A uniform magnetic field is perpendicular to the plane of a circular loop of diameter 8.4 cm formed from wire of diameter 3.3 mm and resistivity of 2.14 * 10-8Ω·m. At what rate must the magnitude of the magnetic field change to induce a 13 A current in the loop?

Answer

1.55 T/s

Explanation:

diameter of loop = 8.4 cm

radius of loop = 8.4 / 2 = 4.2 cm = 0.042 m

Diameter of wire = 3.3 mm

radius of wire, r = 1.65 x 10^-3 m

ρ = 2.14 x 10^-8 ohm - m

i = 13 A

Let the rate of change of magnetic field is dB/dt.

Let R be the resistance of the wire.

R = ρ L / A

R = ρ x 2 x 3.14 x radius of loop / (3.14 x radius of wire x radius of wire)

R = (2 x 2.14 x 10^-8 x 0.042) / (1.65 x 10^-3 x 1.65 x 10^-3)

R = 6.6 x 10^-4 ohm

induced emf, e = i x R

e = 13 x (6.6 x 10^-4) = 8.58 x 10^-3 V

e = rate of change of magnetic flux

e = dΦ/dt

e = Area of loop x dB/dt

dB/dt = (8.58 x 10^-3) / (3.14 x 0.042 x 0.042) = 1.55 T/s