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Question

(A) The torque $	au$ on an electric dipole placed in a uniform electric field $E$ is given by the formula:$	au = p E \sin 	heta$ ...$(i)$where $p$

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$(a)$

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(A) The torque $	au$ on an electric dipole placed in a uniform electric field $E$ is given by the formula:$	au = p E \sin 	heta$ ...$(i)$where $p$ is the electric dipole moment and $	heta$ is the angle between the dipole moment vector and the electric field direction.Analyzing the torque at different angles:$1$. At $	heta = 0^{\circ}$,$	au = p E \sin 0^{\circ} = 0$.$2$. At $	heta = \frac{\pi}{2}$,$	au = p E \sin \frac{\pi}{2} = p E$.$3$. At $	heta = \pi$,$	au = p E \sin \pi = 0$.$4$. At $	heta = \frac{3\pi}{2}$,$	au = p E \sin \frac{3\pi}{2} = -p E$.$5$. At $	heta = 2\pi$,$	au = p E \sin 2\pi = 0$.This variation follows a sine wave pattern starting from zero,reaching a maximum at $\frac{\pi}{2}$,passing through zero at $\pi$,reaching a minimum at $\frac{3\pi}{2}$,and returning to zero at $2\pi$. The graph representing this behavior is the standard sine curve.

Similar Questions

An electric dipole of length $3 \text{ cm}$ is placed with its axis making an angle of $60^\circ$ with a uniform electric field of $5 \times 10^4 \text{ N/C}$. It experiences a torque of $9\sqrt{3} \text{ Nm}$. The magnitude of charge on the dipole is $(\sin 60^\circ = \frac{\sqrt{3}}{2})$

The force of interaction between two co-axial short electric dipoles whose centers are $R$ distance apart varies as:

For an electric dipole with charge $q = 2 \times 10^{-6} \ C$ and separation distance $d = 0.01 \ m$,if the external electric field is $E = 5 \times 10^{5} \ N/C$,calculate the maximum torque acting on the dipole.

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