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## Homework Statement

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 coils 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 counter-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 0.14 m.

Coil 1 has N_1 = 565 turns of wire, and its radius is R_1 =0.07 m. The current through coil 1 is changing with time. At t=0 s, the current through coil 1 is I_0 = 15 A. At t=0.4 s,the current through coil 1 is I_0.4 =6 A.

Coil 2 has N_2 = 280 turns of wire, and its radius is R2 = 0.03 m.

Inside coil 2, what is the direction of – d/dt during this interval?

+Z (correct)

What is the direction of the electric field inside the wire of coil 2, at a location on the top of coil 2?

-X(correct)

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 field. Note also that the coils are not very far apart(compared to their radii), so you can't use an approximate formula here.

At t=0 Phi_1 turn = ??? T m2

***THIS IS WHERE I'M STUCK***

At t=0.4 s, what is the magnetic flux through one turn ofcoil 2?

At t=0.4 s Phi_1 turn = ??? T m2

What is the emf in one turn of coil 2 during this timeinterval?

|emf1 turn| = ??? V

The voltmeter is connected across all turns of coil 2. What is thereading on the voltmeter during this time interval?

voltmeter reading is ??? V

During this interval, what is the magnitude of the non-Coulombelectric field inside the wire of coil 2? Remember that the emfmeasured by the voltmeter involves the entire length of the wiremaking up coil 2.

ENC = ??? V/m

At t=0.5 seconds, the current in coil 1 becomes constant, at 5 A. Which of the following statements are true?

1. The electric field inside the wire of coil 2 now points in the opposite direction.

2. The voltmeter now reads 0 V.

3. The voltmeter reading is about the same as it was at t=0.4 seconds.

4. The electric field inside the wire of coil 2 is now 0 V/m.

## Homework Equations

I = dV/R

dV= Emf

Emf= -N*dPhi_mag/dt = -N*(d/dt)(B*n*dA)

Phi = B*n*dA

N=number of turns, n = nhat normal unit vector to area.

R = resistance

## The Attempt at a Solution

If I had a resistance I know I could find emf and from there find the flux phi, but without it I'm stuck and don't know what to do.

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