1)Find approximately the mutual inductance of this pair of coils. 2)If the curre

Question

1)Find approximately the mutual inductance of this pair of coils.

2)If the current in coil A varies with time according to I = 20 t3 - 65 t2 - 1, where I is in amps and t is in s, find the magnitude of the EMF induced in coilB at time t = 10.0 s.

If someone could point me in the right direction that would be great. For 1) i was using L=mu*N1*N2*A/L. This was wrong.

Coil A is a large 800 turn circular coil of radius 96.0 cm. Circular coil B has 450 turns, a radius of 1.0 cm and is located L-68.0cm from aoil A along the same axis. The Planes of the two coils are parellel.

Explanation / Answer

a)

B = (N_A) u0 i (r_A)^2/(2(L^2+(r_A)^2)^(3/2))

phi = (N_B) pi (r_B)^2 (N_A) u0 i (r_A)^2/(2(L^2+(r_A)^2)^(3/2))

M = phi/i

==> M = (N_B) pi (r_B)^2 (N_A) u0 (r_A)^2/(2(L^2+(r_A)^2)^(3/2))

==> M = (450)*3.1416*(0.01*0.01)*(800)*4*3.1416e-7*(0.96*0.96)/(2*(0.68*0.68+0.96*0.96)y(3/2))

==> M = 4.0223e-5

==> M = 4.02 x 10^-5 Hn

b)

i = 20 t^3 - 65 t^2 - 1

==> di/dt = 60 t^2 - 130 t

emf = M di/dt = M (60 t^2 - 130 t)

==> emf = 4.0223e-5 * (60*10*10 - 130*10) = 0.189 V

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