A dipole of dipole moment $\vec{P} = 2 \overset{\land}{i} - 3 \overset{\land}{j} + 4 \overset{\land}{k}$ 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) $___\times 10^{9}$ volts

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answer is 2.

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Detailed Solution

$r = (4 - 2) \overset{\land}{i} + (- 1 + 3) \overset{\land}{i} + (0 - 1) \overset{\land}{k}$

$r = 2 \overset{\land}{i} + 2 \overset{\land}{j} - \overset{\land}{k}$

$V = \frac{1}{4 π \in_{0}} \frac{P . r}{r^{3}}$

$V = 9 \times 10^{9} \frac{(4 - 6 - 4)}{3^{3}}$

$V = - 2 \times 10^{9}$

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