Question

A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 30.0 ? with the direction of the field. when the magnetic field is increased uniformly from 200 ?t to 600 ?t in 0.400 s, an emf of magnitude of 80.0 mv is induced in the coil. what is the total length of the wire?

Answer 1

The induced voltage is N(-dΦ/dt)  where N=50 and flux is Φ=BAcos(θ).  B is the field and A is the area.  The trick is to see that because the loop is a square with side length L, that the area is L^2.  For your magnetic flux density values I'm seeing "200 ?t" and 600 ?t"  Am I right in thinking these are microTesla, uT?  I will assume so but if it's something else you'll have to find the answer again So dB/dt = (600e-6-200e-6)/0.4=1e-3.  Now,
80mV=(50)(1e-3)(L^2)cos(30)
L = 1.359m
Thus the perimeter of the square is 4(1.359m) = 5.437m
And the total length is (50)(5.437m) = 271.85m