A uniform field of 2.0 N C^ -1 exists in space in the x -direction. Assuming the potential at the origin is zero, determine the expression for the potential at an arbitrary point (x, y, z) .

Question

Quantrex Academy · Accepted Answer

Correct answer: A. -(2.0 V m^ -1 ) x

The relation between electric potential and electric field is given by

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

Given

\vec{E} = 2.0 \hat{i} \text{ N C}^{-1}

and

d\vec{r} = dx \hat{i} + dy \hat{j} + dz \hat{k}

dV = -(2.0 \hat{i}) \cdot (dx \hat{i} + dy \hat{j} + dz \hat{k}) = -2.0 dx

Integrating from the origin

(0,0,0)

to an arbitrary point

(x,y,z)

:

\int_{0}^{V} dV = -\int_{0}^{x} 2.0 dx

V - 0 = -2.0 x

Since

1 \text{ N C}^{-1} = 1 \text{ V m}^{-1}

, the expression for the potential at

(x,y,z)

is

-(2.0 \text{ V m}^{-1}) x

A uniform field of 2.0 N C^ -1 exists in space in the x -direction....

Options

Correct answer

Step-by-step solution

More from Electric Field and Potential