Question

A total charge Q is uniformly distributed through-out a spherical volume of radius a. Which of the following is a dimensionally correct expression for the potential difference between the center of the sphere and its surface?

a. (1/8πε0)Q
b. (1/8πε0)Qa^2
c. (1/8πε0)Qa
d. (1/8πε0)Q/a
e. (1/8πε0) Q/a^2

Answer 1

Answer:

d. (1/8πε0)Q/a

Explanation:

The potential difference $v = \dfrac{1}{4 \pi \epsilon _0} \dfrac{Q}{r}$

$= (\dfrac{1}{4 \pi \epsilon _0}Q) \dfrac{1}{r}$

Suppose we separate the quantity $(\dfrac{1}{4 \pi \epsilon _0}Q)$ which is dimensionally and equally the same as $(\dfrac{1}{8 \pi \epsilon _0}Q)$. Then, we will have $\dfrac{1}{r}$ and $\dfrac{1}{a}$ as the same dimension.

Therefore, the correct option is:

d. (1/8πε0)Q/a