Question

long straight wire (extending indefinitely in the ty direction) is carrying current I-5 A in the ay direction and conducting coll having (a) At the instant that the wire is distance x with speed v 2 m/s in the «x-direction toward a small circular N 12 closely packed turns of radius r 2 cm. The ends of a voltmeter, and the coil lies in the xy plane, centered at th that the wire is distance x- 0.2 m from the center of the coll, what is the magnitude of the reading of the voltmeter? Express yourr er? impedance of the voltmeter is much, much higher than that of the coll and connecting wires. Assume x is large enough Express your result both symbolically and that the field is approximately uniform over the area of the coil and Ignore the emf in the loop f (b) Assuming a small current (due to the high but non-infinite impedance of the voltmeter) fl on the +z axis? by the connection to the meter ows in the col, will that current be clockwhe or counter -clockwise as viewed froma circular cod

Answer 1

a)

magnetic field by the long wire at the location of the circular loop is given as

B = ($\mu _{o}$/4$\pi$) (2 I)/x

taking derivative both side relative to "t"

dB/dt = ($\mu _{o}$/4$\pi$) (2 I) (- 1/x²) (dx/dt)

dB/dt = ($\mu _{o}$/4$\pi$) (2 I) (- 1/x²) v

r = radius of the circular loop = 2 cm = 0.02 m

A = area of the circular loop = $\pi$ r² = (3.14) (0.02)² = 0.001256 m²

magnetic flux through the loop due to magnetic field by the long wire is given as

$\phi$ = N B A

induced emf is given as

E = - d$\phi$/dt

E = - N A (dB/dt )

E = - (N A) ($\mu _{o}$/4$\pi$) (2 I) (- 1/x²) v

inserting the values

E = (12 x 0.001256) (10^-7) (2(5)) (1/0.2²) (2)

E = 7.54 x 10^-7 volts

b)

counterclockwise