Magnetic Flux - Revision history

Kpeng63 at 01:44, 1 December 2025

2025-12-01T01:44:27Z

← Older revision		Revision as of 21:44, 30 November 2025
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	There are a few important real-world applications of magnetic flux. As described by Faraday's Law, when a coiled wire moves through a magnetic field, a voltage is produced. This voltage is dependent on the magnetic flux (due to the surrounding magnetic field) through the area of the coiled wire, as seen below. Additionally, whenever the magnetic flux changes, an electric field is made. For example, if a square wire changes area inside of a magnetic field, it can cause a current to run through the wire. Of course, this is a later unit and can be explored through [[Faraday's Law]].		There are a few important real-world applications of magnetic flux. As described by Faraday's Law, when a coiled wire moves through a magnetic field, a voltage is produced. This voltage is dependent on the magnetic flux (due to the surrounding magnetic field) through the area of the coiled wire, as seen below. Additionally, whenever the magnetic flux changes, an electric field is made. For example, if a square wire changes area inside of a magnetic field, it can cause a current to run through the wire. Of course, this is a later unit and can be explored through [[Faraday's Law]].

			The primary things that affect magnetic flux include:
			1. current flowing through a loop/coil/solenoid
			2. a magnet moves closer or farther from the loop (changes B)
			3. the area through which the magnetic field is crossing is changing

	At the present, there are several applications of magnetic flux that we use on a day to day basis. The first thing someone might think about is the usage of flux as a way detect magnetic fields through certain surfaces. Magnetic sensors do just that: they can be used to measure the output of a magnetic field. You can also detect and sense current readings using a galvanometer. There have also been recent studies that utilise magnetic flux for pipe leakage detection [https://www.mdpi.com/1424-8220/15/12/29845], and the usage of magnetic flux is strongly linked to induction, so an induction stove also uses the properties of magnetic flux for cooking.		At the present, there are several applications of magnetic flux that we use on a day to day basis. The first thing someone might think about is the usage of flux as a way detect magnetic fields through certain surfaces. Magnetic sensors do just that: they can be used to measure the output of a magnetic field. You can also detect and sense current readings using a galvanometer. There have also been recent studies that utilise magnetic flux for pipe leakage detection [https://www.mdpi.com/1424-8220/15/12/29845], and the usage of magnetic flux is strongly linked to induction, so an induction stove also uses the properties of magnetic flux for cooking.

Kpeng63: /* A Mathematical Model */

2025-12-01T01:38:41Z

A Mathematical Model

← Older revision		Revision as of 21:38, 30 November 2025
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	Note- The integral sign with a circle in the middle is commonly used in electromagnetism, and it represents a "closed integral" for the entirety of a surface or object.		Note- The integral sign with a circle in the middle is commonly used in electromagnetism, and it represents a "closed integral" for the entirety of a surface or object.

	~~Realistically,~~ the magnetic ~~flux though~~ any ~~CLOSED surface is~~ zero. ~~This is because~~ magnetic ~~field lines are continuous loops~~. ~~This means that if there is a non-zero~~ magnetic field ~~through~~ the ~~top face of a cube for example~~, the ~~entering magnetic field from the bottom face will cancel out the top one. The~~ magnetic flux ~~through an area~~ will be ~~its own individual value~~. This rule is useful when solving for a an unknown magnetic field that's coming from a side of a surface when the other fields from the other sides are known. Magnetic flux is measured in SI units of Weber (Wb), named after German physicist and co-inventor of the telegraph Wilhelm Weber. A Weber is equal to T*m^2.		So why is the magnetic field through any closed loop zero? Because splitting a bar magnet in half just results in two separate bar magnets each with their own N and S poles, magnetic charges can't be isolated. Therefore, they will all act as magnetic dipoles. The amount of magnetic field entering a closed surface will equal the amount exiting that surface, so then the magnetic flux of a closed surface will always be zero.
			This rule is useful when solving for a an unknown magnetic field that's coming from a side of a surface when the other fields from the other sides are known. Magnetic flux is measured in SI units of Weber (Wb), named after German physicist and co-inventor of the telegraph Wilhelm Weber. A Weber is equal to T*m^2.

	This is the Gauss's law general form for finding magnetic flux through an area (through a non-closed surface).		This is the Gauss's law general form for finding magnetic flux through an area (through a non-closed surface).

Kpeng63 at 01:34, 1 December 2025

2025-12-01T01:34:00Z

← Older revision		Revision as of 21:34, 30 November 2025
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	'''Claimed by Jonathan Xue (Fall 2023)'''		'''Claimed by Jonathan Xue (Fall 2023)'''

	'''Claimed by Kathy Peng (Fall 2025)'''		'''Claimed by Kathy Peng (Fall 2025)'''

Kpeng63 at 01:33, 1 December 2025

2025-12-01T01:33:49Z

← Older revision		Revision as of 21:33, 30 November 2025
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	'''Claimed by Jonathan Xue (Fall 2023)'''		'''Claimed by Jonathan Xue (Fall 2023)'''
			'''Claimed by Kathy Peng (Fall 2025)'''

Jxue76 at 21:23, 26 November 2023

2023-11-26T21:23:52Z

← Older revision		Revision as of 17:23, 26 November 2023
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	There are a few important real-world applications of magnetic flux. As described by Faraday's Law, when a coiled wire moves through a magnetic field, a voltage is produced. This voltage is dependent on the magnetic flux (due to the surrounding magnetic field) through the area of the coiled wire, as seen below. Additionally, whenever the magnetic flux changes, an electric field is made. For example, if a square wire changes area inside of a magnetic field, it can cause a current to run through the wire. Of course, this is a later unit and can be explored through [[Faraday's Law]].		There are a few important real-world applications of magnetic flux. As described by Faraday's Law, when a coiled wire moves through a magnetic field, a voltage is produced. This voltage is dependent on the magnetic flux (due to the surrounding magnetic field) through the area of the coiled wire, as seen below. Additionally, whenever the magnetic flux changes, an electric field is made. For example, if a square wire changes area inside of a magnetic field, it can cause a current to run through the wire. Of course, this is a later unit and can be explored through [[Faraday's Law]].

			At the present, there are several applications of magnetic flux that we use on a day to day basis. The first thing someone might think about is the usage of flux as a way detect magnetic fields through certain surfaces. Magnetic sensors do just that: they can be used to measure the output of a magnetic field. You can also detect and sense current readings using a galvanometer. There have also been recent studies that utilise magnetic flux for pipe leakage detection [https://www.mdpi.com/1424-8220/15/12/29845], and the usage of magnetic flux is strongly linked to induction, so an induction stove also uses the properties of magnetic flux for cooking.

	[[File:FluxinMagField.jpg]]		[[File:FluxinMagField.jpg]]
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	Prior to Gauss's study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.		Prior to Gauss's study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.

			It is also important to note that while Gauss's Law establishes the magnetic flux through a closed surface, Faraday's Law establishes the magnetic flux through an open surface.

	Lagrange: [[File:lgsingi.jpg]]		Lagrange: [[File:lgsingi.jpg]]
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	Gauss: [[File:gsingi.jpg]]		Gauss: [[File:gsingi.jpg]]

	~~===Applications===~~
	At the present, there are several applications of magnetic flux that we use on a day to day basis. The first thing someone might think about is the usage of flux as a way detect magnetic fields through certain surfaces. Magnetic sensors do just that: they can be used to measure the output of a magnetic field. You can also detect and sense current readings using a galvanometer. There have also been recent studies that utilise magnetic flux for pipe leakage detection [https://www.mdpi.com/1424-8220/15/12/29845], and the usage of magnetic flux is strongly linked to induction, so an induction stove also uses the properties of magnetic flux for cooking.
	==Further Reading==		==Further Reading==
	What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]		What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]

Jxue76: Undo revision 42038 by Jxue76 (talk)

2023-11-26T21:21:53Z

Undo revision 42038 by Jxue76 (talk)

← Older revision		Revision as of 17:21, 26 November 2023
Line 68:		Line 68:

	Via the Faraday-Lenz law, engineers can easily calculate the voltage generated by a coiled wire in a magnetic field. The relationship is electro-motive force equals the negative rate of change of magnetic flux over time.		Via the Faraday-Lenz law, engineers can easily calculate the voltage generated by a coiled wire in a magnetic field. The relationship is electro-motive force equals the negative rate of change of magnetic flux over time.

	At the present, there are several applications of magnetic flux that we use on a day to day basis. The first thing someone might think about is the usage of flux as a way detect magnetic fields through certain surfaces. Magnetic sensors do just that: they can be used to measure the output of a magnetic field. You can also detect and sense current readings using a galvanometer. There have also been recent studies that utilise magnetic flux for pipe leakage detection [https://www.mdpi.com/1424-8220/15/12/29845], and the usage of magnetic flux is strongly linked to induction, so an induction stove also uses the properties of magnetic flux for cooking.
	~~==Further Reading==~~

	<math>\epsilon = -\dfrac{d\Phi}{dt} </math>		<math>\epsilon = -\dfrac{d\Phi}{dt} </math>
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	Prior to Gauss's study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.		Prior to Gauss's study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.

	~~Another distinction that should be made is that Gauss's Law refers to the magnetic flux through a closed surface. Faraday's Law however, talks about the magnetic flux through an open surface.~~

	Lagrange: [[File:lgsingi.jpg]]		Lagrange: [[File:lgsingi.jpg]]
Line 145:		Line 140:
	Gauss: [[File:gsingi.jpg]]		Gauss: [[File:gsingi.jpg]]

			===Applications===
			At the present, there are several applications of magnetic flux that we use on a day to day basis. The first thing someone might think about is the usage of flux as a way detect magnetic fields through certain surfaces. Magnetic sensors do just that: they can be used to measure the output of a magnetic field. You can also detect and sense current readings using a galvanometer. There have also been recent studies that utilise magnetic flux for pipe leakage detection [https://www.mdpi.com/1424-8220/15/12/29845], and the usage of magnetic flux is strongly linked to induction, so an induction stove also uses the properties of magnetic flux for cooking.
			==Further Reading==
	What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]		What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]

Jxue76 at 21:19, 26 November 2023

2023-11-26T21:19:37Z

← Older revision		Revision as of 17:19, 26 November 2023
Line 68:		Line 68:

	Via the Faraday-Lenz law, engineers can easily calculate the voltage generated by a coiled wire in a magnetic field. The relationship is electro-motive force equals the negative rate of change of magnetic flux over time.		Via the Faraday-Lenz law, engineers can easily calculate the voltage generated by a coiled wire in a magnetic field. The relationship is electro-motive force equals the negative rate of change of magnetic flux over time.

			At the present, there are several applications of magnetic flux that we use on a day to day basis. The first thing someone might think about is the usage of flux as a way detect magnetic fields through certain surfaces. Magnetic sensors do just that: they can be used to measure the output of a magnetic field. You can also detect and sense current readings using a galvanometer. There have also been recent studies that utilise magnetic flux for pipe leakage detection [https://www.mdpi.com/1424-8220/15/12/29845], and the usage of magnetic flux is strongly linked to induction, so an induction stove also uses the properties of magnetic flux for cooking.
			==Further Reading==

	<math>\epsilon = -\dfrac{d\Phi}{dt} </math>		<math>\epsilon = -\dfrac{d\Phi}{dt} </math>
Line 135:		Line 138:

	Prior to Gauss's study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.		Prior to Gauss's study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.

			Another distinction that should be made is that Gauss's Law refers to the magnetic flux through a closed surface. Faraday's Law however, talks about the magnetic flux through an open surface.

	Lagrange: [[File:lgsingi.jpg]]		Lagrange: [[File:lgsingi.jpg]]
Line 140:		Line 145:
	Gauss: [[File:gsingi.jpg]]		Gauss: [[File:gsingi.jpg]]

	~~===Applications===~~
	At the present, there are several applications of magnetic flux that we use on a day to day basis. The first thing someone might think about is the usage of flux as a way detect magnetic fields through certain surfaces. Magnetic sensors do just that: they can be used to measure the output of a magnetic field. You can also detect and sense current readings using a galvanometer. There have also been recent studies that utilise magnetic flux for pipe leakage detection [https://www.mdpi.com/1424-8220/15/12/29845], and the usage of magnetic flux is strongly linked to induction, so an induction stove also uses the properties of magnetic flux for cooking.
	~~==Further Reading==~~
	What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]		What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]

Jxue76 at 21:09, 26 November 2023

2023-11-26T21:09:22Z

← Older revision		Revision as of 17:09, 26 November 2023
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	==The Main Idea==		==The Main Idea==
	To put ~~it simply~~, magnetic flux is the amount of magnetic field going through a given area in an instant of time. ~~This~~ can ~~be expressed~~ in the ~~general formula~~:		===A Mathematical Model===
			To put in simple terms, magnetic flux is the amount of magnetic field going through a given area in a singular instant of time. Whether the area is non uniform, or if the magnetic field isn't constant, you can use the magnetic flux formula to calculate the number of Teslas in the given area.
	~~<math>\Phi_B = \int B \cdot dA <~~/~~math>~~		As stated, this page is only considering magnetic flux, which doesn't incorporate time. Faraday's Law however, takes the concept of magnetic flux and uses time to quantify electromotive forces [https://www.physicsbook.gatech.edu/Faraday%27s_Law].

	As stated, this page is only considering magnetic flux, which doesn't incorporate time. Faraday's Law however, takes the concept of magnetic flux and uses time to quantify electromotive forces [https://www.physicsbook.gatech.edu/Faraday%27s_Law].
	~~===A Mathematical Model===~~
	Recall that according to Gauss's law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic 'monopoles', we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don't exist. It follows that the equivalent of Gauss's law for magnetic fields reduces to:		Recall that according to Gauss's law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic 'monopoles', we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don't exist. It follows that the equivalent of Gauss's law for magnetic fields reduces to:

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	Realistically, the magnetic flux though any CLOSED surface is zero. This is because magnetic field lines are continuous loops. This means that if there is a non-zero magnetic field through the top face of a cube for example, the entering magnetic field from the bottom face will cancel out the top one. The magnetic flux through an area will be its own individual value. This rule is useful when solving for a an unknown magnetic field that's coming from a side of a surface when the other fields from the other sides are known. Magnetic flux is measured in SI units of Weber (Wb), named after German physicist and co-inventor of the telegraph Wilhelm Weber. A Weber is equal to T*m^2.		Realistically, the magnetic flux though any CLOSED surface is zero. This is because magnetic field lines are continuous loops. This means that if there is a non-zero magnetic field through the top face of a cube for example, the entering magnetic field from the bottom face will cancel out the top one. The magnetic flux through an area will be its own individual value. This rule is useful when solving for a an unknown magnetic field that's coming from a side of a surface when the other fields from the other sides are known. Magnetic flux is measured in SI units of Weber (Wb), named after German physicist and co-inventor of the telegraph Wilhelm Weber. A Weber is equal to T*m^2.

	This is the Gauss's law general form for finding magnetic flux through an area (~~not~~ closed surface).		This is the Gauss's law general form for finding magnetic flux through an area (through a non-closed surface).

	<math>\Phi_B = \int B \cdot dA </math>		<math>\Phi_B = \int B \cdot dA </math>

	To fully understand the meaning of this equation, an understanding of normal vectors and dot products is required. Relative to a surface, a normal vector runs perpendicular to the surface at a certain point. For curved surfaces, such as the one shown below, there ~~are many different~~ normal vectors ~~for~~ each plane of the surface.		To fully understand the meaning of this equation, an understanding of normal vectors and dot products is required. Relative to a surface, a normal vector runs perpendicular to the surface at a certain point. Note that the normal vector also typically faces outwards. For curved surfaces, such as the one shown below, there normal vectors changes its orientation depending on the angle of each plane of the surface.

	[[File:normalvectors.png]]		[[File:normalvectors.png]]

Jxue76 at 20:59, 26 November 2023

2023-11-26T20:59:08Z

← Older revision		Revision as of 16:59, 26 November 2023
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	This is the Gauss's law general form for finding magnetic flux through an area (not closed surface).		This is the Gauss's law general form for finding magnetic flux through an area (not closed surface).

	<math>\Phi_B = \~~oint~~ B \cdot dA </math>		<math>\Phi_B = \int B \cdot dA </math>

	To fully understand the meaning of this equation, an understanding of normal vectors and dot products is required. Relative to a surface, a normal vector runs perpendicular to the surface at a certain point. For curved surfaces, such as the one shown below, there are many different normal vectors for each plane of the surface.		To fully understand the meaning of this equation, an understanding of normal vectors and dot products is required. Relative to a surface, a normal vector runs perpendicular to the surface at a certain point. For curved surfaces, such as the one shown below, there are many different normal vectors for each plane of the surface.

Jxue76 at 20:56, 26 November 2023

2023-11-26T20:56:23Z

← Older revision		Revision as of 16:56, 26 November 2023
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	To put it simply, magnetic flux is the amount of magnetic field going through a given area in an instant of time. This can be expressed in the general formula:		To put it simply, magnetic flux is the amount of magnetic field going through a given area in an instant of time. This can be expressed in the general formula:

	<math>\Phi_B = \~~oint~~ B \cdot dA </math>		<math>\Phi_B = \int B \cdot dA </math>

	As stated, this page is only considering magnetic flux, which doesn't incorporate time. Faraday's Law however, takes the concept of magnetic flux and uses time to quantify electromotive forces [https://www.physicsbook.gatech.edu/Faraday%27s_Law].		As stated, this page is only considering magnetic flux, which doesn't incorporate time. Faraday's Law however, takes the concept of magnetic flux and uses time to quantify electromotive forces [https://www.physicsbook.gatech.edu/Faraday%27s_Law].
Line 17:		Line 17:
	Recall that according to Gauss's law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic 'monopoles', we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don't exist. It follows that the equivalent of Gauss's law for magnetic fields reduces to:		Recall that according to Gauss's law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic 'monopoles', we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don't exist. It follows that the equivalent of Gauss's law for magnetic fields reduces to:

	<math>\Phi_B = \~~int~~ B \cdot dA = 0</math>		<math>\Phi_B = \oint B \cdot dA = 0</math>

	Note- The integral sign with a circle in the middle is commonly used in electromagnetism, and it represents a "closed integral" for the entirety of a surface or object.		Note- The integral sign with a circle in the middle is commonly used in electromagnetism, and it represents a "closed integral" for the entirety of a surface or object.