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In a certain region of space, electric field is along the $z$-direction throughout. The magnitude of electric field is however not constant, but increases uniformly along the positive $z$-direction at the rate of $10^5 \mathrm{~N} \mathrm{C}^{-1} \mathrm{~m}^{-1}$. The force experienced by the system having a total dipole moment equal to $10^{-7} \mathrm{C} \mathrm{m}$ in the negative $z$-direction is
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$-10^{-2} \mathrm{~N}$
Consider an electric dipole with $-q$ charge at $A$ and $+q$ charge at $B$, placed along $z$-axis, such that its dipole moment is in negative $z$ direction.
i.e., $p_{\mathrm{z}}=-10^{-7} \mathrm{Cm}$
The electric field is along positive direction of $z$-axis, such that
$\frac{d E}{d z}=10^5 \mathrm{NC}^{-1} \mathrm{~m}^{-1}$
From, $F=q d E$
$=(q \times d z) \times \frac{d E}{d z}=p \frac{d E}{d z}$
Force experienced by the system in the negative $z$-direction,
$F=-p \times\left(-\frac{d E}{d z}\right)=10^{-7} \times\left(-10^5\right)=-10^{-2} \mathrm{~N}$
i.e., $p_{\mathrm{z}}=-10^{-7} \mathrm{Cm}$
The electric field is along positive direction of $z$-axis, such that
$\frac{d E}{d z}=10^5 \mathrm{NC}^{-1} \mathrm{~m}^{-1}$
From, $F=q d E$
$=(q \times d z) \times \frac{d E}{d z}=p \frac{d E}{d z}$
Force experienced by the system in the negative $z$-direction,
$F=-p \times\left(-\frac{d E}{d z}\right)=10^{-7} \times\left(-10^5\right)=-10^{-2} \mathrm{~N}$
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