A point charge +q, is placed at a distance d from an isolated conducting plane. The field at a point P on the other side of the plane is

Options

A. directed perpendicular to the plane and away from the plane.
B. directed perpendicular to the plane but towards the plane.
C. directed radially away from the point charge.
D. directed radially towards the point charge.

Explanation

To solve the problem of finding the electric field at a point P on the other side of an isolated conducting plane, when a point charge +q is placed at a distance d from the plane, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a point charge +q located at a distance d from an isolated conducting plane.
- The conducting plane will respond to the electric field created by the point charge.

2. **Induction of Charges on the Conducting Plane**:
- The presence of the positive charge +q will induce a negative charge (-q) on the side of the conducting plane that is closest to the charge.
- Consequently, a positive charge (+q) will appear on the opposite side of the conducting plane due to the conservation of charge.

3. **Using the Method of Images**:
- To analyze the electric field on the side of the conducting plane where point P is located, we can use the method of images.
- We replace the conducting plane with an imaginary point charge -q located at a distance d on the opposite side of the plane.

4. **Electric Field Calculation**:
- The electric field at point P due to the point charge +q and the imaginary charge -q can be calculated.
- The electric field due to a point charge is given by the formula:
\[ E = \frac{k \cdot |Q|}{r^2} \]
where \(k\) is Coulomb's constant, \(Q\) is the charge, and \(r\) is the distance from the charge to the point where the field is being calculated.

5. **Direction of the Electric Field**:
- The electric field due to the positive charge +q at point P will be directed away from the charge.
- The electric field due to the negative charge -q will be directed towards the charge.
- Since point P is on the opposite side of the conducting plane, the net electric field at point P will be directed perpendicular to the plane and away from it.

6. **Conclusion**:
- The electric field at point P is directed perpendicular to the conducting plane and away from it.

### Final Answer:
The electric field at point P on the other side of the conducting plane is directed perpendicular to the plane and away from it.