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S_A_V [24]
3 years ago
5

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
Physics
1 answer:
Georgia [21]3 years ago
6 0

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

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