Question

A flat, circular coil has 40 turns of radius 3.6 cm. At t=0 an external magnetic field perpendicular to the plane of the coil has a value of 0.32 T and is decreasing linearly with time. At t = 0, the induced emf is 65 mV. How long does it take for the field to reach zero?

Answer 1

The emf of the circular coil is, e=N(d/dt)=N(A*(dB/dt))

re arranging the term, (dt/dB)=NA/e=(N*pi*r^2)/(e);

(t2-t1)/(B2-B1)=(N*pi*r^2)/(e)

substitute the values in above expression,

(t2) s/(B2-0.32)T =(40*3.14*3.6*10^-2 m*3.6*10^-2 m)/(65*10^-3 V)=2.5042 m^2/V

t2=2.5042(B2-0.32)=2.5042*B2-8.013

But we want,how much time to reach the magnetic field becomes zero, So we can put the B2=0 then t2 becomes,

t2=-8.013 s negative sign represents magnetic field is decreasing linearly with time