In a certain region of space, the electric field is along the z-direction throughout. The magnitude of the ele

Question

In a certain region of space, the electric field is along the z-direction throughout. The magnitude of the electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of $10^5$ NC$^{-1}$ per meter. What is the torque experienced by a system having a total dipole moment equal to $10^{-7}$ C-m in the negative z-direction?

Accepted Answer

The torque $\vec{	au}$ experienced by an electric dipole is given by the cross product $\vec{	au} = \vec{p} 	imes \vec{E}$, with magnitude $	au = pE \sin	heta$. Here, the electric field $\vec{E}$ is along the positive z-direction, and the dipole moment $\vec{p}$ is along the negative z-direction. The angle $	heta$ between them is $180^\circ$. Since $\sin(180^\circ) = 0$, the torque is zero. Note: The non-uniformity of the field ($dE/dz$) results in a net force on the dipole ($F = p \frac{dE}{dz}$), but the torque remains zero because the forces on the charges act along the same line. (See NCERT Physics Class 12, Exercise 1.27).

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