The figure shows two 19-turn coils tightly wrapped on the same 2.0-cm-diameter c

Question

The figure shows two 19-turn coils tightly wrapped on the same 2.0-cm-diameter cylinder with 1.0-mm-diameter wire. The current through coil 1 is shown in the graph. A positive current is into the page at the top of a loop. Assume that the magnetic field of coil 1 passes entirely through coil 2. (Figure 1) Determine the current in coil 2 at t = 0.05s. Express your answer as an integer and include the appropriate units. Determine the current in coil 2 at t = 0.25s. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

i) from fig, at t = 0.05 s, I1 = constant

so flux (@2) = constant ( @ = M*I)

emf, e2 = d@2 / dt = 0

so current I2 ( 0.05) = 0 ( because emf is zero)

b) I2(0.25) = ?

B = magnetic field, A2 = area of second coil= pie*r22, N2 = no of turns of second coil = 19   

I2 = e2 / R2   ( e2 = N2*d@2 / dt , @2 = B.A2)

= (1/R2)*  N2*d@2 / dt

= ( 1/R2)* N2*A2 * dB/dt

= ( N2*pie*r22 / R) * d/dt( u0*N1*I1 / L1) ( B = uo*N1*I1 / L1 , L1 = 19*1*10-3m)

= (N2*pie*r22* u0*N1 / R*L )* dI1 / dt ( dI1/dt = 2 - ( -2) / 0.2 = 20A/s)

= 19*3.14* ( 0.01m)2*4*3.14*10-7*19 *20 / (2ohm)*19*10-3

= 7.49*10-5A

  

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