Two conducting concentric spherical shells are given positive charges. Choose the correct outcome.

Options

A. Outer shell will be at higher potential
B. Inner shell will be at higher potential
C. Outer will always be at higher potential irrespective of the sign of charges given to two spheres
D. No prediction can be made using the given data

Answer

To solve the problem of determining which conducting spherical shell has a higher electric potential when both are given positive charges, we can follow these steps:

### Step 1: Understand the Setup
We have two concentric spherical shells:
- Inner shell with radius \( R_1 \) and charge \( Q_1 \)
- Outer shell with radius \( R_2 \) and charge \( Q_2 \)

### Step 2: Define the Charges
Let:
- \( Q_1 = Q \) (charge on the inner shell)
- \( Q_2 = Q \) (charge on the outer shell)

### Step 3: Calculate the Potential on the Inner Shell
The potential \( V_i \) at the surface of the inner shell due to its own charge is given by:
\[ V_i = \frac{kQ}{R_1} \]
where \( k \) is Coulomb's constant.

Additionally, the potential at the inner shell due to the outer shell (which acts as a point charge from the perspective of the inner shell) is:
\[ V_{\text{outer}} = \frac{kQ}{R_2} \]
Thus, the total potential \( V_{\text{inner}} \) at the inner shell is:
\[ V_{\text{inner}} = V_i + V_{\text{outer}} = \frac{kQ}{R_1} + \frac{kQ}{R_2} \]

### Step 4: Calculate the Potential on the Outer Shell
The potential \( V_o \) at the surface of the outer shell due to its own charge is:
\[ V_o = \frac{kQ}{R_2} \]
The potential at the outer shell due to the inner shell is:
\[ V_{\text{inner}} = \frac{kQ}{R_1} \]
Thus, the total potential \( V_{\text{outer}} \) at the outer shell is:
\[ V_{\text{outer}} = V_o + V_{\text{inner}} = \frac{kQ}{R_2} + \frac{kQ}{R_1} \]

### Step 5: Compare the Potentials
Now, we compare \( V_{\text{inner}} \) and \( V_{\text{outer}} \):
- \( V_{\text{inner}} = \frac{kQ}{R_1} + \frac{kQ}{R_2} \)
- \( V_{\text{outer}} = \frac{kQ}{R_2} + \frac{kQ}{R_1} \)

Since both expressions are equal, we need to analyze the terms:
- The potential due to the inner shell is higher because \( R_1 < R_2 \).

### Conclusion
Since \( R_1 < R_2 \), it follows that:
\[ V_{\text{inner}} > V_{\text{outer}} \]
Thus, the inner shell has a higher potential than the outer shell.

### Final Answer
The inner shell will be at a higher potential.

---