An electric dipole consists of two equal and opposite charges placed 2 cm apart. When the dipole is placed in a uniform electric field of strength 105 NC -1, it experiences a maximum torque of 0.2 × 10-3 N m. Find the magnitude of each charge.

Question

An electric dipole consists of two equal and opposite charges placed 2 cm apart. When the dipole is placed in a uniform electric field of strength 105 NC -1, it experiences a maximum torque of 0.2 × 10-3 N m. Find the magnitude of each charge. (A) 20 μ C (B) 10 μ C (C) 15 μ C (D) 40 μ C

Tardigrade Admin · Accepted Answer

Here, 2 a=2 cm =0.02 m , τ max =0.2 × 10-3 Nm and E=105 NC -1. Now, maximum torque on the dipole, τ max =p E=q(2 a) × E ∴ q=(τ max /(2 a) E) =(0.2 × 10-3/0.02 × 105) =10-7 C =10 μ C

Q. An electric dipole consists of two equal and opposite charges placed $2 c m$ apart. When the dipole is placed in a uniform electric field of strength $1 0^{5} N C^{- 1}$ , it experiences a maximum torque of $0.2 \times 1 0^{- 3} N m$ . Find the magnitude of each charge.

$20 μ C$

$10 μ C$

$15 μ C$

$40 μ C$

Here, $2 a = 2 c m = 0.02 m, τ_{m a x}$
$= 0.2 \times 1 0^{- 3} N m$
and $E = 1 0^{5} N C^{- 1}$ .
Now, maximum torque on the dipole,
$τ_{m a x} = pE = q (2 a) \times E$
$∴ q = \frac{τ _{m a x}}{( 2 a ) E}$
$= \frac{0.2 \times 1 0 ^{- 3}}{0.02 \times 1 0 ^{5}}$
$= 1 0^{- 7} C = 10 μ C$

Q. An electric dipole consists of two equal and opposite charges placed 2cm apart. When the dipole is placed in a uniform electric field of strength 105NC−1, it experiences a maximum torque of 0.2×10−3Nm. Find the magnitude of each charge.

20μC

10μC

15μC

40μC