Question

A 28-turn coil with a diameter of 6.00 cm is placed in a constant, uniform magnetic field of 1.00 T directed perpendicular to the plane of the coil. Beginning at time

*t* = 0 s,

the field is increased at a uniform rate until it reaches 1.30 T at

*t* = 10.0 s.

The field remains constant thereafter. What is the magnitude of the induced emf in the coil at the following times?

(a) *t* < 0 s

mV

(b) *t* = 5.00 s

mV

(c) *t* > 10.0 s

mV

Answer #1

**Given**

**number of turns are N = 28**

**diameter d = 0.06 m , radius r = 0.03 m**

**magnetic field B = 1 T**

**at t= 0s , B1 = 1 T **

**later at t = 10s , B2 = 1.30 T**

**induced emf = -dphi/dt**

**emf = -d(B*A*N cos theta) /dt**

**emf = -d(B*A*N*cos0)/dt**

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

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

**emf = pi*r^2*dB/dt**

**emf = pi*0.03^2*0.3*28/10 V **

**emf = 0.0023750440461 V = 2.375 mV**

**at t < 0 there is no change in magnetic field so the
emf = 0 mV**

**and after t > 10 s the magnetic field is not varying
so the induced emf = 0 mV**

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