An electric field E = ( i · 20 + j · 30) N C^ -1 exists in a region of space. Assuming the potential at the origin is taken to be zero, determine the potential at the point (2 m, 2 m) .

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Quantrex Academy · Accepted Answer

Correct answer: B. -100 V

The relationship between electric potential and a uniform electric field is given by:

V - V_0 = -\vec{E} \cdot \vec{r}

Given the electric field

\vec{E} = 20\hat{i} + 30\hat{j} \text{ N C}^{-1}

and the position vector of the point

\vec{r} = 2\hat{i} + 2\hat{j} \text{ m}

.

Since the potential at the origin is

V_0 = 0

, the potential at the point

(2, 2)

is:

V = -(20\hat{i} + 30\hat{j}) \cdot (2\hat{i} + 2\hat{j})

V = -(20 \times 2 + 30 \times 2)

V = -(40 + 60) = -100 \text{ V}

An electric field E = ( i · 20 + j · 30) N C^ -1 exists in a region...

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