A small conducting sphere of radius a, carrying a charge `+Q`, is placed inside an equal and oppositely charged conducting shell of radius b such that their centers coincide. Determine the potential at a point which is at a distance c from center such that `a lt c lt b`.

Options

A. `k(Q//c + Q//b)`
B. `k(Q//a + Q//b)`
C. `k(Q//a - Q//b)`
D. `k(Q//c - Q//b)`

Explanation

To determine the potential at a point which is at a distance \( c \) from the center of a small conducting sphere of radius \( a \) carrying a charge \( +Q \), placed inside an oppositely charged conducting shell of radius \( b \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have a small conducting sphere with charge \( +Q \) and radius \( a \).
- Surrounding this sphere is a conducting shell with charge \( -Q \) and radius \( b \).
- The centers of both the sphere and the shell coincide.

2. **Identifying the Region**:
- We need to find the electric potential at a point located at a distance \( c \) from the center, where \( a < c < b \).

3. **Potential Due to the Inner Sphere**:
- The potential \( V_c \) at a distance \( c \) from the center due to the inner sphere (which has charge \( +Q \)) is given by the formula:
\[ V_{\text{inner}} = \frac{kQ}{c} \]
- Here, \( k \) is Coulomb's constant.

4. **Potential Due to the Outer Shell**:
- The outer shell has a charge of \( -Q \). The potential inside a conducting shell is constant and equal to the potential at its surface.
- The potential at the surface of the shell (at radius \( b \)) due to the charge \( -Q \) is:
\[ V_{\text{outer}} = -\frac{kQ}{b} \]
- Since we are at a distance \( c \) (where \( c < b \)), the potential due to the outer shell remains constant and is equal to \( -\frac{kQ}{b} \).

5. **Calculating the Total Potential**:
- The total potential \( V \) at the point \( c \) is the sum of the potentials due to both the inner sphere and the outer shell:
\[ V = V_{\text{inner}} + V_{\text{outer}} = \frac{kQ}{c} - \frac{kQ}{b} \]
- We can factor out \( kQ \):
\[ V = kQ \left( \frac{1}{c} - \frac{1}{b} \right) \]

### Final Result:
The potential at the point which is at a distance \( c \) from the center is:
\[ V = kQ \left( \frac{1}{c} - \frac{1}{b} \right) \]