A long solenoid of radius a carrying n turns per unit length is looped by a wire of resistance R as shown in the figure 6. O 1 Figure 6: A solenoid looped by a wire of resistance R a) The current I(t) in the solenoid is decreasing at a constant rate = -a, and a is a positive constant. The magnetic field inside the solenoid is B = μonI. dI (t) dt (i) Derive an expression for the induced current that flows through the loop. (iii) Use Faraday's Law [5 marks] (ii) Copy the drawing in your submission and indicate the direction of the induced current through the loop. Justify your answer. f. E.d² = -d/f. B.as == dt and find the direction and magnitude of the electric field inside the solenoid.

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Question B1
A long solenoid of radius a carrying n turns per unit length is looped by a wire of resistance R as
shown in the figure 6.
03
1
1
(iii) Use Faraday's Law
a
1
Figure 6: A solenoid looped by a wire of resistance R
di (t)
dt
a) The current I(t) in the solenoid is decreasing at a constant rate = -a, and a is a positive
constant. The magnetic field inside the solenoid is B = μonI.
(i) Derive an expression for the induced current that flows through the loop.
[5 marks]
(ii) Copy the drawing in your submission and indicate the direction of the induced current
through the loop. Justify your answer.
d
f. E.di - - / // B.d$
dt
and find the direction and magnitude of the electric field inside the solenoid.
2 marks]
18 marks]
b) At a time t₁: consider that the solenoid from part a has a constant current I, i.e. (d = 0). At
the time tf: the solenoid is pulled out of the loop and set out in the loop in the opposite direction,
compared to its position at time tį.
(i) Calculate the changes in magnetic flux through the loop in the time interval At, i.e. A o(t) =
o(tf) - (ti).
Transcribed Image Text:Question B1 A long solenoid of radius a carrying n turns per unit length is looped by a wire of resistance R as shown in the figure 6. 03 1 1 (iii) Use Faraday's Law a 1 Figure 6: A solenoid looped by a wire of resistance R di (t) dt a) The current I(t) in the solenoid is decreasing at a constant rate = -a, and a is a positive constant. The magnetic field inside the solenoid is B = μonI. (i) Derive an expression for the induced current that flows through the loop. [5 marks] (ii) Copy the drawing in your submission and indicate the direction of the induced current through the loop. Justify your answer. d f. E.di - - / // B.d$ dt and find the direction and magnitude of the electric field inside the solenoid. 2 marks] 18 marks] b) At a time t₁: consider that the solenoid from part a has a constant current I, i.e. (d = 0). At the time tf: the solenoid is pulled out of the loop and set out in the loop in the opposite direction, compared to its position at time tį. (i) Calculate the changes in magnetic flux through the loop in the time interval At, i.e. A o(t) = o(tf) - (ti).
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