Four charges + q , + q , - q , and - q are placed on X - Y plane at the points whose coordinates are 0 . 5 , 0 , 0 , 0 . 5 , - 0 . 5 , 0 and 0 , - 0 . 5 respectively. The electric field due to these charges at a point P r , r , where r > > 0 . 5 , will be

Step-by-step solution

The four charges can be considered two dipoles of equal magnitude and directed along the +x axis and +y axis. The magnitude of dipole moment = q x (distance between positive and negative charges on x-axis) p = q × 1 = q The resultant dipole moment of these two dipoles with be, p r = q 2 + q 2 = q 2 The direction of the resultant dipole moment will be at 45 ° from the x-axis The distance of the point ( r ,   r ) from the dipole is r 2 m The resultant electric field is E = 1 4 π ε 0 × 2