Part A A circular loop of wire with radius 00290 m and resis

Part A A circular loop of wire with radius 0.0290 m and resistance 0.350 is in a region of spatially uniform magnetic field, as shown in the following figure(Figure 1) What is the current in the loop (magnitude) at the instant when 1.42 T? Express your answer with the appropriate units. 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) ( 0.350 T/s*) t3 I-.018 A Submit My Answers Give Up Incorrect; Try Again; 27 attempts remaining Figure 1 of1 Part B What is the direction of the current in the loop? counterclockwise clockwise Submit Give Up Correct Continue

Solution

a)
let at time \"t\" B = 1.42 T

B(t) = 0.35*t^3

1.42 = 0.35*t^3

==> t = (1.42/0.35)^(1/3)

= 1.595 s

induced emf in the loop at time t = 1.595 s,

emf = A*dB/dt

= pi*r^2*0.35*3*t^2

= pi*0.029^2*0.35*3*1.595^2

= 0.00706 volts

induced current in the loop, I = emf/R

= 0.00706/0.35

= 0.0202 A

B) counterclockwise