First slide

Electric dipole

Question

Three point charges + q, -2q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

Difficult

A

$\sqrt{2} qa$ along +y direction
B

$\sqrt{2} qa$ along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)
C

qa along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)
D

$\sqrt{2} qa$ along +x direction

Solution

Electric dipole moment is a vector quantity directed from negative charge to the similar positive charge. Choose the three coordinate axes as x, y and z and plot the charges with the given coordinates as shown.
O is the origin at which -2q charge is placed. The system is equivalent to two dipoles along x and y-directions, respectively. The dipole moments of two dipoles are shown in the figure. The resultant dipole moment will be directed along OP, where co-ordinates of P is (a, a, 0). The magnitude of resultant dipole moment is $p^{'} = \sqrt{p^{2} + p^{2}} = \sqrt{(qa)^{2} + (qa)^{2}} = \sqrt{2} qa$

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