Question

Two spheres A and B of radius \(a\) and \(b\) respectively are at the same electric potential. The ratio of the surface charge densities of A to that of B is

• A. \(\frac{a^{2}}{b^{2}}\)
• B. \(\frac{b^{2}}{a^{2}}\)
• C. \(\frac{b}{a}\)
• D. \(\frac{a}{b}\)

Hint:

For a sphere, the potential is surface charge density times radius divided by epsilon-zero.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The potential on the surface of a sphere of radius \(r\) with charge \(Q=\sigma\cdot 4\pi r^{2}\) is \(V=\frac{Q}{4\pi\varepsilon_{0}r}=\frac{\sigma r}{\varepsilon_{0}}\).

Step 2: Equal potentials
\(\frac{\sigma_{A}a}{\varepsilon_{0}}=\frac{\sigma_{B}b}{\varepsilon_{0}}\).

Step 3: Calculation
\(\frac{\sigma_{A}}{\sigma_{B}}=\frac{b}{a}\).

Step 4: Compare the options
This is option (C).

Final Answer:
The ratio of the surface charge densities is \(\frac{b}{a}\). \[ \boxed{\text{(C) }\dfrac{b}{a}} \]