Question

Three point charges +q, –3q and +2q are placed in x – y plane at points (x = 0, y = a),(x = 0, y = 0) and (x = a, y = 0) respectively. The magnitude and direction of electric dipole moment of the charge system are

Answer 1

ANSWER

The given charge assembly can be represented using the three co-ordinate axes x, y and z as shown in figure.

The charge -2q is placed at the origin O. One + q charge is place at (a,0, 0) and the other +q charge is placed at(0, a, 0). Thus the system has two dipoles along x-axis and y-axis respectively.

As the electric dipole moment is directed from the negative to the positive charge hence the resultant dipole moment will be along OA where co-ordinates of point A are (a, a, 0). The magnitude of each dipole moment,

, p=qa

So, the magnitude of resultant dipole moment is

P

R

=

p

2

+P

2

=

(qa)

2

+(qa)

2

=

2

qa

Answer 2

Answer:

The magnitude and direction of electric dipole moment of the charge system are $\sqrt{5}qa$ along with positive x-axis

Explanation:

The given charge assembly can be represented using the three coordinate axes x,y, and z.

The charge -3q is placed at the origin O. One +2q charge is placed at (a,0) and the other +q charge is placed at(0, a). Thus the system has two dipoles along the x-axis and y-axis respectively.

The electric dipole moment is directed from the negative to the positive charge hence the resultant dipole moment will be along with  OA where coordinatess of point A are (a, a, 0). The magnitude of each dipole moment,

, p=2qa

q = qa

So, the magnitude of resultant dipole moment is

$P_{R}$ = $\sqrt{p^{2} +q^{2} }$

$P_{R}$ = $\sqrt{(2qa)^{2}+(qa)^{2} }$

    =  $\sqrt{5}qa$ along with positive x-axis