A large loop of current-carrying wire, with radius r = 60 cm, carries a current

Question

A large loop of current-carrying wire, with radius r = 60 cm, carries a current I = 15 A, in the direction shown. At the centre of the wire is a small solenoid loop consisting of N = 5 loops with radius r = 1 mm. A. Calculate the magnetic flux through the solenoid. Assume that the solenoid is small enough that the magnetic field in the vicinity of the solenoid is uniform, and equal to the value at the centre of the loop. B. The solenoid is set to rotate, such that point a moves into the page, and point solenoid b moves out of the page. In which direction will the initial induced current be produced within the solenoid? C. If the solenoid rotates through one-quarter revolution in 5 seconds, what is the average induced emf? D. Suppose that, instead of rotating, the solenoid was lifted directly out of the page. What direction would the induced current be in this case, clockwise or counter-clockwise?

Explanation / Answer

B = u0 I / 2 R

B = (4pi x 10^-7)(15) / (2 x 0.60)

B = 1.57 x 10^-5 T

(A) flux = N B A

= (5) (1.57 x 10^-5) (pi x (0.001)^2)

= 2.47 x 10^-10 Wb

(B) now field is into the page.

as a goes into the paper, flux will decreases.

so induced will current will such that field will be into the page

current - > clockwise

(c) e = d(flux) / dt

= ( 2.47 x 10^-10 - 0) / 5

= 4.93 x 10^-11 Volt

(D) clockwise

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