Question

Magnitude of a electric field at distance r on the axial point of a short electric dipole of dipole movement p will be​

Answer 1

Answer:

Derive an expression for electric potential at any point due to an electric dipole. Potential at point P due to the dipole along the equatorial line will be zero as P is equidistant from the two charges. Also r1 and r2 are distances of point P away from charges +q and -q respectively.

Answer 2

electric field due to dipole on axial point is 2kp/r³.

we have to find the magnitude of electric field at a distance r on axial point of a short electric dipole of dipole moment P.

let Q and -Q are seperated by a small distance x. so, P = Qx......(1)

if r is the distance between point of observation, O and midpoint of polar axis.

distance of O from charge Q = (r - x/2)

distance of O from charge -Q = (r + x/2)

now electric field due to Q (let A) , E₁ = kQ/(r - x/2)² along AO

electric field due to -Q (let B), E₂ = kQ/(r + x/2)² along OB

now net electric field , E = E₁ + E₂

= kQ/(r - x/2)² - kQ/(r + x/2)²

= kQ [1/(r - x/2)² - 1/(r + x/2)²]

= kQ [(r² + x²/4 + rx - r² - x²/4 + rx]/(r² - x²/4)²

= kQ2rx/(r² - x²/4)²

here r >> x so r² >> x²/4

so, (r² - x²/4) ≈ r²

= kQ2rx/r⁴

= 2k(Qx)/r³

= 2kp/r³ [ from equation (1).]

therefore electric field due to dipole on axial point is 2kp/r³.