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

Answer:

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

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

$\epsilon=\dfrac{d(BA)}{dt}$

$\epsilon=\dfrac{B(A_{f}-A_{i})}{t}$

$\epsilon=\dfrac{B(\pi r_{f}^2-\pi r_{i}^2)}{t}$

Put the value ino the formula

$\epsilon=\dfrac{1.5(\pi\times(0.125)^2-\pi(0.075)^2)}{1.5}$

$\epsilon=0.0314\ V$

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