Question

An electric dipole `vecP = 2qa  hati` is placed in x-y plane, centred at the origin. Let E₁ and E₂ be the magnitudes of electric field at a point distant r (>> a) from its centre, along its aixs and on its equatorial plane, respectively. Then the value of `(E_1/E_2)` is ______.

Options

• `1/4`

• `1/2`

• 2

• 4

Answer 1

An electric dipole `vecP = 2qa  hati` is placed in x-y plane, centred at the origin. Let E₁ and E₂ be the magnitudes of electric field at a point distant r (>> a) from its centre, along its aixs and on its equatorial plane, respectively. Then the value of `(E_1/E_2)` is 2.

Explanation:

For a short electric dipole (r >> a):

Axial field (E₁):

`E_1 = 1/(4piε_0) (2p)/r^3`   

Equatorial field (E₂):

`E_2 = 1/(4piε_0) p/r^3` 

Compute ratio

`(E_1)/(E_2) = (1/(4piε_0) (2p)/r^3)/(1/(4piε_0) p/r^3)`

= 2