Question

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.

Answer 1

Answer:

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