Two point charges

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

Problem

Two point charges,

q_{1}=+1.8\,\mu\text{C}

and

q_{2}=-1.2\,\mu\text{C}

, are held fixed in a homogeneous liquid of unknown relative permittivity

\varepsilon_{r}

. They are separated by a distance

d=0.35\,\text{m}

. An experiment shows that the magnitude of the electrostatic force between the charges is measured to be

0.16\,\text{N}

. A student wishes to quantify the error that would arise if the calculation had incorrectly assumed the medium to be vacuum. Complete the tasks below. (a) Derive an algebraic expression for the relative permittivity

\varepsilon_{r}

of the liquid in terms of

q_{1}

q_{2}

d

, the measured force magnitude

F_{\text{exp}}

, and fundamental constants. (b) Use your expression to calculate

\varepsilon_{r}

for the liquid. (c) Derive an expression for the percent error that would occur in the computed force if vacuum were assumed instead of the liquid. Express your result entirely in terms of

\varepsilon_{r}

. (d) Compute the numerical value of this percent error using the

\varepsilon_{r}

obtained in part (b) and interpret its significance in an experimental context.

Related theory

Browse the problem library