The figure shows a cross-sectional view of a single-turn conducting loop, with a

Question

The figure shows a cross-sectional view of a single-turn conducting loop, with a radius of 10.0 cm, inside a long current-carrying solenoid. The loop has a resistance of 7.00 . The solenoid has a radius of 20.0 cm, and has 200 turns per meter. The current in the solenoid is directed counterclockwise, and is increasing at the rate of 0.500 A/s. 20 c 10)cm (a) At a particular instant, the current happens to be 1.60 A. At that instant, what is the magnitude of the uniform magnetic field in the solenoid? (b) What is the magnitude and direction of the induced current in the single-turn loop? Denote the direction with a or - sign, +for clockwise or - for counterclockwise

Explanation / Answer

(a)

Given that,

radius of loop, r = 10 cm = 0.10 m

resistance R = 7 ohm

number of turns per sec, n = 200

di / dt = 0.50 A / s

(a)

uniform magnetic field in the solenoid,

B = u*n*i

B = 4*pi*10^(-7)*200*1.6

B = 4.02*10^(-4) T

(b)

lnduced emf in single turn loop,

E = A*dB / dt

E = pi*r^2*d(u*n*i) / dt

E = pi*r^2*u*n*di / dt

E = 3.14*(0.10)^2*4*pi*10^(-7)*200*0.5

E = 39.47*10^(-7) V

induced current in loop,

l = E / R

l = 39.47*10^(-7) / 7

l = 5.64*10^(-7) A

current is positive so direction is clockwise (+).

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