Physics

Problem

A point charge of

+6.0\,\mu\text{C}

is fixed at the origin

O

of the

x

-axis. A second point charge of unknown value

q

is located on the positive

x

-axis at an unknown distance

a

from

O

. The electric potentials measured (relative to infinity) are

450\,\text{kV}

at the point

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

and

250\,\text{kV}

at the point

Q(0.80\,\text{m},0)

. Take

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

. a. (i) Using the given data, set up two simultaneous equations involving

q

and

a

. b. (ii) Solve these equations to obtain the numerical values of

q

and

a

. c. (iii) State the sign of

q

and explain briefly what this indicates about the nature of the charge.