Question

A coil is wrapped with 238 turns of wire on the perimeter of a square frame of sides 17.7cm. Each turn has the same area, equal to that of the frame, and the total resistance of the coil is 1.39ohms. A uniform magnetic field is turned on perpendicular to the plane of the coil. If the field changes linearly from 0 to 0.455Wb/m^2 in a time of 1.06s find the magnitude of the induced emf in the coil while the field is changing. Answer is units of V.

Answer 1

Answer:

3.19V

Explanation:

To solve this problem, the application of Farady's law is necessary.

Which summarizes the way in which the electric potential can be generated.

The equation is given by,

$\epsilon_{emf} = -N\frac{d\phi}{dt}$

Where,

N= Number of turns

$\phi = BA =$Magnetic Flux

B = Extenral magnetic field

A = Area of coil

So our equation can be rewritten as:

$\epsilon_{emf} = \frac{BAN}{t}$

Our values are given as,

$A = 17.7cm*17.7cm = 0.013m^2 \\B = 0.455Wb/m^2\\N = 238 Turns\\t = 1.06$

Replacing,

$\epsilon_{emf} = \frac{(-238)(0.455)(0.0313)}{1.06}\\\epsilon_{emf} = 3.19V$