Question

A 22-turn circular coil of radius 5.00 cm and resistance 1.00 ?
is placed in a magnetic field directed perpendicular to the plane
of the coil. The magnitude of the magnetic field varies in time
according to the expression *B* = 0.010 0*t* + 0.040
0*t*^{2}, where *B* is in teslas and
*t* is in seconds. Calculate the induced emf in the coil at
*t* = 5.40 s.

mV

Answer #1

**total flux through the coil = N*B*A**

**N = number of turns**

**B = magnetic field = 0.01t + 0.04t^2**

**A = area= pi*r^2 = 3.14*0.05*0.05 = 0.00785
m^2**

**N = 22**

**lenz law :The direction of motion induced emf is always
such that it opposes the rate of change in flu**

**emf = -rate of change in flux**

**emf = (d/dt)*flux**

**emf = (d/dt)*N*B*A**

**here A,N is constant**

**emf = N*A*(dB/dt)**

**dB/dt = 0.01 + 2*0.04*t**

**at t= 5.4 s**

**dB/dt = 0.01+(2*0.04*5.4) = 0.442**

**emf = N*A*dB/dT**

**emf = 22*0.00785*0.442 = 0.0763334 v = 76.33 mv
<---answer**

**indued current = emf / Resistance =
76.33 milli ohms <-answer**

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