Question

The magnetic field inside a 4.0-cm-diameter superconducting solenoid varies sinusoidally between 8.0 T and 12.0 T at a frequency of 15 Hz . What is the maximum electric field strength at a point 1.7 cm from the solenoid axis? What is the value of B at the instant E reaches its maximum value?

Answer 1

answer) we know that in solenoid at a distance r<R,

B.ds=E*2pir

taking the derivative of E.2pir

E=-d/dt B*pir²=-r/2*B

we can see that the field is varying from 8 T to 12 T

so b(t)=Bc+B_osin(2pif)t=2+10 sin(30pit) , Bc= constant

a) we have found that E=-r/2*B

so d/dt B=30picos(30pit)

so E=-30*pi*r*cos(30pit)

E will have the maximum value when 30pift=pi, 3pi..etc

so cos 30pit=1

E=30*pi*r=30*3.14*0.017m=1.6 V/m

b) the sine function is zero at 30 pit , so when electric field is maximum then

B(t)=Bc+B sin ( 30pit)=Bc

so B=10T.

a) 1.6 V/m and b) 10T.

answered by: anonymous