Electric field intenisty at any point due to an ideal dipole (Derivation)
(3 mark)
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Suppose, we take z axis along dipole . The point z=0 is at the center of the dipole. The distances of different points are measured from z=0. We take dipole made of -q and +q situated at z=-a and z=+a. Then dipole moment is vector pp^, where p^ is unit vector in the direction from -q to +q. The magnitude of dipole moment is p= 2aq. The electric field intensity E(z), at z=z point on the axis of dipole is given by
E(z)= 2kpzp^/(z^2- a^2)^2.
Here, k is constant appearing in Coulomb's law.
Note that E is vector in the direction of p^.
If z>>a, then dipole can be regarded as small and a^2 can be neglected as compared to z^2. Then we have
E(z)=(2kp/z^3)p^
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