An electric dipole is placed at an angle of with an electric field intensity . It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is [2016]

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Solution

Q.
An electric dipole is placed at an angle of $30 °$ with an electric field intensity $2 \times 10^{5}$ $N$ $C^{- 1}$ . It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is [2016]

1 8 mC

2 2 mC

3 5 mC

4 7 $μC$

Ans.
(2)

Here, $θ = 30 °,$ $E = 2 \times 10^{5}$ $N$ $C^{- 1},$ $τ = 4$ $N$ $m$

$l = 2$ $cm = 0.02$ $m,$ $q = ?$ ; $τ = p E \sin θ = (q l) E \sin θ$

$∴$ $q = \frac{τ}{E l \sin θ} = \frac{4}{2 \times 10^{5} \times 0.02 \times \frac{1}{2}}$

$= \frac{4}{2 \times 10^{3}} = 2 \times 10^{- 3}$ $C = 2$ $mC$

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