There are a lot of numbers in this problem. Just about the only way to get it ri
ID: 1561379 • Letter: T
Question
There are a lot of numbers in this problem. Just about the only way to get it right is to work out each step symbolically first, and then plug numbers into the final symbolic result. Two cells of wire are aligned with their axes along the z-axis, as shown in the diagram. Coil 1 is connected to a power supply and conventional current flows clockwise through coil 1, as seen from the location of coil 2. Coil 2 is connected to a voltmeter. The distance between the centers of the coils is 0.18 m. Coil 1 has N_1 = 595 turns of wire, and its radius is R_1 = 0.09 m. The current through coil 1 is changing with time. At t=0 s, the current through coil 1 is I_0 = 17 A. At t=0.4 s, the current through coil 1 is I_0 4 = 6 A. Coil 2 has N_2 = 270 turns of wire, and its radius is R_2 = 0.04 m. Inside coil 2, what is the direction of -dB/dt during this interval? What is the direction of the electric field inside the wire of coil 2, at a location on the top of coil 2? At time t=0, what is the magnetic flux through one turn of coil 2? Remember that all turns of coil 1 contribute to the magnetic flux. Note also that the cells are not very far apart (compared to their radii), so you can't use an approximate formula here. At t=0 Theta_1 tum = T m^2 At t=0.4 s, what is the magnetic flux through one (urn of coil 2? At t=0.4 s Theta_1 turn = T m^2 What is the emf in one turn of coil 2 during this time interval? i emf_1 turn 1 = v The voltmeter is corrected across all turns of coil 2. What is the reading on the voltmeter during this time interval? voltmeter reading is During this interval, what is the magnitude of the non-Coulomb electric field inside the wire of coil 2? Remember that the emf measured by the voltmeter involves the entire length of the wire making up coil 2. E_NC - V/m At t=0.5 seconds, the current in coil 1 becomes constant, at 5 A. Which of the following statements are true? The electric field inside the wire of coil 2 now points in the opposite direction. The voltmeter reading is about the same as it was at t=0.4 seconds. The electric field inside the wire of coil 2 is now 0 V/m. The voltmeter now reads 0 V.Explanation / Answer
(a)
flix = B A cos theta
= uo / 4pi * 2 I1 A1 N1/ ( z^2 + R1^2)^3/2 A2
= uo/ 4pi * ( 2 ( 17A) pi (0.09)^2 ( 595) pi ( 0.04)^2/(0.18^2 +0.09^2)^3/2
=3.17 * 10^-5 T m^2
(b)
A t= 0.4 s , I 1 = 6A
flix is directly proportional to I
so since I1 = Io/3
the magnetic flix decreases by the same factor
flux 1 = flux 1/ 3 = 1.05 * 10^-5 T m^2
(3)
emf = dflux/ dt
=1.05 * 10^-5 /0.4
=2.64 * 10^-5 V
(4)
del V = N2 emf
=270*2.64 * 10^-5
=0.007128 V
(5)
E = del V/L
= del V/ N2 2pi R2
= 0.007128/ 270* 2 pi (0.04)
=1.05* 10^-4 V/m
the last two options are correct because if I is constant then B is constant and flux is constnat and d flux /dt = 0
so emf = 0
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