(a) An electric dipole with dipole moment 4 × 10^-9 cm is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 10^4 NC^-1. Calculate the magnitude of the torque acting on the dipole. (2)
(b) The maximum value of torque experienced by the dipole will be w

Question

(a) An electric dipole with dipole moment 4 × 10^-9 cm is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 10^4 NC^-1. Calculate the magnitude of the torque acting on the dipole. (2)
(b) The maximum value of torque experienced by the dipole will be when it is aligned at an angle θ = ________. (1)

Accepted Answer

>

> [!TLDR]
> The torque on a dipole is $	au = pE\sin	heta$; here it works out to $10^{-4}$ N·m at 30°, and the torque is maximum when the dipole is perpendicular to the field (θ = 90°).
>
> **(a)** The torque on an electric dipole of moment $p$ placed at angle θ to a uniform field E is
> $$	au = pE\sin	heta$$
> Given $p = 4	imes10^{-9}$ C·m, $E = 5	imes10^4$ N/C, $	heta = 30°$:
> $$	au = (4	imes10^{-9})(5	imes10^4)\sin30° = (4	imes10^{-9})(5	imes10^4)(0.5)$$
> $$	au = 1	imes10^{-4}\ 	ext{N·m}$$
>
> **(b)** Since $	au = pE\sin	heta$, torque is maximum when $\sin	heta = 1$, i.e. when the dipole moment is perpendicular to the field, $	heta = 90°$.
> …

Q.(a) An electric dipole with dipole moment 4 × 10^-9 cm is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 10^4 NC^-1. Calculate the magnitude of the torque acting on the dipole.

Concept understanding — Electric Dipole in a Field

Electric Dipole in a Uniform Field — First Look

What happens? Two forces, one twist

The torque formula

What does this mean physically?

Q.(a) An electric dipole with dipole moment 4 × 10^-9 cm is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 10^4 NC^-1. Calculate the magnitude of the torque acting on the dipole.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days