Question

The loop is in a magnetic field 0.20 T whose direction is perpendicular to the plane of the loop. At t = 0, the loop has area A = 0.285 square m.Suppose the radius of the elastic loop increases at a constant rate, dr/dt = 3.70 cm/s .

A) Determine the emf induced in the loop at t = 0.
B)Determine the emf induced in the loop at t = 1.00 s .

Answer 1

Part a)

`EMF = 14 * 10^(-3) V`

Part b)

`EMF = 15.67 * 10^(-3) V`

Step-by-step explanation:

As we know that magnetic flux through the loop is given as

`\phi = B.A`

now we have

`\phi = B\pi r^2`

now rate of change in flux is given as

`(d\phi)/(dt) = B(2\pi r)(dr)/(dt)`

now we know that

`A = \pi r^2`

`0.285 = \pi r^2`

`r = 0.30 m`

Now plug in all data

`EMF = (0.20)* 2\pi* (0.30) * (0.037)`

`EMF = 14 * 10^(-3) V`

Part b)

Now the radius of the loop after t = 1 s

`r_1 = r_0 + (dr)/(dt)`

`r_1 = 0.30 + 0.037`

`r_1 = 0.337 m`

Now plug in data in above equation

`EMF = (0.20)* 2\pi* (0.337) * (0.037)`

`EMF = 15.67 * 10^(-3) V`