Electromagnetic Induction and Faraday's Law

 

 

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"I am Michael Faraday"

Discovery: Michael Faraday (1831) - Electromagnetic induction phenomenon When bringing a magnet closer to or away from a coil, an induced current is generated in the coil That is, an induced potential difference
arises due to the effect of the changing magnetic field on the coil And this electric current is generated in a conducting coil when the magnetic field around it changes
Reason: The movement of the magnet (bringing it closer or away) leads to a change in magnetic flux through the coil
Separately, the scientist Henry researched generating an induced current through changing the field penetrating the coil

Useful information: Electromagnet

From our previous knowledge, passing current through a coil turns the coil into an electromagnet

By applying the right-hand grip rule, we determine the direction of the field

The thumb points to the direction of the field inside the coil (points to the north pole)

Note the north pole rotates current counterclockwise and the south pole rotates current clockwise provided you look at the coil from the side you want to determine its pole

Electromagnetic induction and Faraday's experiment
The scientist Michael Faraday practically found that when moving a conductor within an external magnetic field, an electric current is induced in this conductor Note approaching the magnet to the coiled wire and forming a field opposite to the cause to reduce the change in flux Note moving away the magnet from the coiled wire and forming a field similar to the cause to reduce the change in flux Faraday demonstrated through the experiment that the average induced electromotive force generated in a specific conductor equals the rate of temporal change in magnetic flux And if the wire is coiled, multiply by the number of turns

Test what you learned

Answer the following questions

When bringing the magnet (north pole) closer to the coil an induced current is generated

What is the direction of current rotation What is the name of the pole directly in front of you

Counterclockwise
(North pole)

Clockwise
(South pole)

Click here to show solution

When bringing the magnet (south pole) closer to the coil an induced current is generated

What is the direction of current rotation What is the name of the pole directly in front of you

Clockwise
(South pole )

Counterclockwise
(North pole )

Click here to show solution

When moving the magnet (north pole) away from the coil an induced current is generated

What is the direction of current rotation What is the name of the pole directly in front of you

Clockwise
(South pole )

Counterclockwise
(North pole )

Click here to show solution

When moving the magnet (south pole) away from the coil an induced current is generated

What is the direction of current rotation What is the name of the pole directly in front of you

Counterclockwise
(North pole)

Clockwise
(South pole)

Click here to show solution

In the figure below, there are two circuits: the first is a coil connected to a battery and a resistor, and the second circuit is a coil connected to a galvanometer

The switch in the circuit was closed \[A\]Determine the poles of the first coil

P
(South pole )

P
(North pole )

Click here to show solution

After closing the first circuit \[A\]
Determine the poles of the coil in circuit \[B\]

Q
(South pole )

Q
(North pole )

Click here to show solution

The resistance in circuit \[A\] was increased
While it is closed, determine the poles of circuit \[B\]

Q
(North pole )

Q
(South pole )

Click here to show solution

Mutual Induction Simulation Between Electrical Circuits

First Experiment: Closing/opening the first electrical circuit

When closing the first circuit, a current is generated in the second circuit for a short time in the opposite direction of the current in the first circuit (according to Lenz's law). When opening the first circuit, a current is generated in the second circuit in the same direction as the original current.

Important Results

In case of increasing field on the affected coil An opposite field to the cause is formed

In case of decreasing field on the affected coil A similar field to the cause is formed

Useful information: Magnetic flux

An induced current is generated in the adjacent coil

By bringing and moving the magnet and coil away from each other

Note the number of field lines penetrating the coil changes Increases when approaching or decreases when moving away

We call the number of magnetic field lines that perpendicularly pass through a surface area the magnetic flux

[latex]\Phi_\text{B} = \iint_\text{A} \mathbf{\text{B}} \cdot \text{d}\mathbf {\text{A}}[/latex].

By performing integration and scalar multiplication we obtain the magnetic flux relation

[latex]\Phi_\text{B} = \mathbf{\text{B}} \cdot \mathbf{\text{A}} = \text{BA} \cos \theta[/latex],

\[A\] surface area measured in square meters \[B\] magnetic field strength measured in tesla \[\theta\] angle between field and perpendicular to surface

Magnetic Flux Calculator

Magnetic Field Strength (B): Area (A): Angle: Angle Type: Between Field and Normal Between Field and Surface

A circular loop with surface area \[A=0.1 m^2\] is placed in a uniform magnetic field with strength
\[B=0.3 T\] as shown in the figure. Calculate the flux in the following cases:

The field makes an angle of \[60^0\] with the normal to the surface \[.................\]\[.................\] Click here to show solution	The field makes an angle of \[60^0\] with the surface \[.................\]\[.................\] Click here to show solution
The field is parallel to the surface \[.................\]\[.................\] Click here to show solution	The field is perpendicular to the surface \[.................\]\[.................\] Click here to show solution

Important Results.

Maximum flux occurs when the field is perpendicular to the surface

Flux is zero when the field is parallel to the surface

If given the angle between field and surface, subtract it from 90 to get the angle between field and normal

Useful Information: Magnetic Flux

We observed that an induced electromotive force is generated in a coil when the rate of flux changes

[latex]\Phi_\text{B} = \mathbf{\text{B}} \cdot \mathbf{\text{A}} = \text{BA} \cos \theta[/latex]

\[∆𝑉_{𝑖𝑛𝑑} = -d\frac{{{ф_B}}}{{{dt}}} \]

\[∆𝑉_{𝑖𝑛𝑑} = -d\frac{{{A .B .Cos 𝜃}}}{{{dt}}} \]

The negative sign is based on Lenz's Law which we will learn about later

According to the product rule of differentiation

\[∆𝑉_{𝑖𝑛𝑑} = -B.Cos 𝜃 \frac{{{dA }}}{{{dt}}} - A.Cos 𝜃 \frac{{{dB }}}{{{dt}}} + A.B Sin 𝜃 \frac{{{ d𝜃}}}{{{dt}}} \]

If the change in flux is due to the magnetic field \[∆𝑉_{𝑖𝑛𝑑} = -A.Cos 𝜃 \frac{{{dB }}}{{{dt}}} \]

Induced Voltage Calculator

Number of Turns (N):

Coil Area (m²):

Field Angle (degrees):

Initial Magnetic Field (T):

Final Magnetic Field (T):

Change Duration (s):

Example 1

A circular loop with radius
0.2 m
placed perpendicular to a changing magnetic field according to the function
B= 0.3 t³ +2t
The magnitude of the induced voltage in the loop at the third second equals

\[\Delta V_{ind}=-3.16\;\; V\;\;\;\;\;\;-C\]	\[\Delta V_{ind}=-1.27\;\; V\;\;\;\;\;\;-A\]
\[\Delta V_{ind}=-1.38\;\; V\;\;\;\;\;\;-D\]	\[\Delta V_{ind}=-2.08\;\; V\;\;\;\;\;-B\]

Click here to show solution

Choose the correct answer

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A

---

B

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C

---

D

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If the change in flux is due to surface area \[∆𝑉_{𝑖𝑛𝑑} = -B.Cos 𝜃 \frac{{{dA }}}{{{dt}}} \]

Induced Voltage Calculator

Magnetic Field Strength (Tesla):

Initial Area (m²):

Final Area (m²):

Change Duration (seconds):

Tilt Angle (degrees):

Example 2

A flexible loop with variable area is exposed to a magnetic field with strength
0.5 × 10^-4T
and perpendicular to the surface area. If its surface area increases by
0.1 m²
during a time of
0.4 s
then the average induced voltage in the loop equals

\[\Delta V_{ind}=1.25 \times 10^{-5}\;\; V\;\;\;\;\;\;-C\]	\[\Delta V_{ind}=1.11 \times 10^{-5}\;\; V\;\;\;\;\;\;-A\]
\[\Delta V_{ind}=2.24 \times 10^{-5}\;\; V\;\;\;\;\;\;-D\]	\[\Delta V_{ind}=4.35 \times 10^{-5}\;\; V\;\;\;\;\;-B\]

Click here to show solution

Choose the correct answer

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A

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B

---

C

---

D

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If the change in flux is due to the angle between field and normal to surface
\[∆𝑉_𝑖𝑛𝑑 = A.B Sin 𝜃 \frac{{{ d𝜃}}}{{{dt}}} =A.B .W Sin 𝜃 \]

Example 3

A rotatable loop with surface area
0.1 m²
placed in a uniform magnetic field with strength
0.2 T
with its surface parallel to the field begins to rotate around its axis due to an external force with angular velocity of
5 Rad /s
The induced voltage at the fourth second equals

\[\Delta V_{ind}=0.06\;\; V\;\;\;\;\;\;-C\]	\[\Delta V_{ind}=0.09\;\; V\;\;\;\;\;\;-A\]
\[\Delta V_{ind}=0.02\;\; V\;\;\;\;\;\;-D\]	\[\Delta V_{ind}=0.05\;\; V\;\;\;\;\;-B\]

Click here to show solution

Choose the correct answer

---

A

---

B

---

C

---

D

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Applications of Lenz's Law Eddy Currents
Eddy current or Foucault currents are currents generated by changing magnetic flux penetrating a conductive body, in accordance with one of two laws discovered by Michael Faraday. Faraday's law states that if the flux of the magnetic field changes in a wire or coil, an electric voltage is generated between the ends of the wire or coil.
In this simulation, there are two pendulums consisting of plates, one perforated and the other solid. The plates are left to oscillate within the field, and eddy currents form in the solid plate. The currents intensify and create an opposing field that stops the plate, while the perforated plate doesn't intensify currents, allowing oscillations to continue longer.



Metal Detector Device


The device consists of two coils - a transmitter coil and a receiver coil. The transmitter coil is connected to an alternating current source, generating a changing magnetic field that affects the receiver coil. According to Lenz's law, an opposing field is generated. When a coin or metal object passes through, it acts as a receiver coil that in turn affects the main receiver coil, creating an opposing field that reduces the receiver coil's field, resulting in an audio and visual signal indicating the field reduction due to the metal object.

Source
https://phet.colorado.edu/zh_CN/simulations/filter?sort=alpha&view=grid
https://www.vascak.cz/?page_id=2355&language=it#demo
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