An infinite straight wire carries a current I that varies with time as shown abo
ID: 1522222 • Letter: A
Question
An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 5.2 A at t = t1 = 15 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -5.2 A at t = t4 = 26 s, passing through zero at t = t3 = 23 s. A conducting loop with sides W = 27 cm and L = 50 cm is fixed in the x-y plane at a distance d = 57 cm from the wire as shown.
*magnitude of the magnetic flux ? through the loop at time t = t1 = 15 s = 1.77*10^-7 T-m^2
1-What is ?1, the induced emf in the loop at time t = 7.5 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.? (Answer in V)
2-What is ?4, the induced emf in the loop at time t = 24.5 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise. (Answer in V)
110 I(t) 0 -rExplanation / Answer
1) E = -d(Flux)/dt =- (d/dt)[(u*I*w/2pi)*(ln(d+L)/d)] = -(uw/2pi)*ln[(d+L)/d]*(dI/dt)
E = -(2*10^-7*0.27)*ln(1.07/0.57)*(5.2/7.5) =- 2.36*10^-8
2) E = -d(Flux)/dt =- (d/dt)[(u*I*w/2pi)*(ln(d+L)/d)] = -(uw/2pi)*ln[(d+L)/d]*(dI/dt)
E = -(2*10^-7*0.27)*ln(1.07/0.57)*(5.2/24.5) = 7.22*10^-9