Question

Two charge of $+25\times {10}^{-9}$ C and $-25\times {10}^{-9}$ C are placed 6 m apart. Find the electric field intensity ratio at point 4 m from the centre of the electric dipole

(i) on axial line

(ii) on equatorial line

Answer 1

Given charges $a=25\times {10}^{-9}C$ are separated by $d=6m,L=3m$

Electric field on axial line is given by

$E_{ax}=k\frac{2\overrightarrow{p}r}{{(r_A^2-L^2)}^2}$ for point $A,r_A=4m$

and that on equiatorial line

$E_{eq}=\frac{k\overrightarrow{p}}{{(r_B^2-L^2)}^{3/2}}$ for point $B,R_B=4m$

Thus ratio

$\frac{E_{ax}}{E_{eq}}=\frac{2{(r_B^2-L^2)}^{3/2}}{{(r_A^2-L^2)}^2}=\frac{2{(4^2-3^2)}^{3/2}}{{(4^2-3^2)}^2}=\frac{250}{49}$