# Magnetic Flux and Induced EMF in a Coil

• erik-the-red
In summary, In a physics laboratory experiment, a coil with 210 turns enclosing an area of 12.7 cm^2 is rotated during the time interval 3.70 \cdot 10^{−2} sfrom a position in which its plane is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is 5.20 \cdot 10^{−5} T. The change in magnetic flux is merely the negative of the initial magnetic flux. I use the equation {\cal{E}} = - N \frac{d \Phi_1}{dt} to get -\frac{210 \cdot (-1.39 \cd
erik-the-red
In a physics laboratory experiment, a coil with 210 turns enclosing an area of 12.7 cm^2 is rotated during the time interval $$3.70 \cdot 10^{−2}$$ sfrom a position in which its plane is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is $$5.20 \cdot 10^{−5}$$ T.

What is the magnitude of the average emf induced in the coil?

I've already found the total magnitude of the magnetic flux through the coil before and after rotation.

Since the magnitude after rotation is zero, the change in magnetic flux is merely the negative of the initial magnetic flux.

I use the equation $${\cal{E}} = - N \frac{d \Phi_1}{dt} = - N \frac{\Delta \Phi_1}{\Delta t}$$.

Plugging in, I get $$-\frac{210 \cdot (-1.39 \cdot 10^{-5})}{3.70 \cdot 10^{-2}}$$.

The negatives cancel out, leaving me with a positive answer.

But, my answer is wrong.

What happened?

Last edited:
erik-the-red said:
In a physics laboratory experiment, a coil with 210 turns enclosing an area of 12.7 cm^2 is rotated during the time interval $$3.70 \cdot 10^{−2}$$ sfrom a position in which its plane is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is $$5.20 \cdot 10^{−5}$$ T.

What is the magnitude of the average emf induced in the coil?

I've already found the total magnitude of the magnetic flux through the coil before and after rotation.

Since the magnitude after rotation is zero, the change in magnetic flux is merely the negative of the initial magnetic flux.

I use the equation $${\cal{E}} = - N \frac{d \Phi_1}{dt} = - N \frac{\Delta \Phi_1}{\Delta t}$$.

Plugging in, I get $$-\frac{210 \cdot (-1.39 \cdot 10^{-5})}{3.70 \cdot 10^{-2}}$$.

The negatives cancel out, leaving me with a positive answer.

But, my answer is wrong.

What happened?
How did you calculate the flux?

The first part of the question asked:

What is the total magnitude of the magnetic flux ($$\Phi_i$$) through the coil before it is rotated?

I used the equation $$\Phi_i = B \cdot A \cdot \cos(\phi)$$. My answer of 1.39e(-5) is correct.

erik-the-red said:
The first part of the question asked:

What is the total magnitude of the magnetic flux ($$\Phi_i$$) through the coil before it is rotated?

I used the equation $$\Phi_i = B \cdot A \cdot \cos(\phi)$$. My answer of 1.39e(-5) is correct.
?

The initial angle in the problem you stated is 0; cos(0) = 1.

B*A*cos(0) = 5.2e-5T*12.7cm^2*(1m/100cm)^2=6.6e-8Tm^2

Where have I gone wrong?

There are actually 10,000 square centimeters in one square meter. This is a problem from an online assignment. I know the first and second parts are correct.

The third part is still puzzling me.

erik-the-red said:
There are actually 10,000 square centimeters in one square meter. This is a problem from an online assignment. I know the first and second parts are correct.

The third part is still puzzling me.
(100cm/m)^2 is 10,000 cm^2/m^2

I think I see the problem.

1.39e-5 = 6.6e-8*210

In the earlier part of the problem you already multiplied the flux times the number of turns. Now you are doing it again to calculate the emf. I don't know what the earlier question was, but you only get to multiply by N once to calculate emf.

OlderDan, thanks!

## 1. What is magnetic flux?

Magnetic flux is a measure of the total amount of magnetic field passing through a given area. It is represented by the symbol Φ and is measured in units of webers (Wb).

## 2. How is magnetic flux related to induced EMF?

When there is a change in magnetic flux passing through a coil, it induces an electromotive force (EMF) in the coil. This is known as Faraday's Law of Induction and is the basis for many electrical generators.

## 3. How is the direction of induced EMF determined?

The direction of induced EMF is determined by Lenz's Law, which states that the induced current will flow in a direction that opposes the change in magnetic flux that caused it. This means that the induced current will create a magnetic field that opposes the original change in flux.

## 4. What factors affect the magnitude of induced EMF in a coil?

The magnitude of induced EMF is affected by the rate at which the magnetic flux changes, the number of turns in the coil, and the strength of the magnetic field. It is also influenced by the orientation of the coil relative to the magnetic field and the material of the coil.

## 5. How can induced EMF be used in practical applications?

Induced EMF is used in a variety of practical applications, including electrical generators, transformers, and induction cooktops. It is also used in technologies such as RFID (radio-frequency identification) and wireless charging.

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