CBSE Class 12 Physics 2017 Delhi Set 1 Paper

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Question : 18
Total: 26
(i) Derive the expression for electric field at a point on the equatorial line of an electric dipole.
(ii) Depict the orientation of the dipole in (i) stable, (ii) unstable equilibrium in a uniform electric field.
Solution:  
(i) Derivation of expression of electric field on the equatorial line of the dipole
(ii) Depiction of orientation for stable and unstable equilibrium

(i) Let the point ' P ' be at a distance ' r ' from the mid point of the dipole.
‌E+q=‌
q
4πε0(r2+a2)

‌E−q=‌
q
4πε0(r2+a2)

Both are equal and their directions are as shown in the figure. Hence net electric field
E+q=[−(E+q+E−q)‌cos‌θ]
^
p

Ep=−‌
2qa
4πε0(r2+a2)‌
3
2
^
p

(ii) Stable equilibrium, θ=0∘
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