An infinite wire carrying current I0 sin(wt) is positioned along the x-axis. A s

Question

An infinite wire carrying current I0 sin(wt) is positioned along the x-axis. A square loop is positioned in the x-y plane with two sides parallel to the x-axis and two sides perpendicular to the x-axis. The edge closest to the wire is a distance a from the wire and the edged farthest from the wire is a distance b from the wire. Thus the square loop has sides of length b – a . The square is composed of wire and its total resistance is R . Answer the following in terms of quantities given or a subset thereof and relevant physical constants.
(a) What is the magnitude of the B-field as a function of the distance y away from the wire?
(b) What is the magnetic flux through the square loop?
(c) What is the emf induced in the loop?
(d)What is the current in the loop?

Explanation / Answer

i=Iosin(t)

a) the magnetic field is oi/2r here r is y

b) the magnetic flux in the loop can be manipulated by considering a strip of parallel to x axis

and hence the flux through that loop is

(oi/2y)*(b-a)*dy

integration from a to b     (oi/2)*(b-a)ln(b/a)

c)emf induced=-d/dt=-(oIo/2)*(b-a)ln(b/a)cos(t)

d)current=emf/resistance

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