An electric dipole is placed at an angle of 30° with an electric field intensity 2×10⁵ N/C. It experiences a t

Question

An electric dipole is placed at an angle of 30° with an electric field intensity 2×10⁵ N/C. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is:

Accepted Answer

The magnitude of torque ($	au$) exerted on an electric dipole in a uniform electric field ($E$) is given by the formula:
$	au = pE \sin	heta$
where $p$ is the dipole moment, defined as the product of the magnitude of one of the charges ($q$) and the distance separating them ($2a$).
$p = q(2a)$
Substituting this into the torque equation:
$	au = q(2a)E \sin	heta$

Given:
$	au = 4$ N m
$E = 2 	imes 10^5$ N/C
$	heta = 30^\circ$ (so $\sin 30^\circ = 0.5$)
Dipole length ($2a$) = 2 cm = $2 	imes 10^{-2}$ m

Substituting these values to solve for charge $q$:
$4 = q 	imes (2 	imes 10^{-2}) 	imes (2 	imes 10^5) 	imes 0.5$
$4 = q 	imes (2 	imes 10^3)$
$q = \frac{4}{2 	imes 10^3} = 2 	imes 10^{-3}$ C
$q = 2$ mC

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