A point charge is held fixed in space

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A point charge

q_{0}=+4.0\,\mu\text{C}

is held fixed in space. A second point charge

q=-2.0\,\mu\text{C}

is moved along the radial line that passes through

q_{0}

. Initially the separation between the charges is

0.30\,\text{m}

. The charge

q

is first moved slowly to a separation of

0.18\,\text{m}

and then, in a second stage, from

0.18\,\text{m}

0.10\,\text{m}

. (a) Calculate the total change in electric potential energy of the two–charge system for the overall displacement from

0.30\,\text{m}

0.10\,\text{m}

. Indicate the sign of the change. (b) Compute the work done by the external agent during stage 1 (

0.30\,\text{m}

0.18\,\text{m}

) and during stage 2 (

0.18\,\text{m}

0.10\,\text{m}

). (c) Using your results from part (b), discuss whether the net work done depends on the specific intermediate position at

0.18\,\text{m}

or only on the initial and final separations. Provide a brief justification based on energy principles.