# Calculate Average Emf in Rectangular Coil

• theshonen8899
In summary, using Faraday's law, the magnitude of the average emf induced in a rectangular coil of 65 turns, with dimensions 30.0cm by 43.0cm, initially perpendicular to a uniform external magnetic field of magnitude 1.90T and rotated to an angle of 35.0∘ in a total time of 7.00×10−2s is calculated to be -186 volts. However, this result seems unusually large and further investigation is needed. The average emf is defined as the integral of the emf over the rotation time divided by the total time. To avoid errors, it is recommended to first use variables and then substitute actual values at the end.
theshonen8899

## Homework Statement

A rectangular coil of wire has 65.0 turns and is 30.0cm by 43.0cm . Initially the plane of the coil is perpendicular to a uniform external magnetic field. It is then rotated till its plane is at an angle of 35.0∘ with that field. The magntude of the external field is 1.90T and total time to rotate the coil is 7.00×10−2s .

Calculate the magnitude of the average emf that is induced in the coil.

## The Attempt at a Solution

So Faraday's law states that the induced emf is equal to $\frac{-d\Phi_{B}}{dt}$.
What I get is
A is area
A = (0.3m)(0.43m) = 0.129m^2
B is magnetic field
dB/dt = (1.90T)/(7.00*10^2 s) = 27.14 T/s
$\frac{-d\Phi_{B}}{dt}$ = -dB/dt * A * cos(35) = -2.87
N is # of turns
EMF = N * ($\frac{-d\Phi_{B}}{dt}$) = 65 * -2.87 = -186

This number seems very large to me. Can anyone point out what I've done wrong?
Many thanks!

According to your formula, if the angle = 0 you get even more voltage! So we get big volts and we don't even move the coil! So that's bad.

What is average emf? What is the average of a function f(t) over a time interval T?
You need to integrate the emf and then divide by T. The emf varies how as you rotate the coil away from 0 degrees?

I would initially replace the coil dimensions with a and b, the field with B, the final angle with θf and the no. of turns with N, then substitute actual numbers only at the very end. That way you can check dimensions of your terms and keep the math nice and tidy.

## 1. What is the formula for calculating average EMF in a rectangular coil?

The formula for calculating average EMF in a rectangular coil is:
Average EMF = (Number of turns x Area of coil x Angular frequency x Magnetic field strength) / Time

## 2. How do you determine the number of turns in a rectangular coil?

The number of turns in a rectangular coil can be determined by counting the number of loops or windings around the coil. If the coil is made up of multiple layers, you will need to count the number of turns in each layer and add them together.

## 3. What is the significance of the area of the coil in calculating average EMF?

The area of the coil is a crucial factor in calculating average EMF as it represents the size of the coil that is interacting with the magnetic field. A larger area means a larger amount of the coil is exposed to the field, resulting in a higher average EMF.

## 4. Can the average EMF in a rectangular coil be negative?

Yes, the average EMF in a rectangular coil can be negative if the direction of the magnetic field or angular frequency is reversed. This indicates that the induced current in the coil is flowing in the opposite direction.

## 5. How does changing the time affect the average EMF in a rectangular coil?

Changing the time will have a direct impact on the average EMF in a rectangular coil. The faster the time, the higher the average EMF will be, as the coil will be exposed to the magnetic field for a shorter duration. Similarly, a longer time will result in a lower average EMF.

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