An infinite straight wire carries a current I that varies with time as shown abo
ID: 1439710 • 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 = 2.1 A at t = t1 = 13 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -2.1 A at t = t4 = 23 s, passing through zero at t = t3 = 20.5 s. A conducting loop with sides W = 34 cm and L = 71 cm is fixed in the x-y plane at a distance d = 35 cm from the wire as shown.
1)
What is the magnitude of the magnetic flux through the loop at time t = t1 = 13 s?
= T-m2
2)
What is 1, the induced emf in the loop at time t = 6.5 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
= V
Explanation / Answer
(a) = 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*0.34/2/3.14)* ln((0.35+0.71)/(0.35))
= 4.65x10-7Wb
(b)current in the loop is clockwise and negative if the current is counter-clockwise.
=Li
L (2.1)=4.65x10-7
L=2.22x10-7H
= d = dt = L(di/dt) =2.22x10-7 * (2.1/13) = -3.58x10-8V
Counterclockwise