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The method of electrical images is used ...

The method of electrical images is used to solve the electrostatic problems, where charge distribution is not specified completely. The method consists of replacement of given charge distribution by a simplified charge distribution or a signal point charge or a number of point charges [rovided the original boundary conditions are still satisfied. For example consider a system consider a system containing a point charge q placed at a distance d of form an infinite conducting plane. The boundary conditions are :
(i) Potential is zero at infinity (ii) Potential is zero at each point on the conducting plane If we replaced the conducting plane by a point charge (-q) placed at a distance 'd' opposite to conducting plane. The charge (-q) is called the electrical image.
Now system consists of two charge +q an -q at seperation`2d`. If charge +q moves to a distance 'y' from the boundary of conducting plane (now absent), the electrical image -q also moves to the same 'y' from the boundary of conducting plane, so that the new distance between +q and -q is `2y`

The force between point charge +q and earthed conducting plane is

A

`(1)/(4pi in_(0)) q^(2)/d^(2)` (repulsive)

B

`(1)/(4pi in_(0)) q^(2)/d^(2)` (attractive)

C

`(1)/(4pi in_(0)) q^(2)/(4d^(2))` (repulsive)

D

`(1)/(4pi in_(0)) q^(2)/(4d^(2))` (attractive)

Text Solution

Verified by Experts

The correct Answer is:
D

As given in paragraph, it is treated as `+q` and `-q` point charge at a distance `2a`
`F=1/(4pi in_(0))((-q)(q))/((2d)^(2))`
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The method of electrical images is used to solve the electrostatic problems, where charge distribution is not specified completely. The method consists of replacement of given charge distribution by a simplified charge distribution or a signal point charge or a number of point charges [rovided the original boundary conditions are still satisfied. For example consider a system consider a system containing a point charge q placed at a distance d of form an infinite conducting plane. The boundary conditions are : (i) Potential is zero at infinity (ii) Potential is zero at each point on the conducting plane If we replaced the conducting plane by a point charge (-q) placed at a distance 'd' opposite to conducting plane. The charge (-q) is called the electrical image. Now system consists of two charge +q an -q at seperation 2d . If charge +q moves to a distance 'y' from the boundary of conducting plane (now absent), the electrical image -q also moves to the same 'y' from the boundary of conducting plane, so that the new distance between +q and -q is 2y The potential energy of system of charge +q placed at a distance d from the earthed conducting plane is

The method of electrical images is used to solve the electrostatic problems, where charge distribution is not specified completely. The method consists of replacement of given charge distribution by a simplified charge distribution or a signal point charge or a number of point charges [rovided the original boundary conditions are still satisfied. For example consider a system consider a system containing a point charge q placed at a distance d of form an infinite conducting plane. The boundary conditions are : (i) Potential is zero at infinity (ii) Potential is zero at each point on the conducting plane If we replaced the conducting plane by a point charge (-q) placed at a distance 'd' opposite to conducting plane. The charge (-q) is called the electrical image. Now system consists of two charge +q an -q at seperation 2d . If charge +q moves to a distance 'y' from the boundary of conducting plane (now absent), the electrical image -q also moves to the same 'y' from the boundary of conducting plane, so that the new distance between +q and -q is 2y The work done in carrying charge q from distance d to distance y from earthed conducting plane is

Knowledge Check

  • 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

    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.
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