A circular loop of wire with radius r=0.0250 m and resistance r=0.390 ohms is in a region of spatially uniform magnetic field. the magnetic field is directed into the plane. at t=0, b=0. the magnetic field then begins increasing, with b (t) = (0.380t/s^3) t^3. what is the current in the loop (magnitude and direction) at the instant when b=1.33 t.

Question

Physics

Darien Spence

11 October, 17:30

A circular loop of wire with radius r=0.0250 m and resistance r=0.390 ohms is in a region of spatially uniform magnetic field. the magnetic field is directed into the plane. at t=0, b=0. the magnetic field then begins increasing, with b (t) = (0.380t/s^3) t^3. what is the current in the loop (magnitude and direction) at the instant when b=1.33 t.

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Tanya Jefferson · Answer 1

0.0133 A

Explanation:

The time at which B=1.33 T is given by

1.33 = 0.38*t^3

t = (1.33/0.38) ^ (1/3) = 1.52 s

Using Faraday's Law, we have

emf = - dΦ/dt = - A dB/dt = - A d/dt (0.380 t^3)

Area A = pi * r² = 3.141 * (0.025 * 0.025) = 0.00196 m²

emf = - A * (3*0.38) * t^2

thus, the emf at t=1.52 s is

emf = - 0.00196 * (3*0.38) * (1.52) ^2 = - 0.0052 V

if the resistance is 0.390 ohms, then the current is given by

I = V/R = 0.0052/0.390 = 0.0133 A