1. Two nested, ideal solenoids are aligned concentrically along the same axis, a

Question

1. Two nested, ideal solenoids are aligned concentrically along the same axis, as shown above. The outer solenoid is connected to a variable current supply, and it initially carries a current I1 in its coils in the direction shown in its wires above. The inner solenoid's current, I2 is initially zero. Assume that both solenoids have some small, but non-zero, resistance.

Outer Solenoid: l1 = 55cm r1= 4.0cm N1= 780 turns

Inner Solenoid: l2 = 22cm r2= 3.0cm N2 = 250 turns

A. Based on the direction of I, at the instance shown above, what is the direction of the magnetic field B1 inside the outer (larger) solenoid's coils?

Suppose that I1 decreases linearly from 20.0A to 10.0A during a time period of 33.3 ms.

B. Ignoring the inner solenoid, what is the change in energy of the outer (larger) solenoid during this time period? (Recall: For an ideal straight solenoid, L= (uo*N2*A)/(little l) _______________

Now, including the inner solenoid...

C. In which direction is the current I2 induced in the inner (smaller) solenoid during this time period? A. In the same direction as the circulation of I1 B. In the opposite direction as the circulation of I1

D. Assuming that the outer (larger) solenoid is ideal, what is the strength fo the total emf induced in the inner (smaller) solenoid during this time period? _______________

Suppose that I1(t) now begins to oscillate in a sinusoidal AC fashion. The pair of soleniods forms an (inefficient) transformer, where the outer solenoid is the primary coil and the inner solenoid is the secondary coil. (Ignore the different radii of the two solenoids.)

E. This forms a __________ transformer.

A. Step-up B. Step-down

F. If there were a 100% efficient transformer, the rms primary voltage would be _______ times the rms secondary voltage. (Fill in the blank with a numberical value.)

G. The current I2(t) induced in the inner (smaller) solenoid will be:

A. constant in both strength and direction

B. Varying in strenght, but alwasy in the same direction

C. Varying in both strength and direction

Explanation / Answer

a) use right hand rule and get to the left
B)

b) E= 1/2 L I^2

so dE = 0.5*4*pi*10^(-7)*780^2*pi*4.0E-2^2/.55*(10^2-20^2)=-1.048 J

c) so therewill be less flux to the left so it will put its fieldtothe left as well
so same as I1 A)

d) emf = dflux/dt = N A dB/dt
but B = u0 N I/L

so emf = N A u0 N1 dI/dt/L1

= 250*pi*3.0E-2^2*4*pi*10^(-7)*780*(10/33.3E-3)/.55= 0.378 v

e) since less turns in N2

V2/V1 = N2/N1
step down A)

b) N1/N2 = 780/250 = 3.12

g) c) since it will be sinuosoidal as well, since
the emf varies as dI/dt and derivative of sinusoidal is sinusoidal

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