Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. [2023]

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Q.
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 $' \vec{E}'$ of 10 dyne/C making $30 °$ angle with $\vec{E}$ , the magnitude of torque acting on the dipole is [2023]

1 $4.0 \times 10^{- 10} Nm$

2 $2.0 \times 10^{- 10} Nm$

3 $1.0 \times 10^{- 8} Nm$

4 $1.5 \times 10^{- 9} Nm$

Ans.
(2)

$| \vec{P} |$ $= q d = 0.04 \times 0.4 \times 10^{- 3} = 4 \times 10^{- 6}$

$| \vec{τ} |$ $= P E \sin θ = 4 \times 10^{- 6} \times 10 \times 10^{- 5} \times \sin 30 °$

$= 4 \times 10^{- 6 - 5 + 1} \times \frac{1}{2} = 2 \times 10^{- 10}$

Solution

Q.
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 $' \vec{E}'$ of 10 dyne/C making $30 °$ angle with $\vec{E}$ , the magnitude of torque acting on the dipole is [2023]

1 $4.0 \times 10^{- 10} Nm$

2 $2.0 \times 10^{- 10} Nm$

3 $1.0 \times 10^{- 8} Nm$

4 $1.5 \times 10^{- 9} Nm$

Ans.
(2)

$| \vec{P} |$ $= q d = 0.04 \times 0.4 \times 10^{- 3} = 4 \times 10^{- 6}$

$| \vec{τ} |$ $= P E \sin θ = 4 \times 10^{- 6} \times 10 \times 10^{- 5} \times \sin 30 °$

$= 4 \times 10^{- 6 - 5 + 1} \times \frac{1}{2} = 2 \times 10^{- 10}$

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Solution

Q. 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 30° angle with E→, the magnitude of torque acting on the dipole is [2023]

1 4.0×10-10 Nm

2 2.0×10-10 Nm

3 1.0×10-8 Nm

4 1.5×10-9 Nm

Ans. (2) |P→|=qd=0.04×0.4×10-3=4×10-6 |τ→|=PEsinθ=4×10-6×10×10-5×sin30° =4×10-6-5+1×12=2×10-10

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Q.
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 $' \vec{E}'$ of 10 dyne/C making $30 °$ angle with $\vec{E}$ , the magnitude of torque acting on the dipole is [2023]

1 $4.0 \times 10^{- 10} Nm$

2 $2.0 \times 10^{- 10} Nm$

3 $1.0 \times 10^{- 8} Nm$

4 $1.5 \times 10^{- 9} Nm$

Ans.
(2)

$| \vec{P} |$ $= q d = 0.04 \times 0.4 \times 10^{- 3} = 4 \times 10^{- 6}$

$| \vec{τ} |$ $= P E \sin θ = 4 \times 10^{- 6} \times 10 \times 10^{- 5} \times \sin 30 °$

$= 4 \times 10^{- 6 - 5 + 1} \times \frac{1}{2} = 2 \times 10^{- 10}$