Question

An electric dipole having charges +q and -q are at a separation r.At distance greater greater than r along the axis of the dipole,the field is
proportional to?

Answer 1

Let an observation point T is located at d distance from centre of dipole along its axis.

electric field due to charge +q at T , E1 = kq/(d + r/2)² i

electric field due to charge -q at T, E2 = - kq/(d - 4r/2)² i

so, net electric field = kq/(d + r/2)² - kq/(d - r/2)²

= kq [ (d² + r² - dr - d² - r² - dr)/(d² - r²/4)²]

= kq(dr)/(d² - r²/4)²

= k(qr)d/(d² - r²/4)²

= kpd/(d² - r²/4)² [ as dipole moment, p = qr]

if d >> r

then, d² >> r²/4

so, (d² - r²/4) ≈ d²

so, net electric field , E = kp/d³

hence, electric field is inversely proportional to d³. where, d is separation between point of observation to centre of dipole.

Answer 2

Explanation:

QR/d³ Is the option

hope it helps