being protected from spambots. You need JavaScript enabled to view it.)

Briefing Document: Lorentz Force on a Wire Simulation

1. Overview

This document reviews an interactive, web-based simulation designed to demonstrate the Lorentz force acting on a current-carrying wire within a magnetic field. The simulation is an open educational resource (OER) from Open Source Physics @ Singapore, built using Easy JavaScript Simulations (EJS). It aims to provide students with a hands-on understanding of electromagnetism principles, specifically Fleming's Left Hand Rule and the factors affecting the force on a wire in a magnetic field.

2. Key Concepts and Principles

Lorentz Force: The core principle explored is the Lorentz force, which is the force exerted on a moving charged particle (in this case, electrons in a wire) by a magnetic field. This force is perpendicular to both the direction of the current and the magnetic field.
Fleming's Left Hand Rule: The simulation and supporting materials emphasize Fleming's Left Hand Rule as a way to determine the direction of the force. "O level: Fleming’s Left Hand Rule predicts the using the left hand, F (thumb) B (index finger) I (middle finger)."
Factors Affecting Force: The document clearly outlines the variables that influence the magnitude of the Lorentz force:
Current (I): The magnitude and direction of the current flowing through the wire.
Magnetic Field (B): The strength and direction of the magnetic field.
Length (L): The length of the wire exposed to the magnetic field.
Angle (ϑ): The angle between the direction of the current and the magnetic field.
Mathematical Representation: The document presents both basic and advanced formulas for the Lorentz force:
Basic (O/A Level): F = I . B . L . sin ϑ
Advanced: F = I ^ B . L (where ^ denotes the vector cross-product)

3. Simulation Description

Interactive Model: The simulation visually represents a wire suspended by a spring within a magnetic field. Users can adjust parameters such as:
Magnetic field strength (By)
Current (Ix)
Initial position of the wire (z)
Initial velocity of the wire (vz)
Drag coefficient (b)
Observable Effects: When the simulation runs, users can observe the following:
The wire oscillates due to the Lorentz force.
The motion changes depending on adjustments made to parameters like current, magnetic field and initial conditions.
Users can plot the height vs. time of the wire.
No Gravity: The simulation deliberately neglects gravity to isolate the effects of the Lorentz force. "This computer model does not build in gravity..."

4. Learning Objectives and Pedagogical Approach

Target Audience: The resource is intended for secondary and junior college students, with differentiated learning goals for "O level" and "A level" students.
Inquiry-Based Learning: The simulation encourages exploration through a series of guided questions designed to prompt students to test hypotheses and develop an understanding of the physics at play. For example, users are encouraged to, "...play the simulation for different initial condition and design an experiment with tables of values to record systematically, determine whether the hypothesis is accurate."
Engagement: The document uses engaging prompts to motivate students to think about the application of the principles in real-world scenarios, e.g. "Would you believe that a wire can jump up even though it is not alive?" and "Have you thought about how a direct current can cause a rotating motion which can be used to drive some simple toys (e.g Tamiya cars) ?"
Progression: The simulation and guide are intended to take students from simple observations using default values, through to manipulating several variables, and ultimately formulating a better hypothesis than provided.

5. Technical Details

Technology: The simulation is developed using JavaScript/HTML5, making it accessible on various platforms, including desktops, laptops, tablets, and smartphones. "Android/iOS including handphones/Tablets/iPads, Windows/MacOSX/Linux including Laptops/Desktops, ChromeBook Laptops"
Open Source: The model is available under a Creative Commons Attribution license, allowing users to modify and remix it for educational purposes, with the Easy JavaScript Simulations library being subject to a separate commercial license.
EJS Customization: The simulation is built on EJS, an open-source modelling tool. The document explains that users can examine and modify the simulation by double-clicking on the .jar file, right-clicking, and then selecting the 'Open EJS Model' command - provided the user has EJS installed on their machine.
External Resources: The document links to several external resources, such as a YouTube video demonstrating the effect of the Lorentz force on a current carrying conductor, and online applets which cover similar physics.

6. Key Quotes:

"The wire is suspended on a spring and will oscillate when the battery (which is connected to the ends of the wire) is turned on and off, the angle of the wire with respect to the magnetic field is changed, or the poles of the magnets are switched." (Describing the core simulation behavior)
"A current-carrying wire in a magnetic field experiences a force. The magnitude and direction of this force F, depend on four variables: the magnitude and direction of the current (I), the strength and direction of the magnetic field (B), the length of the wire expose to magnetic field is (L), the angle between the current I and field B is (ϑ)" (Defining the variables influencing force)
"O level: Fleming’s Left Hand Rule predicts the using the left hand, F (thumb) B (index finger) I (middle finger)" (Defining the left hand rule)
"The direction of the force F is perpendicular to both the current I and the magnetic field B, and is predicted by the Advanced: right-hand cross-product rule. O level and A level: Fleming’s Left Hand Rule" (Defining the rule for direction of force)
"This computer model does not build in gravity, suggest with reason(s) why you agree or disagree with this statement." (Engaging students in evaluating the simulation's limitations)
"A real live demo is the best!!" (Highlighting the real world application of the theory)

7. Conclusion

The Lorentz force simulation is a valuable OER for teaching electromagnetism. Its interactive nature and the included guided questions make it useful for students to explore the relationship between current, magnetic fields, and force. The resource's open-source nature and accessibility across devices adds to its educational value. This is a sophisticated resource with the potential to provide strong learning outcomes.

Lorentz Force on a Wire Study Guide

Quiz

What is the Lorentz force, and how is it demonstrated in the simulation?
Describe the relationship between the current, magnetic field, and force using Fleming's Left Hand Rule.
What is the formula for calculating the magnitude of the force on a current-carrying wire in a magnetic field when the wire and field are perpendicular?
How does the angle between the wire and the magnetic field affect the force on the wire?
Explain how the simulation allows you to observe the effects of changing the magnetic field strength on the wire.
What does the slider 'z' in the simulation control? How does this relate to the wire's position?
How does changing the 'vz' slider in the simulation affect the wire's motion?
What is the effect of the 'b' slider, and how does it relate to the concept of drag?
Explain how the simulation demonstrates Newton's First Law of Motion.
Why is gravity not included in the simulation, according to the source material?

Quiz Answer Key

The Lorentz force is the force exerted on a moving charged particle (or current-carrying wire) by a magnetic field. The simulation demonstrates this force by showing the movement of a wire when an electric current is passed through it within a magnetic field.
Fleming's Left Hand Rule states that if you point your index finger in the direction of the magnetic field, your middle finger in the direction of the current, then your thumb will point in the direction of the force on the wire.
When the current and magnetic field are perpendicular, the magnitude of the force is given by F = I * B * L, where F is the force, I is the current, B is the magnetic field strength, and L is the length of the wire within the magnetic field.
The force on the wire is proportional to the sine of the angle (ϑ) between the wire and the magnetic field. The force is maximum when the angle is 90 degrees (perpendicular) and zero when the angle is 0 degrees (parallel).
By adjusting the simulation's By slider (magnetic field), the user can observe the effect a stronger or weaker magnetic field has on the wire's movement, with a stronger field producing more movement in the wire.
The 'z' slider in the simulation controls the initial position of the wire along the z-axis which corresponds to the vertical displacement of the wire within the simulation.
The 'vz' slider in the simulation controls the initial velocity of the wire along the z-axis, affecting the wire's initial vertical motion.
The 'b' slider controls the drag coefficient which is directly proportional to the drag force exerted on the wire. Higher values of 'b' will increase the drag force on the wire.
When the magnetic field and current are zero the wire remains motionless or continues its current state of motion, demonstrating Newton's first law, which states that an object at rest stays at rest and an object in motion stays in motion at a constant velocity, unless acted upon by a net force.
Gravity is not included in the model to simplify the simulation and focus on the effects of the magnetic force. The simulation wants to show only the force on the wire when the other force of gravity is removed.

Essay Questions

Discuss the real-world applications of the Lorentz force, drawing on examples beyond the immediate scope of the simulation, and analyze how changes in the variables (current, magnetic field, wire length, and angle) influence the device's performance.
Using the simulation and the principles of electromagnetism, explain how an electric motor operates, with a specific focus on the function of the Lorentz force, and discuss potential limitations of the simulation model in representing real-world motors.
Describe the process by which scientists use mathematical models, such as the one demonstrated in the simulation, to make predictions about real-world phenomena, and evaluate the significance of this mathematical model in the development of technologies using electromagnetic forces.
Analyze the effectiveness of using interactive simulations, like the one described in the source material, for teaching complex physics concepts such as the Lorentz force, and discuss both the advantages and potential disadvantages of this teaching approach compared to a lecture and experiment.
Compare and contrast the "O level" and "Advanced" mathematical descriptions of the Lorentz force, and discuss how the simulation can be used to bridge the gap between the simplified and the more complex approaches to understanding this force.

Glossary of Key Terms

Lorentz Force: The force exerted on a moving charged particle (or a current-carrying wire) by a magnetic field. The force is perpendicular to both the direction of the particle's velocity and the magnetic field.
Fleming's Left-Hand Rule: A mnemonic used to determine the direction of the force on a current-carrying wire in a magnetic field; the thumb, index finger, and middle finger, when positioned perpendicular to each other, represent the force, magnetic field, and current directions respectively.
Current (I): The flow of electric charge, measured in amperes (A).
Magnetic Field (B): A field of force generated by moving electric charges, measured in teslas (T).
Length of Wire (L): The length of the current-carrying wire that is exposed to the magnetic field, measured in meters (m).
Angle (ϑ): The angle between the direction of the current and the direction of the magnetic field.
Vector Cross-Product: A mathematical operation that takes two vectors and produces a third vector that is perpendicular to both, used to precisely define the Lorentz force's direction and magnitude.
Drag Force: A force that opposes the motion of an object through a fluid (like air), often modeled as being proportional to the object's velocity.
Newton's First Law of Motion (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Simulation: A computer program that models a real-world process. In this context, it refers to the software that models the behavior of a current-carrying wire in a magnetic field.

Sample Learning Goals

O level: Fleming’s Left Hand Rule predicts the using the left hand, F (thumb) B (index finger) I (middle finger)

A level

For Teachers

This program simulates the force exerted by a magnetic field between two magnets on an electrical current trough a wire.
The wire is kept in equilibrium in the absence of gravity, suspended on a spring and will oscillate when the battery (which is connected to the ends of the wire) is turned on and off, the angle of the wire with respect to the magnetic field is changed, or the poles of the magnets are switched.
reference:http://www.walter-fendt.de/ph14e/lorentzforce.htm

Introduction

A current-carrying wire in a magnetic field experiences a force. The magnitude and direction of this force F, depend on four variables:
the magnitude and direction of the current (I),
the strength and direction of the magnetic field (B)
the length of the wire expose to magnetic field is (L)
the angle between the current I and field B is (ϑ)
Advanced: The force can be described mathematically by the vector cross-product:
O level: Fleming’s Left Hand Rule predicts the using the left hand, F (thumb) B (index finger) I (middle finger)
image from National High Magnetic Field Laboratory http://www.magnet.fsu.edu/education/tutorials/java/handrules/index.html

Advanced: F = I ^ B. L where ^ is the cross product
O level and A level: F = I . B. L.sin ϑ where ϑ is the angle between I and B

where
Force F is in newtons N
current I is in amperes A
length L in meters m
magnetic field B in teslas T

The direction of the force F is perpendicular to both the current I and the magnetic field B, and is predicted by the Advanced: right-hand cross-product rule.
O level and A level: Fleming’s Left Hand Rule

Engage

Engage:
a real live demo is the best.!!
A youtube video http://www.youtube.com/watch?v=_X8jKqZVwoI&feature=player_embedded

Engage 1: Would you believe that a wire can jump up even though it is not alive?
Engage 2: have you thought about how a direct current can cause a rotating motion which can be used to drive some simple toys (e.g Tamiya cars) ?
http://www.tamiya.com/english/products/42183trf502x/top.jpg

Explore

1. Explore the simulation, this simulation is designed with a wire supported by a spring in a system of magnetic fields in y direction.
2 The play button runs the simulation, click it again to pause and the reset button brings the simulation back to its original state.
3 by default values B, I, L, play the simulation. Notice that the wire is in its motionless in its previous state of motion. What is the physics principle simulatted here.
hint: newton's 1st law
4 reset the simulation.
5 using the default values(L = 1 m, ϑ = 90 deg), adjust the value of By =1 and Ix =1 play the simulation. what did you observe? explain the motion in terms of the influences of magnetic field (assume gravitational effect can be neglected, in this computer model gravity is not model)
6 explore the slider z. what do this slider control?
7 explore the slider vz. what does this slider control?
8 by leaving the cursor on the slider, tips will appear to give a description of the slider. you can try it the following sliders such as the drag coefficient b.
9 there are some value of time of simulation t and the checkbox graph for height vs time.
10 vary the simulation and get a sense of what it does.

11 reset the simulation
Mechanics
12 using the default values (By =0, Ix=0) set z = -0.6, vz=0, b=0). Observe the motion of the wire in the absence of magnetic field. Predict what you will see. Describe the motion of the wire. Explain why this it is so?
hint: select the checkbox to view the scientific graph of height vs t.
13 using the default values (By =0, Ix=0) set z = -0.6, vz=0, b=1). Observe the motion of the wire in the absence of magnetic field. Predict what you will see. Describe the motion of the wire. Explain why this it is so?
hint: select the checkbox to view the scientific graph of height vs t.
14 using the default values (By =0, Ix=0) set z = -0.6, vz=1, b=0). Observe the motion of the wire in the absence of magnetic field. Predict what you will see. Describe the motion of the wire. Explain why this it is so?
hint: select the checkbox to view the scientific graph of height vs t.
15 using the default values (By =0, Ix=0) set z = -0.6, vz=1, b=1). Observe the motion of the wire in the absence of magnetic field. Predict what you will see. Describe the motion of the wire. Explain why this it is so?
hint: select the checkbox to view the scientific graph of height vs t.
16 conduct more scientific inquiry into the simulation if need before the next part of the question.
Elaborate
17 explain the effects of b, the model used is drag force = b.v.

18 reset the simulation
Magnetic Force
Evaluate:
19 A scientist hypothesis "O level and A level: F = I . B. L. where ϑ =90 deg" play the simulation for different initial condition and design an experiment with tables of values to record systematically, determine whether the hypothesis is accurate.

20 what is the impact of the ϑ != 90 deg ?
21 Suggest a better hypothesis
22 This computer model does not build in gravity, suggest with reason(s) why you agree or disagree with this statement. You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: and in the OSP comPADRE collection

Have Fun!

Research

[text]

Video

Electromagnetism (part 1): Force acting on a current-carrying conductor in a magnetic field by ETDtogo https://www.youtube.com/watch?v=URgZQ76tV1Y

Version:

Other Resources

http://www.walter-fendt.de/ph14e/lorentzforce.htm

Frequently Asked Questions About the Lorentz Force on a Wire Simulation

What is the Lorentz force, and how does it relate to the simulation?
The Lorentz force is the force exerted on a charged particle moving in a magnetic field. In this simulation, it specifically refers to the force experienced by a current-carrying wire within a magnetic field. The simulation allows users to visualize how changes in the current, magnetic field strength, wire length, and the angle between the current and the magnetic field affect the force on the wire, causing it to move or oscillate. This force is fundamental to the operation of electric motors and other electromagnetic devices.
What are the key variables that affect the Lorentz force on a wire?
The magnitude and direction of the Lorentz force on a wire depend on four main variables: (1) the magnitude and direction of the current (I), measured in amperes (A), flowing through the wire; (2) the strength and direction of the magnetic field (B), measured in teslas (T); (3) the length of the wire exposed to the magnetic field (L), measured in meters (m); and (4) the angle (ϑ) between the current and the magnetic field. The force is proportional to the product of current, magnetic field strength, length of wire, and the sine of the angle between current and magnetic field. Mathematically, this can be represented as F = I * B * L * sin(ϑ).
How does the simulation represent the relationship between the direction of current, magnetic field, and force?
The simulation demonstrates the relationship between the direction of the current, magnetic field, and Lorentz force using Fleming's Left Hand Rule. This rule provides a mnemonic where the thumb, index finger, and middle finger of the left hand, when held mutually perpendicular, represent the directions of the force (F), magnetic field (B), and current (I), respectively. The advanced vector cross-product rule is also applicable, where the force is perpendicular to both the direction of the current and magnetic field (F = I x B).
What is the purpose of the sliders in the simulation?
The sliders in the simulation allow users to adjust various parameters and observe their effects. Sliders control the magnitude of the magnetic field (By), the current (Ix), the initial position (z) and initial velocity (vz) of the wire in the vertical direction, as well as the drag coefficient (b) experienced by the wire as it moves through the magnetic field. By manipulating these sliders, users can investigate how each factor impacts the force and motion of the wire. The simulation also has a checkbox to toggle display of a graph of the wire's height vs time, and a simulation time indicator.
Why does the simulation exclude gravity?
The computer model intentionally excludes gravity to focus specifically on the Lorentz force and its effects. In the real world, gravity would influence the wire's motion, but this simulation aims to isolate the electromagnetic forces to facilitate a clearer understanding. This allows students to focus on the concepts without additional complexity. It's acknowledged that the simulation can be extended to include gravity in other versions of this type of simulation.
What is the role of the spring in the simulation?
The wire in the simulation is suspended on a spring. This spring is important because it provides a restoring force. When the Lorentz force pushes or pulls on the wire, it causes the spring to compress or extend. The spring’s restoring force then pulls the wire back, creating an oscillating motion. Without the spring, the wire would move in one direction and not return to its original position. This system illustrates how the magnetic force can cause a current-carrying wire to move back and forth or up and down.
What is the effect of the drag coefficient (b) on the wire's motion?
The drag coefficient (b) in the simulation represents the resistance experienced by the wire as it moves through the air or other medium. Increasing the drag coefficient will cause the wire's oscillations to slow down, as the drag force opposes its motion. Mathematically, this is represented by the model drag force = b.v. This feature enables the exploration of how resistive forces impact a system involving electromagnetic forces and mechanics.
How can this simulation be used for educational purposes?
This interactive simulation can be used by instructors to demonstrate the relationship between current, magnetic field, and force on a wire, providing a visual and hands-on experience for students learning about electromagnetism. It can be used by students for exploration, scientific inquiry, and designing experiments. Students can adjust parameters, make observations, and collect data, fostering their understanding of the Lorentz force, Fleming's Left Hand Rule, and Newton's laws of motion. By making the simulation customizable, the tool allows students to engage in the scientific method and learn through experimentation. The included challenges also allow instructors to use this tool in their lesson design.

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Details: Written by Loo Kang Wee; Parent Category: 05 Electricity and Magnetism; Category: 08 Electromagnetism; Published: 15 June 2016; Created: 15 June 2016; Last Updated: 08 January 2025; Hits: 18354