5.(20 pts) An infinitely long straight wire carries a current I which flows down

Question

5.(20 pts) An infinitely long straight wire carries a current I which flows downward. 2-pts (a) Find the direction and magnitude of the magnetic field at the center of the loop. a+b) (or the magnetic field at a distance from the wire- 7 3-pts (b) calculate the magnetic flux through the rectangular loop. Now the rectangular loop moves to the right with a speed V 15-pts (c) Determine the direction and magnitude of the induced current in the loop with a resistance R when it moves to the right with a speed v

Explanation / Answer

a] B = u0 i /2pi r

= u0 i /[2pi *(a+b)/2] = u0 i / [pi*(a+b)]

b] Magnetic flux = integral Bw*dx = integral  (u0 i*w /2pi x) dx = (u0 i*w /2pi) ln(b/a)

c] Induced emf = -rate of change of flux = -B2* w*v + B1*w*v

= -u0i/2pib + u0i/2pia = [u0*i/2pi] *[1/a - 1/b]

induced current =   [u0*i/(2pi*R)] *[1/a - 1/b]

direction = counterclockwise (by Lenz Law)

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