Question

The force experience by unit charge when placed at a distance of 0.1 m from the middle of an electric dipole on its axial line is 0.025 N and when it is place at a distance of 0.2 m the force is 0.002 N calculate dipole length​

Answer 1

Given force experienced F₁ = 0.025 N at distance = 0.1 m

force experienced F₂ = 0.002 N at distance = 0.2 m

To determine the dipole length 2a =?

Thus electric field on axial line E = 2 k p r/(r² - a²)

Therefore

E₁/E₂ = (r₁/r₂)×{(r₂² - a²)/(r₁² - a²)}

√(E₁r₂/E₂r₁) = {(r₂² - a²)/(r₁² - a²)}

√(0.025×0.2)/(0.002×0.1) = (0.2² -a²)/(0.1² - a²)

5 =  (0.2² -a²)/(0.1² - a²)

0.05 -5 a² = 0.04 - a²

0.01 = 4 a²

a = 1/20 =0.05 m

a = 5 cm

Hence dipole length = 2a = 2× 5 =10 cm