A metallic shell has a point charge 'q' kept inisde its cavity. Which one of the following diagrams correctly represents the electric lines of forces?

Options

A.
B.
C.
D.

Explanation

To solve the problem regarding the representation of electric lines of force around a metallic shell with a point charge 'q' inside its cavity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a metallic shell with a cavity.
- Inside this cavity, there is a point charge 'q'.

2. **Behavior of Electric Field in Conductors**:
- In electrostatic equilibrium, the electric field inside a conductor is zero.
- Therefore, the electric field inside the metallic shell (the conductor part) will be zero.

3. **Effect of the Point Charge**:
- The point charge 'q' will create an electric field in the space inside the cavity.
- This electric field will radiate outward from the point charge.

4. **Induced Charges on the Shell**:
- The presence of the charge 'q' will induce a charge on the inner surface of the metallic shell.
- If 'q' is positive, negative charge will be induced on the inner surface of the shell, while an equal amount of positive charge will be induced on the outer surface of the shell.

5. **Electric Field Lines**:
- The electric field lines will start from the point charge 'q' and will be directed outward.
- Inside the cavity, the lines will be radial and will point away from the charge.
- Upon reaching the inner surface of the shell, the electric field lines will be perpendicular to the surface of the shell.

6. **Outside the Shell**:
- The electric field outside the shell will behave as if all the charge were concentrated at the center of the shell. The field lines will be radial and directed outward from the shell.

7. **Choosing the Correct Diagram**:
- The correct diagram must show:
- Radial lines emanating from the point charge 'q' inside the cavity.
- Lines that are perpendicular to the inner surface of the shell.
- The outer surface of the shell showing electric field lines that are also radial.

### Conclusion:
After analyzing the behavior of electric fields around a metallic shell with a point charge inside, we can conclude that the correct representation of electric lines of force is the one that shows radial lines from the charge and perpendicular lines at the surface of the shell.