Question

The magnetic field through a single loop of wire, 12 cm in radius and 8·5 Ω resistance, changes with time as shown in graph below. The magnetic field is perpendicular to the plane of the loop.

1. Find the induced emf for the time intervals 0 to 2.0 s, 2.0 to 4.0 s, and 4.0 to 6.0 s.
2. Hence, plot induced current as a function of time.

Answer 1

(a) e = `−("d"phi)/("dt")`

= `-("dNAB" costheta)/("dt")`

e = −0.023 volt

i = `"e"/"R"`

= `- 0.023/8.5` 

= −2.7 × 10^-3 A

t : 0 −2.0 sec : i = −2.7 × 10^-3 A

t : 2.0 sec −4.0 sec : i = 0

t : 4.0 sec −6.0 sec : i = +2.7 × 10^-3 A

(b)