Consider the situation of the previous problem. The force on the central charge due to the shell is

Options

A. Towards left
B. Towards right
C. Upward
D. Zero

Answer

To solve the question regarding the force on the central charge due to the shell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a thin metallic spherical shell that contains a charge \( Q \) on it.
- A point charge \( Q \) is placed at the center of the shell.
- Another charge \( Q_1 \) is placed outside the shell.

2. **Applying Gauss's Law**:
- According to Gauss's Law, the electric field inside a conductor in electrostatic equilibrium is zero. This applies to the interior of the shell.
- Since the shell is metallic and the charges are static, the electric field inside the shell is \( E = 0 \).

3. **Calculating the Force on the Central Charge**:
- The force \( F \) on a charge due to an electric field is given by the formula:
\[ F = Q \cdot E \]
- Here, \( Q \) is the charge at the center, and \( E \) is the electric field at that point.
- Since we established that \( E = 0 \) inside the shell, we can substitute this into the force equation:
\[ F = Q \cdot 0 = 0 \]

4. **Conclusion**:
- Therefore, the force on the central charge due to the shell is \( 0 \).

### Final Answer:
The force on the central charge due to the shell is **zero**.

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