An electric field given by E = i Ax is present in a region of space, where A = 10 V m^ -2 . If the potential at (10 m, 20 m) is assumed to be zero, calculate the potential at the origin.

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Quantrex Academy · Accepted Answer

Correct answer: D. 500 V

The relation between electric field and potential is given by

dV = -\vec{E} \cdot d\vec{r}

.

Given

\vec{E} = A x \hat{i}

, we have:

dV = -(A x \hat{i}) \cdot (dx \hat{i} + dy \hat{j} + dz \hat{k}) = -A x dx

Integrating both sides from the reference point

(10, 20)

to the origin

(0, 0)

:

\int_{V(10, 20)}^{V(0, 0)} dV = -\int_{10}^{0} A x dx

V(0, 0) - V(10, 20) = -A \left[ \dfrac{x^2}{2} \right]_{10}^{0}

Substituting

V(10, 20) = 0

and

A = 10 \text{ V m}^{-2}

:

V(0, 0) - 0 = -10 \left( 0 -

\dfrac{10^2}{2} \right)

V(0, 0) = -10 (-50) = 500 \text{ V}

An electric field given by E = i Ax is present in a region of...

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