Question

You place a point charge q = -4.00 nC a distance of 9.00 cm from an infinitely long, thin wire that has linear charge density 3.00×10−9C/m. What is the magnitude of the electric force that the wire exerts on the point charge?

Answer 1

Answer:

$F=6\times 10^{-7}\ N$

Explanation:

Given:

• quantity of point charge, $q=-4\times 10^{-9}\ C$

• radial distance from the linear charge, $r=0.09\ m$

• linear charge density, $\lambda=3\times 10^{-9}\ C.m^{-1}$

We know that the electric field by the linear charge  is given as:

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

$E=\frac{1}{2}\times 9\times 10^9\times \frac{3\times10^{-9}}{0.09}$

$E=150\ N.C^{-1}$

Now the force on the given charge can be given as:

$F=E.q$

$F=150\times 4\times 10^{-9}$

$F=6\times 10^{-7}\ N$