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Electric Potential at a Point in Space Due to a Point Charge Q

Question

An electric field $\to E = (\to i 20 + \to j 30) N C^{- 1}$ exists in the space. If the potential at the origin is taken to be zero, find the potential at $(2 m, 2 m)$ .

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Solution

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The electric field in the region is given by: $E = (^i 20 +^j 30) N / C$
The position of the point is at $(2 m, 2 m)$
The displacement vcector for the point is $r = (2 i + 2 j)$

Therefore, the potential at the point is:
So, $V = - \to E \times \to r$

$= - (i 20 + 30 J) (2^i + 2 j)$

$= - (2 \times 20 + 2 \times 30) = - 100 V$ .

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