An electric dipole is placed at an angle of with an electric field of intensity . It experiences a torque equal to 4 Nm. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm. [2023]

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Solution

Q.
An electric dipole is placed at an angle of $30 °$ with an electric field of intensity $2 \times 10^{5}$ $N$ $C^{- 1}$ . It experiences a torque equal to 4 Nm. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm. [2023]

1 4 mC

2 2 mC

3 8 mC

4 6 mC

Ans.
(2)

Given, angle, $θ = 30 °,$

Electric field intensity, $E = 2 \times 10^{5}$ $N$ $C^{- 1}$

$τ = 4$ $Nm,$ Dipole length, $l = 2$ $cm = 0.02$ $m$

$τ = p E \sin θ = (q l) E \sin θ$

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

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