A hollow metallic sphere of radius 10 cm is given a charge of `3.2 xx 10^(-9) C.` The electric intensity at a point 4 cm from the center is

Options

A. `9 xx 10^(-9) NC^(-1)`
B. `288 NC^(-1)`
C. `2.88 NC^(-1)`
D. zero

Explanation

To solve the problem of finding the electric intensity at a point 4 cm from the center of a hollow metallic sphere with a radius of 10 cm and a charge of \(3.2 \times 10^{-9} \, C\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Location of the Point**:
The point where we need to find the electric intensity is at a distance of 4 cm from the center of the sphere. Since the radius of the sphere is 10 cm, this point is located inside the hollow sphere.

2. **Understand the Properties of Conductors**:
In electrostatics, a hollow metallic conductor has the property that the electric field inside the conductor is zero. This is because any excess charge resides on the surface of the conductor, and the electric field produced by these charges cancels out any field within the conductor.

3. **Apply Gauss's Law**:
According to Gauss's Law, the electric field inside a closed conductor is zero. Since the point we are considering (4 cm from the center) is inside the hollow sphere, we can conclude that the electric field intensity at this point is zero.

4. **Conclude the Result**:
Therefore, the electric intensity at a point 4 cm from the center of the hollow metallic sphere is:
\[ E = 0 \, \text{N/C} \]

### Final Answer:
The electric intensity at a point 4 cm from the center of the hollow metallic sphere is \(0 \, \text{N/C}\).

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