A coil of wire made of 500 circular loops of radius r=25.0cm is in a uniform magnetic field B=0.200T. The surface of the loop is initially perpendicular to the magnetic field when it is moved within 0.250s such that the surface of the loop then makes an angle of 45 degrees with respect to the magnetic field.

Question

A coil of wire made of 500 circular loops of radius r=25.0cm is in a uniform magnetic field B=0.200T. The surface of the loop is initially perpendicular to the magnetic field when it is moved within 0.250s such that the surface of the loop then makes an angle of 45 degrees with respect to the magnetic field.

(a) What is the change in magnetic flux, in Tesla-square meters, on the coil of wire?
(b)What is the induced emf, in Volts, on the coil of wire?

Answer 1

(a) The change in magnetic flux is equal to the product of the magnetic field strength, the area of the coil, and the cosine of the angle between the magnetic field and the surface of the loop. Therefore, the change in magnetic flux is equal to 0.200T x (π x (25.0cm)^2) x cos(45°) = 7.85 x 10^-3 Tesla-square meters.

(b) The induced emf is equal to the change in magnetic flux divided by the time taken for the change to occur. Therefore, the induced emf is equal to 7.85 x 10^-3 Tesla-square meters / 0.250s = 3.14 Volts.