Question

A circular loop of wire with radius 0.0290 m and resistance 0.370Ω is in a region of spatially uniform magnetic field, as shown in the following figure(Figure 1). The magnetic field is directed into the plane of the figure. At t = 0, B = 0. The magnetic field then begins increasing, with B(t) = (0.400 T/s³)t³ 

Part A 

What is the current in the loop (magnitude) at the instant when B = 1.29 T?  

Answer 1

given
r = 0.029 m
R = 0.370 ohms
B(t) = 0.400*t^3

let at time t, B = 1.29 T

0.400*t^3 = 1.29

t = (1.29/0.4)^(1/3)

= 1.477 s

B = 0.4*t^3

dB/dt = 0.4*3*t^2

= 1.2*t^2

we kow, induced emf in the loop, emf = A*(dB/dt)

= pi*r^2*(dB/dt)

= pi*0.029^2*1.2*t^2

= 0.00317*t^2

at time, t = 1.477 s

emf = 0.00317*1.477^2

= 0.00591 V

induced current, I = induced emf/R

= 0.00591/0.370

= 0.0160 A <<<<<<<<-------------------Answer

B) direction : counterclockwise <<<<<<<<-------------------Answer