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

Answer 2

Force on the charge is defined as the application of the force field of one charge on another charge. The magnitude of the force accomplished on one line of charge exerts on the other line of charge will be 0.0810 N.

what is the electrostatic force?

It is a type of force exerted by one charge on another due to the field.

The electrostatic force exerted by one line charge on another charge separated by distance r depends on the charge potency of each charge, also the distance of separation between them.

The electrostatic force is given by.

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

$\lambda= \frac{Q}{L} \\\\Q = \lambda\times L\\ \\\ Q = 5.20\times(10)^{-6} \times 0.0500\\\\\rm{Q= 2.6\times 10^{-7} coloumb}$

$E = \frac{5.20\times 10^{-6}}{2\times 3.14 \times 8.85 \times 10^{-12} \times 0.300 }$

$E =311715.9 N/C$

The electric force is given by

$F=Q \times E$

$F=311715.9\times 2.6\times {10}^{-7}$  N

Hence the electric force is given by $311715.9\times 2.6\times {10}^{-7}$

To learn more about the electric force refer to the link;

https://brainly.com/question/1076352