1. What is the magnetic flux through the small loop when the current through the
ID: 1456285 • Letter: 1
Question
1. What is the magnetic flux through the small loop when the current through the solenoid is 2.5 A?
2.95 × 10-2 Wb
7.28 × 10-2 Wb
2.95 × 10-4 Wb
4.38 × 10-4 Wb
5.92 × 10-4 Wb
2. What is the induced emf in the loop?
0.7 × 10-3 V
1.4 × 10-3 V
2.8 × 10-3 V
5.6 × 10-3 V
zero
3. What is the induced emf in the loop if the loop is oriented so that its axis is perpendicular to the axis of the solenoid instead of parallel?
0.7 × 10-4 V
1.4 × 10-4 V
2.8 × 10-4 V
5.6 × 10-4 V
zero
4. What is the self-induced emf in the solenoid due to the changing current.
60 V
98 V
130 V
180 V
250 V
Could someone please walk me through this?
Explanation / Answer
1) The field inside the solenoid (ignoring fringe effects, assuming this is in a vacuum) is:
B = u0 N i /L
u0 = permeability of vacuum
N #of turns
i current
L length
B = 1.25 E-6*1.5E4*2.5 / 0.1 = 0.47 T = 0.47 Wb/m2
The area of the loop is pi 0.02^2 = 0.00125 m2
That is a flux of ~5.91 E-4 Wb
answer is E.
2) E = d(Flux)/dt = µ0(dI/dt)(N/L)rl^2 = 5.91*10^-4/0.42 = 1.4*10^-3 V
3) Zero,
Inside a solenoid, the magnetic field is quite uniform, directed along the axis. If you place the loop with its axis perpendicular to that of the solenoid, the area of the loop presented on-edge to the field is zero, so the flux is always zero and so the induced voltage must be zero.
4) Lsol =µ0n^2 V = 130 V
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