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