A 4.0-cm-diameter loop with resistance 0.17? around a 2.0-cm-diameter solenoid.

Question

A 4.0-cm-diameter loop with resistance 0.17? around a 2.0-cm-diameter solenoid. The solenoid is 14cm long, has 100 turns, and carries the current shown in the graph. A positive current is cw when seen from the left.

Find the current in the loop at t = 1.5s.

I(1.5s)=_______________

A 4.0-cm-diameter loop with resistance 0.17? around a 2.0-cm-diameter solenoid. The solenoid is 14cm long, has 100 turns, and carries the current shown in the graph. A positive current is cw when seen from the left. Find the current in the loop at t = 1.5s. I(1.5s)=_______________

Explanation / Answer

Magnetic field inside the solenoid is given by,

B = u0 (N/L)I

magnetic flux through the surrounding coil,

flux = B(pi R1^2) = u0(N/L)I(pi R1^2)

induced emf e = d(flux) / dt

        = u0(N/L)(pi R1^2) dI/dt

         = (2.82 x 10^-7) dI / dt

induced current i = e/R   = 16.59 x 10^-7 dI/dt

at t= 1.5 sec, dI / dt = 40 A /s

i = 16.59 x 10^-7 x 40 = 6.635 x 10^-5 A

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