A very long solenoid of inner radius 3.25 cm creates an oscillating magnetic fie

Question

A very long solenoid of inner radius 3.25 cm creates an oscillating magnetic field of the form. What is the maximum value of the induced electric field at a point 1.45 cm perpendicular from the axis of the solenoid? What is the maximum value of the induced electric field at a point 6.85 cm perpendicular from the axis of the solenoid? The magnetic field inside a very long solenoid and far from the ends of the solenoid is uniform and oriented along the axis of the solenoid. Outside a very long solenoid and far from the ends of the solenoid the magnetic field is zero.

Explanation / Answer

E*dA = - d(Flux)/dt = - A*dB/dt

r = radial distance

R = radius

a.) For r<R,

E*2pi*r = pi*r^2*Bmax*w*sin(wt)

So E= (r/2)*Bmax*w*sin(wt)

So Emax = (r/2)*Bmax*w = (0.0145/2)*0.00675*334 = 0.016345 V/m

b.) For r>R,

E*2pi*r = pi*R^2*Bmax*w*sin(wt)

So E= (R^2/2r)*Bmax*w*sin(wt)

So Emax = (R^2/2r)*Bmax*w = (0.0325^2/2*0.0685)*0.00675*334 = 0.017382 V/m

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