The amount of induced surface charge per unit area of the surface is

Options

A. polarisation
B. torque
C. electric dipole
D. electric flux

Answer

To solve the question regarding the amount of induced surface charge per unit area of the surface, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Induced Charge**:
- When a charged object is brought near a neutral conductor, it causes the charges within the conductor to redistribute. This phenomenon is known as induction.

2. **Concept of Polarization**:
- The redistribution of charges leads to the formation of induced surface charges. If a positive charge is brought close to a neutral metal plate, negative charges in the plate will move towards the positive charge, creating a negative surface charge on the side of the plate facing the positive charge. Conversely, positive charges will be pushed away to the opposite side.

3. **Induced Surface Charge Density**:
- The amount of induced surface charge per unit area is defined as the surface charge density (σ). Mathematically, it is expressed as:
\[ \sigma = \frac{Q}{A} \]
where \(Q\) is the total induced charge and \(A\) is the area over which the charge is distributed.

4. **Polarization**:
- The phenomenon of charge redistribution in the presence of an external electric field is called polarization. The induced surface charge density is directly related to the electric field \(E\) applied to the conductor. The relationship can be expressed as:
\[ \sigma = \epsilon_0 E \]
where \(\epsilon_0\) is the permittivity of free space.

5. **Conclusion**:
- Therefore, the amount of induced surface charge per unit area of the surface is referred to as the polarization of the material, which can be expressed as:
\[ \sigma = \epsilon_0 E \]
- This indicates that the induced surface charge density is proportional to the electric field applied to the conductor.