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. zero
B. E is perpendicular to the surface at every point
C. `E//2`
D. `E//3`

Answer

To solve the problem, we need to analyze the electric field in relation to a conducting spherical shell. Here are the steps to find the electric field at a distance \( \frac{R}{2} \) from the center of the spherical shell:

### Step 1: Understand the properties of a conducting spherical shell
A conducting spherical shell has the property that the electric field inside the shell is zero. This is due to the redistribution of charges on the surface of the conductor when it is in electrostatic equilibrium.

**Hint:** Remember that inside a conductor, the electric field is always zero.

### Step 2: Identify the position of point Q
We are given that point Q is located at a distance \( \frac{R}{2} \) from the center of the spherical shell. Since the radius of the shell is \( R \), point Q lies inside the conducting shell.

**Hint:** Determine whether the point of interest is inside or outside the conducting shell.

### Step 3: Apply the property of the electric field inside the conductor
Since point Q is inside the conducting spherical shell, we can conclude that the electric field at this point is zero.

**Hint:** Recall that the electric field inside a conductor in electrostatic equilibrium is zero.

### Step 4: State the final answer
Thus, the electric field at a distance \( \frac{R}{2} \) from the center of the conducting spherical shell is:

\[ E_Q = 0 \]

### Summary
The electric field at a distance \( \frac{R}{2} \) from the center of the conducting spherical shell is zero, as it lies within the conductor.

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