Question 721: Electrostats & Capacitance

Question

Two charges of $$-4 \mu \mathrm{C}$$ and $$+4 \mu \mathrm{C}$$ are placed at the points $$\mathrm{A}(1,0,4) \mathrm{m}$$ and $$\mathrm{B}(2,-1,5) \mathrm{m}$$ located in an electric field $$\overrightarrow{\mathrm{E}}=0.20 \hat{i} \mathrm{~V} / \mathrm{cm}$$. The magnitude of the torque acting on the dipole is $$8 \sqrt{\alpha} 	imes 10^{-5} \mathrm{Nm}$$, where $$\alpha=$$ _________.

Accepted Answer

$$\begin{aligned}
& \vec{	au}=\vec{p} 	imes \vec{E} \
& \vec{p}=q \vec{\ell} \
& \overrightarrow{\mathrm{E}}=0.2 \frac{\mathrm{V}}{\mathrm{cm}}=20 \frac{\mathrm{V}}{\mathrm{m}} \
& \overrightarrow{\mathrm{p}}=4 	imes(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}) \
& =(4 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) \mu \mathrm{C}-\mathrm{m} \
& \vec{	au}=(4 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) 	imes(20 \hat{\mathrm{i}}) 	imes 10^{-6} \mathrm{Nm} \
& =(8 \hat{\mathrm{k}}+8 \hat{\mathrm{j}}) 	imes 10^{-5}=8 \sqrt{2} 	imes 10^{-5} \
& \alpha=2
\end{aligned}$$

Electrostats & Capacitance

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