An infinite straight wire carries a current l that varies with time as shown abo
ID: 2077031 • Letter: A
Question
An infinite straight wire carries a current l that varies with time as shown above. It increases from 0 at t 0 to a maximum value 3.9 A att t rema constant at this value until t- t2 when it decreases linearly to a value ins l4 3.9 A at t- t 31 s, passing through zero at t- t 25.5 s. A conducting loop with sides W 31 cm and L 62 cm is fixed in the x-y plane at a distance d 47 cm from the wire as shown. 1) What is the magnitude of the magnetic flux D through the loop at time t 15 s? T-m2 Sub mit 2) What is E1, 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. Submit 3) What is E2, the induced emf in the loop at time t- 17 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise. SubmitExplanation / Answer
1)
= B.dA
= (i/2x)(w.dx)
= iw/2 (1/x)dx
integration from d to d+L
= iw/2 ln((d+L)/(d))
= i (4*3.14e-7*0.31 / 2*3.14)* ln[(0.47+0.62) / (0.47) ]
= i * 5.215 e-8
= 3.9 * 5.215 e-8
= 2.03 e-7 Wb
2)
current in the loop is clockwise and negative if the current is counter-clockwise.
= d = dt = - 5.215 e-8 (di/dt)
= - 5.215 e-8 * (3.9 / 15)
= - 1.36 e-8 V
Counterclockwise
3) = 0 V
5)
= d = dt
= 5.215 e-8 (di/dt)
= 5.215 e-8 * (3.9/5.5)
= +3.697 e-8 V
clockwise