Question

A single-turn circular loop of wire of radius 5.0 cm lies in a plane perpendicular to a spatially uniform magnetic field. During a 0.05480.0548-\text{s}s time interval, the magnitude of the field increases uniformly from 200 to 300 mT. Determine the magnitude of the emf induced in the loop.

Answer 1

Induced EMF,
`\epsilon=0.0143\ volts`

Step-by-step explanation:

Given that,

Radius of the circular loop, r = 5 cm = 0.05 m

Time, t = 0.0548 s

Initial magnetic field,
`B_i=200\ mT=0.2\ T`

Final magnetic field,
`B_f=300\ mT=0.3\ T`

The expression for the induced emf is given by :

`\epsilon=(d\phi)/(dt)`

`\phi` = magnetic flux

`\epsilon=(d(BA))/(dt)`

`\epsilon=A(d(B))/(dt)`

`\epsilon=A(B_f-B_i)/(t)`

`\epsilon=\pi (0.05)^2* (0.3-0.2)/(0.0548)`

`\epsilon=0.0143\ volts`

So, the induced emf in the loop is 0.0143 volts. Hence, this is the required solution.