# The force experienced by an unit charge when placed at a distance of 0.10m from the middle of an electric dipole on its axial line is 0.025N and when it is placed at a dustance of 0.2m the force is reduced to 0.002N. Calculate the dipole length

Khimraj
3007 Points
4 years ago
Let length of dipole is 2a then elecrtric field on axial line is given by
E = 2kpr/(r2 – a2)2
Then
E1/E2 = (r1/r2)*((r22 – a2)2/(r12 – a2)2)
$\sqrt{E1*r2/E2*r1} = (r2^{2} - a^{2})/(r1^{2} - a^{2})$
$\sqrt{0.025*0.2/0.002*0.1} = (0.2^{2} - a^{2})/(0.1^{2} - a^{2})$
$5 = (0.2^{2} - a^{2})/(0.1^{2} - a^{2})$
0.05 – 5a2 = 0.04 – a2
0.01 = 4a2
a = 1/20 m = 5 cm
then length = 2a = 10 cm.