Electrostatics Question 232
Question: Two equal charges $ q $ of opposite sign separated by a distance $ 2a $ constitute an electric dipole of dipole moment $ p $ . If $ P $ is a point at a distance $ r $ from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $ \theta $ with the axis of the dipole, then the potential at $ P $ is given by $ (r»2a) $ (Where$ p=2qa $ ) [MP PET 1997]
Options:
A) $ V=\frac{p\cos \theta }{4\pi {\varepsilon _{0}}r^{2}} $
B) $ V=\frac{p\cos \theta }{4\pi {\varepsilon _{0}}r} $
C) $ V=\frac{p\sin \theta }{4\pi {\varepsilon _{0}}r} $
D) $ V=\frac{p\cos \theta }{2\pi {\varepsilon _{0}}r^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
For the given situation, diagram can be drawn as follows component of dipole moment along the line OP will be $ p’=p\cos \theta $ .
Hence electric potential at point P will be $ V=\frac{1}{4\pi {\varepsilon _{0}}}.\frac{p\cos \theta }{r^{2}} $
