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Q.

A dipole of dipole moment $\vec{P} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ is placed at point A (2, - 3, 1). The magnitude of electric potential due to this dipole at the point B (4, - 1, 0) is equal to (All the parameters specified here are in S.I. units) ___ × 10⁹ volts

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Detailed Solution

$\begin{array}{l} \bar{r} = (4 - 2) \hat{i} + (- 1 + 3) \hat{j} + (0 - 1) \hat{k} \\ = 2 \hat{i} + 2 \hat{j} - \hat{k} \\ V = \frac{1}{4 {πε}_{0}} \frac{\bar{P} \cdot \bar{r}}{r^{3}} \Rightarrow V = 9 \times 10^{9} \frac{(4 - 6 - 4)}{(3)^{3}} \\ = - 2 \times 10^{9} \end{array}$

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A dipole of dipole moment P→=2i^−3j^+4k^ is placed at point A (2, - 3, 1). The magnitude of electric potential due to this dipole at the point B (4, - 1, 0) is equal to (All the parameters specified here are in S.I. units) ___ × 109 volts