Electrostatics Question 7
Question 7 - 2024 (27 Jan Shift 2)
Two charges of $-4 \mu \mathrm{C}$ and $+4 \mu \mathrm{C}$ are placed at the points $A(1,0,4) \mathrm{m}$ and $B(2,-1,5) \mathrm{m}$ located in an electric field $\overrightarrow{\mathrm{E}}=0.20 \hat{\mathrm{i}} \mathrm{V} / \mathrm{cm}$. The magnitude of the torque acting on the dipole is $8 \sqrt{\alpha} \times 10^{-5} \mathrm{Nm}$, Where $\alpha=$
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Answer: (2)
$\vec{\tau}=\vec{p} \times \overrightarrow{\mathrm{E}}$
$\overrightarrow{\mathrm{p}}=\mathrm{q} \vec{\ell}$
$\overrightarrow{\mathrm{E}}=0.2 \frac{\mathrm{V}}{\mathrm{cm}}=20 \frac{\mathrm{V}}{\mathrm{m}}$
$\overrightarrow{\mathrm{p}}=4 \times(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$
$=(4 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) \mu \mathrm{C}-\mathrm{m}$
$\vec{\tau}=(4 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) \times(20 \hat{\mathrm{i}}) \times 10^{-6} \mathrm{Nm}$
$=(8 \hat{\mathrm{k}}+8 \hat{\mathrm{j}}) \times 10^{-5}=8 \sqrt{2} \times 10^{-5}$
$\alpha=2$
