In a certain region of space,the electric fie | vedclass

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Question

(A) The dipole moment of the system is $p = -10^{-7} \; C \, m$ (since it is in the negative $z$-direction).The rate of increase of the electric field

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$F = -10^{-2} \; N, 	au = 0$

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(A) The dipole moment of the system is $p = -10^{-7} \; C \, m$ (since it is in the negative $z$-direction).The rate of increase of the electric field per unit length is $\frac{dE}{dz} = 10^{5} \; N \, C^{-1} \, m^{-1}$.The force $F$ experienced by a dipole in a non-uniform electric field is given by $F = p \frac{dE}{dz}$.Substituting the values: $F = (-10^{-7} \; C \, m) 	imes (10^{5} \; N \, C^{-1} \, m^{-1}) = -10^{-2} \; N$.The negative sign indicates that the force is in the negative $z$-direction.Since the dipole moment is in the negative $z$-direction and the electric field is in the positive $z$-direction,the angle $	heta$ between the dipole moment vector and the electric field vector is $180^{\circ}$.The torque $	au$ is given by $	au = pE \sin 	heta$.Since $\sin 180^{\circ} = 0$,the torque $	au = 0$.

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