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If uniform electric field $\vec{E} = E_{0} \hat{i} + 2 E_{0} \hat{j}$ , where E₀ is a constant, exists in a region of space and at (0, 0) the electric potential V is zero, then the potential at (x₀, 0) will be:

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Zero

$- E_{0} x_{0}$

$- 2 E_{0} x_{0}$

$- \sqrt{5} E_{0} x_{0}$

answer is B.

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Detailed Solution

$A = (0, 0), B = (x_{0}, 0) = \int_{A}^{B} \vec{E} . \vec{dr} = V_{A} - V_{B} = 0 - V_{B} E_{0} x_{0} = - V_{B} V_{B} = - E_{0} x_{0}$

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