Physics

Problem

Two point charges are fixed on the

x

-axis at

x=-0.20\,\text{m}

and

x=+0.10\,\text{m}

. The charge at

x=-0.20\,\text{m}

has magnitude

+6.0\,\mu\text{C}

. The charge at

x=+0.10\,\text{m}

has magnitude

-3.0\,\mu\text{C}

. A third point charge

q

is to be placed at the origin such that the net electric field on the

x

-axis at

x=+0.50\,\text{m}

is zero. (a) Derive an expression for the

x

-component of the net electric field at

x=+0.50\,\text{m}

in terms of the unknown charge

q

. (b) Determine the magnitude and sign of

q

that make the net electric field zero at

x=+0.50\,\text{m}

. (c) After

q

is placed as found in part (b), determine whether any additional point(s) on the

x

-axis have zero net electric field. Support your answer with appropriate reasoning or calculation.