A point charge of is fixed at the origin

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

A point charge of

+4.0\,\mu\text{C}

is fixed at the origin

O

. A second point charge of unknown magnitude

q

is placed on the

x

-axis at

x = 0.30\,\text{m}

. When the electric potential is measured relative to infinity at the point

P(0.40\,\text{m},\,0)

on the axis, it is found to be

600\,\text{kV}

. Take

\dfrac{1}{4\pi\varepsilon_{0}} = 9\times10^{9}\,\text{N m}^2\text{C}^{-2}

. (i) Write the expression for the total electric potential at

P

in terms of the given quantities. (ii) Hence calculate the magnitude and sign of the unknown charge

q