Two charges of and are placed at the points A(1,0,4)m and B(2,?1,5)m located in an electric field The magnitude of the torque acting on the dipole is where

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Solution

Q.
Two charges of $- 4 μ C$ and $+ 4 μ C$ are placed at the points A(1,0,4)m and B(2,−1,5)m located in an electric field $\vec{E} = 0.20 \hat{i} V / c m .$ The magnitude of the torque acting on the dipole is $8 \sqrt{α} \times 10^{- 5} N m,$ where $α$ = _________. [2024]

Ans.
(2)

$\vec{τ} = \vec{p} \times \vec{E}$

$\vec{p} = q \vec{ℓ}$

$\vec{E} = 0.2 \hat{i} \frac{V}{cm} = 20 \hat{i} \frac{V}{m}$

$\vec{p} = 4 \times (\hat{i} - \hat{j} + \hat{k}) = (4 \hat{i} - 4 \hat{j} + 4 \hat{k}) μ C - m$

$\vec{τ} = (4 \hat{i} - 4 \hat{j} + 4 \hat{k}) \times (20 \hat{i}) \times 10^{- 6} Nm$

$= (8 \hat{k} + 8 \hat{j}) \times 10^{- 5} \Rightarrow | \vec{τ} | = 8 \sqrt{2} \times 10^{- 5}$

$alpha equals 2$

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