Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. If the dipole is placed in an uniform electric field ' $\overrightarrow{\mathrm{E}}$ ' of 10 dyne/C making $30^{0}$ angle with $\overrightarrow{\mathrm{E}}$, the magnitude of torque acting on dipole is :

(B) $2.0 \times 10^{-10} \mathrm{Nm}$

(A) $4.0 \times 10^{-10} \mathrm{Nm}$

(C) $1.0 \times 10^{-8} \mathrm{Nm}$

(D) $1.5 \times 10^{-9} \mathrm{Nm}$

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Electrostatics

Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. If the dipole is placed in an uniform electric field '

E

' of 10 dyne/C making

3 0^{0}

angle with

E

, the magnitude of torque acting on dipole is :

(A) $4.0 \times 1 0^{- 10} Nm$
(B) $2.0 \times 1 0^{- 10} Nm$ ✓ Correct
(C) $1.0 \times 1 0^{- 8} Nm$
(D) $1.5 \times 1 0^{- 9} Nm$

Answer: (B)

Solution

Dipole moment:

p = q \times d = 0.01 \times 0.4 \times 1 0^{- 3} = 4 \times 1 0^{- 6}

C·m

Electric field:

E = 10

dyne/C

= 10 \times 1 0^{- 5}

N/C

= 1 0^{- 4}

N/C

Torque on a dipole:

τ = pE sin θ

τ = 4 \times 1 0^{- 6} \times 1 0^{- 4} \times sin 3 0^{\circ}

τ = 4 \times 1 0^{- 10} \times 0.5 = 2 \times 1 0^{- 10}

N·m

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option

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