JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Electrostatics

Two ideal electric dipoles A and B, having their dipole moment

p_{1}

and

p_{2}

respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole

A

, the resultant electric field is making an angle of

3 7^{\circ}

with the axis.
The ratio of the dipole moment of

A

and

B

\frac{p _{1}}{p _{2}}

is :
(take

sin 3 7^{\circ} = \frac{3}{5}

)

Answer: (D)

Solution

At point C on the axis of dipole A, the electric field due to A is

E_{1} = k \frac{2 p _{1}}{r ^{3}}

(axial direction), and the field due to B is

E_{2} = k \frac{p _{2}}{r ^{3}}

(equatorial direction). The resultant makes an angle of

3 7^{\circ}

with the axis, so

tan 3 7^{\circ} = \frac{E _{2}}{E _{1}} = \frac{p _{2}}{2 p _{1}}

. Since

tan 3 7^{\circ} = \frac{3}{4}

(from

sin 3 7^{\circ} = \frac{3}{5}

cos 3 7^{\circ} = \frac{4}{5}

), we get

\frac{p _{2}}{2 p _{1}} = \frac{3}{4}

, which gives

\frac{p _{1}}{p _{2}} = \frac{2}{3}

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option