A point charge of magnitude is fixed in space at the origin

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

Problem

A point charge of magnitude

q_{1}=+4.0\,\mu\text{C}

is fixed in space at the origin. A second point charge

q_{2}=-2.0\,\mu\text{C}

is initially located very far from

q_{1}

. The second charge is then moved quasi-statically along the

x

–axis toward

q_{1}

until the electric potential energy of the two–charge system equals

-0.090\,\text{J}

. Assume the vacuum permittivity applies everywhere. The universal constant

k=8.99\times10^{9}\,\text{N}\,\text{m}^{2}\,\text{C}^{-2}

is available for numerical work. (a) Derive an algebraic expression for the separation distance

r

between the two charges as a function of

q_{1}

q_{2}

, and the specified electric potential energy

U

. Do not substitute numerical values until the final answer. (b) Calculate the numerical value of

r

that satisfies the stated energy requirement. Express your result in meters with an appropriate number of significant figures. (c) Indicate whether the external agent must do positive work, negative work, or no net work while bringing

q_{2}

from infinity to the position found in part (b). Justify your answer in terms of the sign of the potential energy change. (d) Suppose the magnitude of

q_{2}

were doubled while all other parameters remained the same. Qualitatively describe how (if at all) the final separation distance would change to achieve the same electric potential energy of

-0.090\,\text{J}

. Provide reasoning without performing a full recalculation.

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