Question

Derive an expression for electric field due to electric dipole at a point on its equatorial line​

Answer 1

Explanation:

Consider an electric dipole AB consisting charges +q and -q separated by distance 2l and pole strength q. Let, P be the point on the equatorial line at distance d from mid-point of the dipole i.e. O as shown in figure 1.

Now,  the electric field, E1 at point P due to north pole along AP is,

E1=4πϵ01AP2q

E1=4πϵ01(d2+l2)2q .........(1)         (∵AP2=OA2+OP2)

Similarly,  the electric field, E2 at point P due to south pole along PB is,

E2=4πϵ01PB2q

E2=4πϵ01(d2+l2)2q .........(2)            (∵PB2=OB2+OP2)

From equations (1) and (2), we get

E1=E

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