Question

A uniformly charged sphere has a potential on its surface of 450 V. At a radial distance of 7.2 m from this surface, the potential is150 V What is the radius of the sphere?

Answer 1

Answer:

The radius of the sphere is 3.6 m.

Explanation:

Given that,

Potential of first sphere = 450 V

Radial distance = 7.2 m

If the potential of sphere =150 V

We need to calculate the radius

Using formula for potential

For 450 V

$V=\dfrac{kQ}{r}$

$450=\dfrac{kQ}{r}$....(I)

For 150 V

$150=\dfrac{kQ}{r+7.2}$....(II)

Divided equation (I) by equation (II)

$\dfrac{450}{150}=\dfrac{\dfrac{kQ}{r}}{\dfrac{kQ}{r+7.2}}$

$3=\dfrac{(r+7.2)}{r}$

$3r=r+7.2$

$r=\dfrac{7.2}{2}$

$r=3.6\ m$

Hence, The radius of the sphere is 3.6 m.