Right Hand Rule - Revision history

Bhavinshah24 at 04:14, 1 December 2025

2025-12-01T04:14:45Z

← Older revision		Revision as of 00:14, 1 December 2025
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	==Performing the Right Hand Rule==		==Performing the Right Hand Rule==

	* Right Hand Rule: ~~Using~~ your right arm~~, point your arm to represent~~ the ~~'''~~r~~'''~~ vector. ~~Now turn~~ your palm in the direction of the momentum ~~or '''p'''~~ vector. Curl your fingers in ~~that~~ direction of ~~the momentum~~, and extend your thumb ~~outward~~. The ~~unit vector representing the direction of the angular momentum is defined to point~~ in the direction of ~~your thumb.~~		Right-Hand Rule:
	*Hint: If the rotational motion is counterclockwise, your right thumb, therefore the unit vector~~, will point out of~~ the ~~plane. If the rotational motion is clockwise, the unit vector will point into the plane~~.		Extend your right arm so that it points in the direction of the r vector. Rotate your wrist so that your palm can curl toward the direction of the p (momentum) vector. Curl your fingers in the direction of p, and extend your thumb. The thumb now points in the direction of the unit vector that represents the angular momentum.

	~~To find~~ the magnetic ~~field induced by~~ a wire~~, you can do the same thing, point~~ your thumb in the direction of current ~~and your~~ fingers ~~show~~ the magnetic field.		Hint:
			If the rotation is counterclockwise, your right thumb—and therefore the angular momentum vector—points out of the plane (+z direction).
			If the rotation is clockwise, the vector points into the plane (–z direction).

			Right-Hand Rule (for magnetic fields around a current-carrying wire):
			Point your thumb in the direction of the current. Your curled fingers naturally wrap around the wire in the direction of the magnetic field lines.

	Counterclockwise example:		Counterclockwise example:
	~~Notice~~ your thumb points up in the +z direction ~~when~~ the ~~direction from '''r''' to '''p''' is counterclockwise~~.		When the direction from r to p is counterclockwise, your curled fingers match that motion, and your thumb points upward in the +z direction. This confirms that the angular momentum vector points out of the page.

	[[File:counterclockwise-example500.png]]		[[File:counterclockwise-example500.png]]

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	==Connectedness==		==Connectedness==
	The Right Hand Rule is a very essential component of solving cross products, such as in Hall Effect, Angular Momentum, Lorentz force and more. The concept is usually very tricky to understand, so I wanted to give my best insight on what helped me understand exactly how and why it works. It also provides a ~~prox~~ for right answers whcih will be useful in a testing environment.		The Right Hand Rule is a very essential component of solving cross products, such as in Hall Effect, Angular Momentum, Lorentz force and more. The concept is usually very tricky to understand, so I wanted to give my best insight on what helped me understand exactly how and why it works. It also provides a proxy for right answers whcih will be useful in a testing environment.

	==History==		==History==
			The right-hand rule emerged in the 1800s as scientists sought a consistent method for describing directions in electricity, magnetism, and rotational motion. After Ørsted and Ampère showed that electric currents generate magnetic fields, physicists needed a standardized way to define the direction of those fields. James Clerk Maxwell later unified electricity and magnetism and adopted a right-handed coordinate system in his equations, helping solidify the convention. By the late 19th century, Josiah Willard Gibbs and Oliver Heaviside formally defined the modern vector cross product and specified its direction using the right hand, embedding the rule into vector calculus. Today, the right-hand rule is universally used to assign consistent directions to physical quantities such as torque, angular momentum, and magnetic forces.

	he right-hand rule developed in the 1800s as scientists tried to standardize how to describe directions in electricity, magnetism, and rotational motion. After Orsted and Ampère discovered that electric currents create magnetic fields, a consistent way to define the field’s direction was needed. Maxwell later unified electromagnetism and used a right-handed coordinate system in his equations, solidifying the convention. In the late 1800s, Gibbs and Heaviside formally defined the modern cross product, specifying its direction with the right hand, which made the rule a permanent part of vector calculus. Today, the right-hand rule is universally used to assign consistent directions to quantities like torque, angular momentum, and magnetic forces.
	== See also ==		== See also ==

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	https://www.mathsisfun.com/algebra/vectors-cross-product.html		https://www.mathsisfun.com/algebra/vectors-cross-product.html

			https://teachingandlearninglabs.com/AllHTML/RightHandRule.shtml


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	All pictures were taken from lecture slides to refrain from infrangement.		All pictures were taken from lecture slides to refrain from infrangement.

	https://www.physicsclassroom.com/class/Magnetic-Fields-and-Electromagnetism/Lesson-2-Electromagnetism/Magnetic-Field-of-a-Current-Carrying-Wire?		https://www.physicsclassroom.com/class/Magnetic-Fields-and-Electromagnetism/Lesson-2-Electromagnetism/Magnetic-Field-of-a-Current-Carrying-Wire

			https://www.khanacademy.org/test-prep/mcat/physical-processes/magnetism-mcat/a/using-the-right-hand-rule

			https://www.vecteezy.com/vector-art/25747595-fleming-s-right-hand-rule

	https://en.wikipedia.org/wiki/Right-hand_rule		https://en.wikipedia.org/wiki/Right-hand_rule

Bhavinshah24 at 04:08, 1 December 2025

2025-12-01T04:08:41Z

← Older revision		Revision as of 00:08, 1 December 2025
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	https://trinket.io/glowscript/31d0f9ad9e		https://trinket.io/glowscript/31d0f9ad9e

	https://www.mathsisfun.com/algebra/vectors-cross-product.html		https://www.mathsisfun.com/algebra/vectors-cross-product.html


	==References==		==References==
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	*All Right Hand Rule visualization pictures		*All Right Hand Rule visualization pictures

	All ~~other~~ pictures ~~and videos~~ were taken from ~~Professor Flavio Fenton's Physics 2211~~ lecture ~~notes~~.		All pictures were taken from lecture slides to refrain from infrangement.

			https://www.physicsclassroom.com/class/Magnetic-Fields-and-Electromagnetism/Lesson-2-Electromagnetism/Magnetic-Field-of-a-Current-Carrying-Wire?

	https://en.wikipedia.org/wiki/Right-hand_rule		https://en.wikipedia.org/wiki/Right-hand_rule

Bhavinshah24: /* External links */

2025-12-01T04:06:58Z

External links

← Older revision		Revision as of 00:06, 1 December 2025
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	https://trinket.io/glowscript/31d0f9ad9e		https://trinket.io/glowscript/31d0f9ad9e
			https://www.mathsisfun.com/algebra/vectors-cross-product.html



	==References==		==References==

Bhavinshah24 at 00:29, 1 December 2025

2025-12-01T00:29:10Z

← Older revision		Revision as of 20:29, 30 November 2025
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	==Connectedness==		==Connectedness==
	The Right Hand Rule is a very essential component of solving cross products, such as in ~~angular momentum problems~~. The concept is usually very tricky to understand, so I wanted to give my best insight on what helped me understand exactly how and why it works.		The Right Hand Rule is a very essential component of solving cross products, such as in Hall Effect, Angular Momentum, Lorentz force and more. The concept is usually very tricky to understand, so I wanted to give my best insight on what helped me understand exactly how and why it works. It also provides a prox for right answers whcih will be useful in a testing environment.


	~~Here are some interesting videos about the conservation of angular momentum:~~


	~~https://www.youtube.com/watch?v=Aw5i994n2bw&feature=youtu.~~be

	~~https://www.youtube~~.~~com/watch?v=OKbawIq3w7U~~

	==History==		==History==
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	[http://mathworld.wolfram.com/Right-HandRule.html Wolfram MathWorld]		[http://mathworld.wolfram.com/Right-HandRule.html Wolfram MathWorld]

			https://trinket.io/glowscript/31d0f9ad9e

Bhavinshah24 at 00:27, 1 December 2025

2025-12-01T00:27:10Z

← Older revision		Revision as of 20:27, 30 November 2025
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	The angular momentum of a particle does not lie in the plane of motion. The magnetic force on a charge depends on a cross product and points perpendicular to the plane of the velocity and magnetic field. The torque exerted on an object is also perpendicular to the plane of applied force and lever arm. The cross product gives a vector that sticks straight out of the plane formed by the two original vectors. But there are two possible directions it could point—one on each side of the plane. The right-hand rule is the convention we use to pick the correct, consistent direction every time. Without this rule, the direction of quantities like torque, angular momentum, or magnetic force would be ambiguous.		The angular momentum of a particle does not lie in the plane of motion. The magnetic force on a charge depends on a cross product and points perpendicular to the plane of the velocity and magnetic field. The torque exerted on an object is also perpendicular to the plane of applied force and lever arm. The cross product gives a vector that sticks straight out of the plane formed by the two original vectors. But there are two possible directions it could point—one on each side of the plane. The right-hand rule is the convention we use to pick the correct, consistent direction every time. Without this rule, the direction of quantities like torque, angular momentum, or magnetic force would be ambiguous.

	===A Mathematical Model===		===A Mathematical and Computational Model===
	The direction of any quantity defined by a cross product—such as torque, magnetic force, or angular momentum—can be found by computing the cross product of two vectors. For any vectors		The direction of any quantity defined by a cross product—such as torque, magnetic force, or angular momentum—can be found by computing the cross product of two vectors. For any vectors
	𝑎		𝑎
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	[[File:problem1.jpg]]		[[File:problem1.jpg]]

			For a computational model i have attached the trinket code below which provides a model of the the right hand rule cross-product.

			https://trinket.io/glowscript/31d0f9ad9e


	Answer:		Answer:
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	[http://mathworld.wolfram.com/Right-HandRule.html Wolfram MathWorld]		[http://mathworld.wolfram.com/Right-HandRule.html Wolfram MathWorld]



	==References==		==References==

Bhavinshah24 at 17:16, 28 November 2025

2025-11-28T17:16:59Z

← Older revision		Revision as of 13:16, 28 November 2025
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	===A Mathematical Model===		===A Mathematical Model===
	The direction of ~~the~~ angular ~~momentum can also~~ be ~~solved through calculating~~ the cross product of ~~the '''r/B''' and '''p/V'''~~ vectors.		The direction of any quantity defined by a cross product—such as torque, magnetic force, or angular momentum—can be found by computing the cross product of two vectors. For any vectors
	~~The cross product looks like this. As shown~~, ~~the magnitude of~~ the cross product ~~is computed by \|a\|\|b\|sinθ. We use the right hand rule to determine direction if this method is used.~~		𝑎
			a and
			𝑏
			b, the cross product

	[[File:crossproduct-vis.png]]		[[File:crossproduct-vis.png]]

Bhavinshah24 at 16:50, 28 November 2025

2025-11-28T16:50:32Z

← Older revision		Revision as of 12:50, 28 November 2025
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	When two vectors lie in a plane—say, the position vector r of a particle and its momentum vector p—their combination often represents something that is not confined to that plane. For example:		When two vectors lie in a plane—say, the position vector r of a particle and its momentum vector p—their combination often represents something that is not confined to that plane. For example:

	The angular momentum of a particle does not lie in the plane of motion.		The angular momentum of a particle does not lie in the plane of motion. The magnetic force on a charge depends on a cross product and points perpendicular to the plane of the velocity and magnetic field. The torque exerted on an object is also perpendicular to the plane of applied force and lever arm. The cross product gives a vector that sticks straight out of the plane formed by the two original vectors. But there are two possible directions it could point—one on each side of the plane. The right-hand rule is the convention we use to pick the correct, consistent direction every time. Without this rule, the direction of quantities like torque, angular momentum, or magnetic force would be ambiguous.

	The magnetic force on a charge depends on a cross product and points perpendicular to the plane of the velocity and magnetic field.

	The torque exerted on an object is also perpendicular to the plane of applied force and lever arm.

	The cross product gives a vector that sticks straight out of the plane formed by the two original vectors. But there are two possible directions it could point—one on each side of the plane.

	The right-hand rule is the convention we use to pick the correct, consistent direction every time. Without this rule, the direction of quantities like torque, angular momentum, or magnetic force would be ambiguous.

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

Bhavinshah24 at 16:49, 28 November 2025

2025-11-28T16:49:59Z

← Older revision		Revision as of 12:49, 28 November 2025
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	==History==		==History==

	~~I wasn't able to find who was the first to apply the Right Hand Rule to angular momentum and torque. However, it seems that the~~ right hand rule ~~is applied~~ to ~~other aspects of physics~~		he right-hand rule developed in the 1800s as scientists tried to standardize how to describe directions in electricity, magnetism, and rotational motion. After Orsted and Ampère discovered that electric currents create magnetic fields, a consistent way to define the field’s direction was needed. Maxwell later unified electromagnetism and used a right-handed coordinate system in his equations, solidifying the convention. In the late 1800s, Gibbs and Heaviside formally defined the modern cross product, specifying its direction with the right hand, which made the rule a permanent part of vector calculus. Today, the right-hand rule is universally used to assign consistent directions to quantities like torque, angular momentum, and magnetic forces.
	~~as well. For example~~, ~~André-Marie Ampère~~, ~~a French physicist~~ and ~~mathematician, created a right hand rule for circuits~~ and electric currents~~. This is used when~~ a ~~vector must be defined~~
	to ~~represent~~ the ~~rotation of~~ a ~~body~~, ~~a magnetic field, or a fluid~~. ~~It reveals a connection between~~ the ~~current~~ and the ~~magnetic field lines in~~ the ~~magnetic field that~~ the ~~current created~~.
	~~This~~ right hand rule ~~works exactly the same way as the one I have described above~~.

	== See also ==		== See also ==

Bhavinshah24 at 16:48, 28 November 2025

2025-11-28T16:48:00Z

← Older revision		Revision as of 12:48, 28 November 2025
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	==The Main Idea==		==The Main Idea==
	The right hand rule is ~~used~~ to ~~find the direction~~ of ~~the cross product between two vectors in 3 dimensions~~. ~~This has uses in many field of physics, including~~ angular momentum and ~~electromagnetism. For example,~~ to ~~describe~~ the ~~motion of Earth's orbit if you are standing on the positive z axis looking toward the origin~~, the ~~Earth~~ is ~~moving counterclockwise in~~ the ~~xy plane. However~~, ~~this statement cannot be used mathematically~~. ~~You can't add "counterclockwise in~~ the ~~xy plane" to "clockwise in~~ the ~~yz plane." Instead~~, we can use ~~the right hand rule~~ to ~~describe the direction of angular momentum~~ as a ~~vector~~. ~~The direction can be specified like this:~~		The right-hand rule is not just a mnemonic that teachers tell you to use—it’s a geometric consequence of how three-dimensional space is defined. Many physical quantities—such as angular momentum, torque, magnetic forces, and rotational motion—are fundamentally tied to the cross product, and the right-hand rule is what gives those quantities a consistent and meaningful direction. Understanding the intuition behind the RHR, combined with practice, allows us as students to move through problems more quickly on tests. By understanding the direction of the resultant vector, we can often use it to guide our work and even use it as a proxy to check whether our answers make sense.
	* The plane in ~~which both~~ the position vector ~~from the two objects~~ and ~~the~~ momentum vector ~~for~~ the ~~object~~ of ~~interest lie can be indicated by~~ a ~~unit vector~~ perpendicular to ~~that~~ plane.
	* The ~~direction of motion within~~ the plane ~~(clockwise or counterclockwise) can be indicated by establishing a right hand rule (RHR) for this unit vector~~.		==Why We Need the Right-Hand Rule==
	* The cross product~~, or~~ the ~~result~~ of the right hand rule ~~will be a vector normal~~ to the ~~plane~~		When two vectors lie in a plane—say, the position vector r of a particle and its momentum vector p—their combination often represents something that is not confined to that plane. For example:

			The angular momentum of a particle does not lie in the plane of motion.

			The magnetic force on a charge depends on a cross product and points perpendicular to the plane of the velocity and magnetic field.

			The torque exerted on an object is also perpendicular to the plane of applied force and lever arm.

			The cross product gives a vector that sticks straight out of the plane formed by the two original vectors. But there are two possible directions it could point—one on each side of the plane.

			The right-hand rule is the convention we use to pick the correct, consistent direction every time. Without this rule, the direction of quantities like torque, angular momentum, or magnetic force would be ambiguous.

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

Bhavinshah24 at 16:28, 28 November 2025

2025-11-28T16:28:49Z

← Older revision		Revision as of 12:28, 28 November 2025
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	This topic covers Right Hand Rule.		This topic covers Right Hand Rule.
	Claimed by: ~~Thomas Chiu fall 2024~~		Claimed by: Bhavin Shah Spring 2025
	<!-- Whoever edits this: please make sure the reader knows that right hand rule refers to cross products in general, not just angular momentum-->		<!-- Whoever edits this: please make sure the reader knows that right hand rule refers to cross products in general, not just angular momentum-->