A solenoid 2m long and 30 cm in diameter consists of 5000 turns of wire (primary

Question

A solenoid 2m long and 30 cm in diameter consists of 5000 turns of wire (primary). A 5 turn coil (seconday) with negligible resistance is wrapped around the solenoid and connected to a 180 ohm resistor. The solenoid current is given by (I=I0 Sin(wt)) where I0=85A, w= 210 rad/s and t is in seconds.

a) determine the magnetic field at the center of the solenoid (primary) at t=1ms.

b) determine the peak emf induced in the secondary loop.

c) what is the current in the secondary coil when the primary coil current is a maximum.

I think the answers should be a)0.0556T, b)19.8v,C) I=0 when primary max

Explanation / Answer

Length of solenoid = 2 m

Diameter = 30 cm = 0.30 m

Number of turns =N = 5000 turns

Solenoid current = 85×Sin(wt)

w = 210 rad /s

Secondary coil turns = 5

Resistance = R = 180 ohm

(a). n = N/L = 5000/2 = 2500

At t = 1 ms = 10-3 s

Current = I = 85×Sin(210×10-3) = 85×0.21 = 17.72 A

Magnetic field at center = = 0.056 T

(b). Emf induced = rate of change of flux

= A.dB/dt

Area = A = (0.15)2 = 0.071 m2

Emf = 5×(0.071)×(4×10-7 ×2500)×(85×210) = 3.98 volt

(c). The current in the secondary coil will be zero when there is maximum current in primary coil is maximum .

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