In a certain region of space the electric potential varies with the X-coordinate…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

In a certain region of space the electric potential varies with the X-coordinate according to

V(x)=\dfrac{200}{x}

, where

V

is in volts and

x

in metres

(x \ge 0.5\,\text m)

. (a) Sketch qualitatively the family of equipotential surfaces in the X–Y plane for

x

ranging from

0.5\,\text m

2.0\,\text m

. Label at least three potential values. (b) Derive an expression for the magnitude of the electric field as a function of

x

in this region. (c) Compute the electric field magnitude at

x = 0.5\,\text m

and at

x = 1.0\,\text m

. Comment on how the field strength varies with distance from the origin. (d) A

2\,\text{nC}

charge is transported slowly from

x = 0.6\,\text m

x = 1.2\,\text m

along a path parallel to the Y-axis. Determine the work done in this process. (e) Verify, for any point in the given region, that the electric field is perpendicular to the equipotential curves you have drawn in part (a).

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