For the dipole shown in the figure, find direction of the electric field at poin

Question

For the dipole shown in the figure, find direction of the electric field at points on the x axis. (Figure 1) horizontally to the right vertically downward vertically upward horizontally to the left Find magnitude of the electric field at points on the x axis Express your answer in terms of the variables q, a, x, and appropriate constants. What does this expression reduce to when the distance between the two charges is much less than x? Express your answer in terms of the variables q, a, x, and appropriate constants.

Explanation / Answer

part A :

at point x, there are two components for +q, 1. towards right 2. vertically upwards

at point x, there are two components for -q, 1. towards right 2. vertically downwards

here both Y components are equal in magnitudes ( due to same charge and distance) gets cancelled

hence net diection at x = horizontally towards right

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part B :

EF on equitorail line E = P/(4 pi eo x^3) or 2aq/(4pi eo x^3)

P = electric dipole moment vector = 2a q

q is charge

a is the distance between Dipoles

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part C:

on axial line, it reduces to the form, E = 2P/ (4 pi eo x^3) or (2*2 a q)/( 4 pi eo x^3)

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