Question

Two very long uniform lines of charge are parallel and are separated by 0.300 m. each line of charge has charge per unit length +5.20 mc>m. what magnitude of force does one line of charge exert on a 0.0500-m section of the other line of charge?

Answer 1

linear charge density of system of two line charges is given as

$\lambda = 5.20 \muC/m$

now as we know that electric field due to a line charge at some distance from it is given by

$E = \frac{\lambda}{2\pi \epsilon_0 r}$

so here we will first find the electric field of first line charge at the position of other line charge

$E = \frac{5.20 * 10^{-6}}{2 \pi * 8.85 * 10^{-12}* 0.300}$

$E = 312000 N/C$

now as we know that

$F = qE$

here q = charge on the line charge system at which force is required

E = electric field on that system of charge where force is required

now we can find the charge by

$q = \lambda * L$

$q = 5.20 * 10^{-6}* 0.05 = 0.26 * 10^{-6} C$

Now using the above formula

$F = qE$

$F = 0.26 * 10^{-6} * 312000$

$F = 0.0811 N$

so force on the part of wire is F = 0.0811 N