Question

A conducting loop with area 0.14 m2 and resistance 10 Ω lies in the x-y plane. A spatially uniform magnetic field points in the z direction. The field varies with time according to Bz=at2−b, where a = 3.0 T/s2 and b = 8.8 T . Find the loop current when Bz = 0.

Answer 1

The emf is given by:

EMF = V = -d(B*A)/dt

where, B = field strength and

A = area perpendicular to the field

Current = I = V/R

So you have a loop of wire with resistance R and radius r.

The B field is given by B = at^2 - b.

A = pi*r^2

BA = pi*r^2*(at^2 - b)

V = -d(BA)/dt = -pi*r^2*(2at)

I = -pi*r^2*(2at)/R

You need to find t such that B= 0

0 = at^2 - b

t = sqrt(8.8/3) = 1.71 s

Now substitute that value of t in the equation for I

I = - A*(2at)/R

= - 0.14*(2*3*1.71)/10

= - 0.14