Question

A balloon has an initial radius of 0.075 m. A circle is painted on the balloon using silver metal paint. When the paint dries, the circle is a very good electrical conductor. With the balloon oriented such that a 1.5-T magnetic field is oriented perpendicular to the plane of the circle, air is blown into the balloon so that it expands uniformly. The silver circle expands to a radius 0.125 m in 1.5 s. Determine the induced emf for this silver circle during this period of expansion.

Answer 1

The induced emf for this silver circle during this period of expansion is 0.0314 V.

Step-by-step explanation:

Given that,

Initial radius = 0.075 m

Magnetic field = 1.5 T

Radius = 0.125 m

Time t =1.5 s

We need to calculate the induced emf for this silver circle

Using formula of emf

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

`\epsilon=(B(A_(f)-A_(i)))/(t)`

`\epsilon=(B(\pi r_(f)^2-\pi r_(i)^2))/(t)`

Put the value ino the formula

`\epsilon=(1.5(\pi*(0.125)^2-\pi(0.075)^2))/(1.5)`

`\epsilon=0.0314\ V`

Hence, The induced emf for this silver circle during this period of expansion is 0.0314 V.