Question

A dipole consists of two charges -2uC and +2uC placed on y-axis and separated by a small distance 'a' (in cm). The magnitude of electric potential due to this dipole at a point which is at
a distance 100 m whose positition vector is at an angle 60° from the y-axis is (centre of dipole is at origin)
(1) 9a x 10-3 V (2) 2 x 10-3 V
(3) 3a x 10-9 V (4) 3a x 10-3 V

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Answer 1

answer : option (1) 9a × 10^-3 V

explanation : electric potential due to dipole at the observation point is given by, $V=\frac{KPcos\theta}{r^2}$

where P is magnitude of dipole moment, r is the seperation of point of observation to centre of dipole and $\theta$ is angle made by r with the axis of dipole moment.

here, P = qa

= 2 × 10^-6 C × a × 10^-2 Cm

= 2 × 10^-8a Cm

$\theta$= 60° , r = 100m

so, V = 9 × 10^9 × 2 × 10^-8acos60°/(100)²

= 90a/10000

= 9a × 10^-3 Volts