Two fixed point charges are located in the -plane: a charge at the origin and a charge at

PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

Two fixed point charges are located in the

xy

-plane: a

+4.0\,\mu\text{C}

charge at the origin and a

-4.0\,\mu\text{C}

charge at

(0,\,0.10\,\text{m})

. A

+1.0\,\mu\text{C}

test charge is to be moved slowly from point P at

(0.30\,\text{m},\,0)

to point Q at

(0.30\,\text{m},\,0.10\,\text{m})

. Ignore all forces except those due to the two fixed charges. (a) Derive an algebraic expression for the electric potential at an arbitrary point on the

x

-axis

(x,0)

due to the two fixed charges, using the zero of potential at infinity. (b) Use the result of part (a) to calculate the potentials

V_{P}

and

V_{Q}

at points P and Q, respectively. (c) Determine the numerical value (including sign) of the work that an external agent must do to move the test charge slowly along the straight line segment from P to Q. (d) Suppose instead the test charge is moved slowly from P to Q via the intermediate point R at

(0.30\,\text{m},\,0.050\,\text{m})

. Calculate the external work for each segment and show that the total work for the two-segment path is equal to the result from part (c). (e) Explain how your results in parts (c) and (d) illustrate a fundamental property of electrostatic fields.

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