A point charge is kept at the centre of a metallic insulated spherical shell. Then

Options

A. Electric field out side the sphere is zero
B. electric field inside the sphere is zero
C. Net induced charge on the sphere is zero
D. Electric potential inside the sphere is zero

Answer

To solve the problem, we need to analyze the situation of a point charge placed at the center of a metallic insulated spherical shell. Let's break down the steps:

### Step 1: Understand the Setup
We have a point charge (let's denote it as \( +Q \)) located at the center of a metallic insulated spherical shell. The shell is a conductor, which means it has free electrons that can move.

**Hint:** Visualize the setup clearly. Draw a diagram showing the point charge at the center and the spherical shell surrounding it.

### Step 2: Effect of the Point Charge on the Shell
Since the point charge is positive, it will attract the free electrons in the metallic shell. These electrons will move towards the center, accumulating on the inner surface of the shell. This creates a layer of negative charge on the inner surface of the shell.

**Hint:** Remember that in conductors, free charges can move in response to electric fields.

### Step 3: Induced Charges on the Shell
The accumulation of negative charge on the inner surface will leave an equal amount of positive charge on the outer surface of the shell. Therefore, if \( -Q \) is induced on the inner surface, \( +Q \) will be induced on the outer surface.

**Hint:** Consider the principle of conservation of charge. The total charge must remain constant.

### Step 4: Net Induced Charge
The net induced charge on the shell is the sum of the charges on the inner and outer surfaces. Since the inner surface has \( -Q \) and the outer surface has \( +Q \), the net induced charge is:

\[ \text{Net Induced Charge} = -Q + Q = 0 \]

**Hint:** This step is crucial for understanding the overall charge distribution.

### Step 5: Electric Field Inside the Shell
Inside the metallic shell, the electric field is zero. This is because the charges on the inner surface redistribute themselves in such a way that they cancel out any electric field within the conductor.

**Hint:** Recall Gauss's law, which states that the electric field inside a conductor in electrostatic equilibrium is zero.

### Step 6: Electric Field Outside the Shell
Outside the shell, the electric field is not zero. The outer surface has a positive charge \( +Q \), which creates an electric field that can be calculated using Gauss's law.

**Hint:** Use a Gaussian surface outside the shell to analyze the electric field.

### Step 7: Electric Potential Inside the Shell
The electric potential inside the shell is not zero. Since there is an electric field present due to the point charge at the center, the potential will vary and will not be zero.

**Hint:** Remember that electric potential is related to the electric field. If the electric field is non-zero, the potential cannot be zero.

### Conclusion
The correct statement regarding the point charge at the center of the metallic insulated spherical shell is that the net induced charge on the sphere is zero. The electric field inside the shell is zero, while the electric field outside the shell is non-zero due to the charge on the outer surface.

### Summary of Steps:
1. Understand the setup with a point charge at the center of a spherical shell.
2. Recognize the effect of the point charge on the free electrons in the shell.
3. Determine the induced charges on the inner and outer surfaces.
4. Calculate the net induced charge.
5. Analyze the electric field inside the shell.
6. Analyze the electric field outside the shell.
7. Discuss the electric potential inside the shell.