Two point charges are fixed in otherwise empty space

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

Problem

Two point charges are fixed in otherwise empty space. Charge

q_{1}=+4\,\mu\text{C}

is at the origin, and charge

q_{2}=+9\,\mu\text{C}

is on the x–axis at

x=6\,\text{cm}

. A small positive test charge

q_{0}

is placed at

x=2\,\text{cm}

on the same axis. Ignore all other forces. (a) Calculate the magnitude of the electric force

F_{1}

exerted on the test charge by

q_{1}

. (b) Calculate the magnitude of the electric force

F_{2}

exerted on the test charge by

q_{2}

. (c) Using your results from parts (a) and (b), determine which of the two fixed charges exerts the greater magnitude of force on the test charge. Explain how both charge magnitude and distance factored into your conclusion. (d) The two fixed charges are simultaneously moved so that each is now twice as far from the test charge as before (while their separation from each other changes accordingly). Without further calculation, state the numerical factor by which each individual force on the test charge changes, and briefly justify your answer.

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