The electric field at a distance `3R//2` from the centre of a charge conducting spherical shell of radius `R` is `E`. The electric field at a distance `R//2` from the centre of the sphere is

Options

A. E
B. `(E )/(2)`
C. `(E )/(3)`
D. Zero

Answer

To solve the problem, we need to analyze the electric field at two different distances from the center of a conducting spherical shell.

### Given:
- Radius of the conducting spherical shell = \( R \)
- Distance from the center where electric field is given = \( \frac{3R}{2} \)
- Electric field at this distance = \( E \)

### Step 1: Understanding the electric field outside the conducting shell
For a conducting spherical shell, the electric field outside the shell (at a distance greater than the radius of the shell) behaves as if all the charge were concentrated at the center. Therefore, at a distance \( r \) from the center (where \( r > R \)), the electric field \( E \) is given by:
\[ E = \frac{kQ}{r^2} \]
where \( k \) is the Coulomb's constant and \( Q \) is the total charge on the shell.

### Step 2: Electric field inside the conducting shell
Inside a conducting shell, the electric field is always zero. This is because the charges redistribute themselves on the surface of the conductor in such a way that the electric field inside cancels out.

### Step 3: Finding the electric field at \( \frac{R}{2} \)
Now, we need to find the electric field at a distance \( \frac{R}{2} \) from the center of the shell. Since \( \frac{R}{2} < R \), this point is inside the conducting shell.

According to the properties of conductors:
- The electric field inside a conducting shell is zero.

Thus, the electric field at a distance \( \frac{R}{2} \) from the center of the spherical shell is:
\[ E_{\frac{R}{2}} = 0 \]

### Final Answer:
The electric field at a distance \( \frac{R}{2} \) from the center of the spherical shell is \( 0 \).

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