Two wires, parallel to the z axis and distance 4r apart, carry equal currents I

Question

Two wires, parallel to the z axis and distance 4r apart, carry equal currents I =0.48 A in opposite directions, as shown in Fig. 32-40. A circular cylinder of radius r and length L=8 cm has its axis on the z axis, midway between the wires. Use Gauss' law for electromagnetism to calculate the net outward magnetic flux through the half of the cylindrical surface above the x axis. (Hint: Find the flux through that portion of the xz plane that is within the cylinder. )

? mWb

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(a) What is the magnitude of the emf induced in the loop when t=8 s?

Magnitude = ? V   

(b) What is the direction of the current through R?

Explanation / Answer

1)According to Gauss's law both the wires would produce magnetic fields in such a way that cancels the field of the other.

So, the flux is zero.

2)

a)V = d/dt *(B) = d/dt *B = 5.7t2+ 9.3t = 11.4t + 9.3

at t=8

V=100.5mV = 0.1005V

(b) What is the direction of the current through R?

1,From right to left,

because that tends to cancel the increase in flux.

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