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

Question

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]

Smart Achievers · Accepted Answer

(2)

$\vec{τ} = \vec{p} \times \vec{E}$

$\vec{p} = q \vec{ℓ}$

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

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

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

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

$alpha equals 2$

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]

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Solution

Q. Two charges of -4μC and +4μC are placed at the points A(1,0,4)m and B(2,−1,5)m located in an electric field E→=0.20i^V/cm. The magnitude of the torque acting on the dipole is 8α×10-5Nm, where α = _________. [2024]

Ans. (2) τ→=p→×E→ p→=qℓ→ E→=0.2i^Vcm=20i^Vm p→=4×(i^-j^+k^)=(4i^-4j^+4k^) μC-m τ→=(4i^-4j^+4k^)×(20i^)×10-6 Nm =(8k^+8j^)×10-5⇒|τ→|=82×10-5

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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]