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Potential Gradient and Relation between Electric Field and Potential

The electric ...

Question

The electric field in a region of space is given as $\to E = (5 x^i - 2^j)$ . Potential at point $x = 1, y = 1$ is $V_{1}$ and potential at point (x = 2, y = 3)\) is $V_{2}$ . Then $| V_{1} - V_{2} | = \frac{n}{2}$ . Find $n$ volts. (All quantities are in SI units)

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Solution

$V_{1} - V_{2} = - \int_{(2, 3)}^{(1, 1)} (5 x d x - 2 d y)$
$V_{1} - V_{2} = - [{[\frac{5 x^{2}}{2}]}_{2}^{- 1} - 2 [y]_{3}^{1}]$
$= - [\frac{5}{2} (- 3) - 2 (1 - 3)] = \frac{15}{2} - 4 = \frac{7}{2} V$

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