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, let's analyze the electric field strengths at points A, B, and C in relation to the charged conductor with a cavity.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a conductor that has a cavity inside it and is given a positive charge.
- Points A, B, and C are defined as follows:
- Point A: Inside the cavity.
- Point B: Inside the conductor but outside the cavity.
- Point C: Outside the conductor.

2. **Electric Field Inside the Cavity (Point A)**:
- According to electrostatic principles, the electric field inside a conductor is zero when it is in electrostatic equilibrium.
- Since point A is inside the cavity of the conductor, the electric field at point A (EA) is also zero because the charges on the conductor redistribute themselves in such a way that they cancel any electric field within the cavity.
- **Result**: \( E_A = 0 \)

3. **Electric Field Inside the Conductor (Point B)**:
- For point B, which is inside the conductor but outside the cavity, the electric field is also zero. This is because the electric field inside a conductor in electrostatic equilibrium is always zero.
- **Result**: \( E_B = 0 \)

4. **Electric Field Outside the Conductor (Point C)**:
- For point C, which is outside the conductor, the positive charge on the conductor creates an electric field. The electric field outside a charged conductor behaves as if all the charge were concentrated at a point at the center of the conductor.
- The electric field at point C can be calculated using Coulomb's law:
\[ E_C = \frac{kQ}{r^2} \]
where \( k \) is Coulomb's constant, \( Q \) is the total charge on the conductor, and \( r \) is the distance from the center of the conductor to point C.
- **Result**: \( E_C \neq 0 \)

5. **Final Summary**:
- The electric field strengths at points A, B, and C are:
- \( E_A = 0 \)
- \( E_B = 0 \)
- \( E_C \neq 0 \)

### Conclusion:
The final answer is:
- \( E_A = 0 \)
- \( E_B = 0 \)
- \( E_C \neq 0 \)

Since none of the options provided in the question match this conclusion, the answer is option D: none of the above.