Magnetic Force - Revision history

Ritwic Verma: /* A Mathematical Model */

2025-11-23T03:37:24Z

A Mathematical Model

Ritwic Verma: /* A Computational Model */

2025-11-23T03:26:52Z

A Computational Model

← Older revision		Revision as of 23:26, 22 November 2025
Line 85:		Line 85:


	In addition to examining how individual charged particles behave in a magnetic field, it is equally important to understand how an entire current-carrying wire experiences magnetic forces. A current is simply a collection of moving charges, and each charge experiences a magnetic force. When these individual forces are combined, the total magnetic force acting on a segment of wire inside a magnetic field is given by:		In addition to examining how individual charged particles behave in a magnetic field, it is equally important to understand how an entire current-carrying wire experiences magnetic forces. A current is simply a collection of moving charges, and each charge experiences a magnetic force. When these individual forces are combined, the total magnetic force acting on a segment of wire inside a magnetic field is given by:

	<math>\vec F = I\, \vec L \times \vec B</math>		<math>\vec F = I\, \vec L \times \vec B</math>

	Here:		Here:
	~~- <math>I</math> is the conventional current through the wire,~~
	~~- <math>\vec L</math> is a vector whose direction represents the direction of current and whose magnitude is the length of the wire segment inside the magnetic field,~~
	~~- <math>\vec B</math> is the magnetic field vector.~~

	Because the force is described by a cross product, the resulting magnetic force is always perpendicular to both the direction of the current and the direction of the magnetic field. This means that changing either the orientation of the wire or the direction of the magnetic field will change the ~~direction—and~~ sometimes even the ~~sign—of~~ the resulting magnetic force.		* <math>I</math> is the conventional current through the wire
			* <math>\vec{L}</math> is a vector whose direction represents the direction of current and whose magnitude is the length of the wire segment inside the magnetic field
			* <math>\vec{B}</math> is the magnetic field vector

			Because the force is described by a <b>cross product</b>, the resulting magnetic force is always <b>perpendicular</b> to both the direction of the current and the direction of the magnetic field. This means that changing either the orientation of the wire or the direction of the magnetic field will change the direction — and sometimes even the sign — of the resulting magnetic force.

	The following GlowScript model demonstrates exactly how the direction of the magnetic field and the orientation of the wire determine the force on the wire. Sliders allow you to independently change the x, y, and z components of the magnetic field vector, as well as rotate the wire in the plane. As these quantities change, the magnetic force vector updates instantly to reflect the geometry of the cross product in real time.		The following GlowScript model demonstrates exactly how the direction of the magnetic field and the orientation of the wire determine the force on the wire. Sliders allow you to independently change the x, y, and z components of the magnetic field vector, as well as rotate the wire in the plane. As these quantities change, the magnetic force vector updates instantly to reflect the geometry of the cross product in real time.

	This simulation provides an intuitive way to understand:		This simulation provides an intuitive way to understand:
	- how the magnitude of the force depends on the angle between <math>\vec L</math> and <math>\vec B</math>,
	- how the direction of the force rotates smoothly as either vector is rotated,		* how the magnitude of the force depends on the angle between <math>\vec{L}</math> and <math>\vec{B}</math>
	~~- and~~ why the right-hand rule naturally follows from the properties of the cross product.		* how the direction of the force rotates smoothly as either vector is rotated
			* why the <b>right-hand rule</b> naturally follows from the properties of the cross product

	You can interact with this model here:		You can interact with this model here:

	[[~~Magnetic Force on a Current-Carrying Wire~~ https://www.glowscript.org/#/user/Ritwic_Verma/folder/wiki/program/magneticforceonacurrentcarryingwire)]		[[https://www.glowscript.org/#/user/Ritwic_Verma/folder/wiki/program/magneticforceonacurrentcarryingwire Magnetic Force on a Current-Carrying Wire ]]

	==Examples==		==Examples==

Ritwic Verma: /* A Computational Model */

2025-11-23T03:23:26Z

A Computational Model

← Older revision		Revision as of 23:23, 22 November 2025
Line 83:		Line 83:

	Also, take note of the iterative calculations made in the code. Within the code, we must initalize values for the initial velocity and momentum, position, mass, and charge of the particle, and magnetic field present in the location of the electron. In the iterative calculations, we must update the value of the magnetic force, as it is constantly changing directions since the electron's velocity is also changing in direction. Similarly, a net force causes a change in momentum, so we must update the momentum and velocity of the particle by utilizing the momentum principle where the derivative of momentum with respect to time is equivalent to the net force acting upon the particle. Furthermore, we update the particle's position and extend and append the trail with the particle's current location to display the path.		Also, take note of the iterative calculations made in the code. Within the code, we must initalize values for the initial velocity and momentum, position, mass, and charge of the particle, and magnetic field present in the location of the electron. In the iterative calculations, we must update the value of the magnetic force, as it is constantly changing directions since the electron's velocity is also changing in direction. Similarly, a net force causes a change in momentum, so we must update the momentum and velocity of the particle by utilizing the momentum principle where the derivative of momentum with respect to time is equivalent to the net force acting upon the particle. Furthermore, we update the particle's position and extend and append the trail with the particle's current location to display the path.


			In addition to examining how individual charged particles behave in a magnetic field, it is equally important to understand how an entire current-carrying wire experiences magnetic forces. A current is simply a collection of moving charges, and each charge experiences a magnetic force. When these individual forces are combined, the total magnetic force acting on a segment of wire inside a magnetic field is given by:

			<math>\vec F = I\, \vec L \times \vec B</math>

			Here:
			- <math>I</math> is the conventional current through the wire,
			- <math>\vec L</math> is a vector whose direction represents the direction of current and whose magnitude is the length of the wire segment inside the magnetic field,
			- <math>\vec B</math> is the magnetic field vector.

			Because the force is described by a cross product, the resulting magnetic force is always perpendicular to both the direction of the current and the direction of the magnetic field. This means that changing either the orientation of the wire or the direction of the magnetic field will change the direction—and sometimes even the sign—of the resulting magnetic force.

			The following GlowScript model demonstrates exactly how the direction of the magnetic field and the orientation of the wire determine the force on the wire. Sliders allow you to independently change the x, y, and z components of the magnetic field vector, as well as rotate the wire in the plane. As these quantities change, the magnetic force vector updates instantly to reflect the geometry of the cross product in real time.

			This simulation provides an intuitive way to understand:
			- how the magnitude of the force depends on the angle between <math>\vec L</math> and <math>\vec B</math>,
			- how the direction of the force rotates smoothly as either vector is rotated,
			- and why the right-hand rule naturally follows from the properties of the cross product.

			You can interact with this model here:

			[[Magnetic Force on a Current-Carrying Wire https://www.glowscript.org/#/user/Ritwic_Verma/folder/wiki/program/magneticforceonacurrentcarryingwire)]

	==Examples==		==Examples==

Ritwic Verma: /* Examples */

2025-11-23T03:08:45Z

Examples

Show changes

Ritwic Verma at 15:18, 10 November 2025

2025-11-10T15:18:06Z

← Older revision		Revision as of 11:18, 10 November 2025
Line 1:		Line 1:
	Claimed by Ritwic Verma, Fall 2025		Claimed by '''Ritwic Verma, Fall 2025'''
	==The Main Idea==		==The Main Idea==

Ritwic Verma at 15:17, 10 November 2025

2025-11-10T15:17:44Z

← Older revision		Revision as of 11:17, 10 November 2025
Line 1:		Line 1:
	Claimed by ~~Janel Ennin~~ Fall ~~2023~~		Claimed by Ritwic Verma, Fall 2025
	==The Main Idea==		==The Main Idea==

Ritwic Verma: /* The Main Idea */

2025-11-10T15:16:57Z

The Main Idea

← Older revision		Revision as of 11:16, 10 November 2025
Line 21:		Line 21:

	The excited molecules and atoms, having absorbed the energy imparted by the electrons, undergo a subsequent relaxation process. As they return to lower energy levels, a radiant emission of light ensues — the hallmark Northern Lights spectacle. The distinctive hues and vibrant colors characterizing the display are contingent upon the specific molecules and atoms involved in these collisions. The variance in colors is a testament to the diversity of atmospheric constituents participating in this cosmic ballet. This celestial dance, orchestrated by the interaction between charged particles and the Earth's magnetic field, not only enchants observers but also serves as a captivating reminder of the intricate interplay between astrophysical phenomena and the Earth's atmospheric composition.		The excited molecules and atoms, having absorbed the energy imparted by the electrons, undergo a subsequent relaxation process. As they return to lower energy levels, a radiant emission of light ensues — the hallmark Northern Lights spectacle. The distinctive hues and vibrant colors characterizing the display are contingent upon the specific molecules and atoms involved in these collisions. The variance in colors is a testament to the diversity of atmospheric constituents participating in this cosmic ballet. This celestial dance, orchestrated by the interaction between charged particles and the Earth's magnetic field, not only enchants observers but also serves as a captivating reminder of the intricate interplay between astrophysical phenomena and the Earth's atmospheric composition.

	==A Mathematical Model==		==A Mathematical Model==

Jennin3 at 04:51, 27 November 2023

2023-11-27T04:51:01Z

← Older revision		Revision as of 00:51, 27 November 2023
Line 19:		Line 19:

	The Aurora Borealis or more commonly called, 'The Northern Lights' is caused by the acceleration of electrons when they collide with the upper atmosphere of the Earth. These electrons then follow the magnetic field of the Earth towards the polar regions (in our case, specifically the North Pole). Once there, the accelerated electrons collide with and transfer their energy to other molecules/atoms in the atmosphere. The molecules/atoms are then excited to higher energy levels, and when they settle back down to lower energy levels, they emit light -- THE NORTHERN LIGHTS!! Depending on what kind of molecules/atoms the electrons collide with, determines the color of the light emitted.		The Aurora Borealis or more commonly called, 'The Northern Lights' is caused by the acceleration of electrons when they collide with the upper atmosphere of the Earth. These electrons then follow the magnetic field of the Earth towards the polar regions (in our case, specifically the North Pole). Once there, the accelerated electrons collide with and transfer their energy to other molecules/atoms in the atmosphere. The molecules/atoms are then excited to higher energy levels, and when they settle back down to lower energy levels, they emit light -- THE NORTHERN LIGHTS!! Depending on what kind of molecules/atoms the electrons collide with, determines the color of the light emitted.

			The excited molecules and atoms, having absorbed the energy imparted by the electrons, undergo a subsequent relaxation process. As they return to lower energy levels, a radiant emission of light ensues — the hallmark Northern Lights spectacle. The distinctive hues and vibrant colors characterizing the display are contingent upon the specific molecules and atoms involved in these collisions. The variance in colors is a testament to the diversity of atmospheric constituents participating in this cosmic ballet. This celestial dance, orchestrated by the interaction between charged particles and the Earth's magnetic field, not only enchants observers but also serves as a captivating reminder of the intricate interplay between astrophysical phenomena and the Earth's atmospheric composition.
	==A Mathematical Model==		==A Mathematical Model==

Jennin3 at 04:35, 27 November 2023

2023-11-27T04:35:35Z

← Older revision		Revision as of 00:35, 27 November 2023
Line 1:		Line 1:
			Claimed by Janel Ennin Fall 2023
	==The Main Idea==		==The Main Idea==

	An electric field can act on a charged particle, causing a force. This applied force is based on the magnitude of the electric field applied and the sign of the particle that the electric field is acting on. The electric field is generated regardless of whether the source charge (i.e. what was responsible for that electric field) is stationary or moving.		An electric field can act on a charged particle, causing a force. This applied force is based on the magnitude of the electric field applied and the sign of the particle that the electric field is acting on. The electric field is generated regardless of whether the source charge (i.e. what was responsible for that electric field) is stationary or moving.

			By applying forces to charged particles depending on both their charges and the properties of the electric field itself, an electric field acts as a mediator in interactions between charged particles. A charged particle encounters a force because of the existence of an electric field while it is in one. This force is closely correlated with the particle's charge and the strength of the electric field. The equation \( \mathbf{F} = q \cdot \mathbf{E} \) mathematically expresses this relationship, with \( \mathbf{F} \) representing the force, \( q \) representing the particle's charge, and \( \mathbf{E} \) representing the electric field vector.

			The sign of the particle's charge determines the force's direction. The force acts in the direction of the electric field if the charge is positive. In contrast, the force acts in the opposite direction of the electric field when the charge is negative. This differentiation emphasizes that the force and the electric field are both vectors.

			Crucially, the existence of the electric field is independent of the mobility or stationary state of the source charge that generates it. This notion follows from the fact that an electric field is created when there are changes in the distribution of charge, whether such changes are brought about by the motion of charges or by other factors.

	Magnetic forces are on moving particles, not stationary particles which means that the calculation of magnetic force '''MUST''' relate to the particle's velocity (we see this quantitatively with the Biot-Savart Law).		Magnetic forces are on moving particles, not stationary particles which means that the calculation of magnetic force '''MUST''' relate to the particle's velocity (we see this quantitatively with the Biot-Savart Law).

Yalmonte3: /* Simple */

2020-11-23T15:13:42Z

Simple

← Older revision		Revision as of 11:13, 23 November 2020
Line 100:		Line 100:
	<math>{\vec{F} = (1.6 \times 10^{-19}) <4 \times 10^5,0,0> \times <0,0,0.2>}</math>		<math>{\vec{F} = (1.6 \times 10^{-19}) <4 \times 10^5,0,0> \times <0,0,0.2>}</math>

	The right-hand rule indicates that because the velocity vector is in the positive x-direction (index-finger), and this is crossed with the magnetic field vector (middle finger) in the positive z-direction, then the resulting force vector (direction of your thumb) must be in the ~~positive~~ y-direction.		The right-hand rule indicates that because the velocity vector is in the positive x-direction (index-finger), and this is crossed with the magnetic field vector (middle finger) in the positive z-direction, then the resulting force vector (direction of your thumb) must be in the negative y-direction.

	Thus...		Thus...

	<math>{\vec{F} = (1.6 \times 10^{-19})(4 \times 10^5 * 0.2) = <0, 1.28 \times 10^{-14}, 0> N}</math>		<math>{\vec{F} = (1.6 \times 10^{-19})(4 \times 10^5 * 0.2) = <0, -1.28 \times 10^{-14}, 0> N}</math>

	===Middling===		===Middling===