Two point charges are fixed on a straight line in vacuum

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

Problem

Two point charges are fixed on a straight line in vacuum. Charge

q_1=+6.0\,\mu\text{C}

is located at

x=0

. Charge

q_2=-3.0\,\mu\text{C}

is at

x=0.50\,\text{m}

on the same line. Along the

x

–axis there exists a point (or points) where a positive test charge would experience zero net electric force. (a) Determine all positions on the

x

–axis where the net electric field is zero. Express each position as a coordinate relative to

x=0

. (b) Explain, using physical reasoning rather than additional calculations, why no other points off the

x

–axis can satisfy the zero-field condition for this two-charge configuration.