A conductor having a cavity is given a positive charge. Then field strength `E_(A) , E_(B)and E_(C)` at point A( within cavity ), at B ( within conducutor but outside cavity ) and C( near conductor and outside ) respectively will be :

Options

A. `E_(A) = 0 , E_(B) = 0 ,E_(C) = 0 `
B. `E_(A)ne 0 , E_(B) = 0 , E_(C) ne 0`
C. `E_(A)ne0 , E_(B) ne 0,E_(C)ne 0`
D. None of the above

Explanation

To solve the problem, we need to analyze the electric field strength at three different points (A, B, and C) in relation to a charged conductor with a cavity.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a conductor with a cavity inside it.
- The conductor is given a positive charge.

2. **Electric Field Inside the Cavity (Point A)**:
- According to electrostatic principles, the electric field inside a conductor in electrostatic equilibrium is zero.
- Since point A is located within the cavity of the conductor, there are no charges present in the cavity.
- Therefore, the electric field strength at point A, \( E_A \), is **zero**.

\[ E_A = 0 \]

3. **Electric Field Inside the Conductor (Point B)**:
- Point B is located within the material of the conductor but outside the cavity.
- Again, since the conductor is in electrostatic equilibrium, the electric field inside the conductor is also zero.
- Thus, the electric field strength at point B, \( E_B \), is **zero**.

\[ E_B = 0 \]

4. **Electric Field Outside the Conductor (Point C)**:
- Point C is located outside the conductor.
- The positive charge placed on the conductor will distribute itself uniformly on the outer surface of the conductor.
- As a result, there will be an electric field present in the region outside the conductor due to this surface charge.
- Therefore, the electric field strength at point C, \( E_C \), is **non-zero**.

\[ E_C \neq 0 \]

5. **Final Summary**:
- The electric field strengths at the three points are:
- \( E_A = 0 \)
- \( E_B = 0 \)
- \( E_C \neq 0 \)

### Conclusion:
The electric field strengths at points A, B, and C are:
- \( E_A = 0 \)
- \( E_B = 0 \)
- \( E_C \) is non-zero.