Question

A +40.0 𝑛𝐶 charge is placed at the origin of a coordinate system, and a −30.0 𝑛𝐶 charge is placed in the 𝑥𝑦-plane at the point(𝑥=0.200 𝑚,𝑦=−0.100 𝑚).

a) Determine the magnitude and the direction of the force that the positive charge exerts on the negative charge. Use 𝑖𝑗𝑘 notation for your result.

b) Determine the magnitude and direction of the force of the negative charge on the positive charge.

Answer 1

(a)

$F=k\frac{q_1q_2}{r^2}=9\cdot10^9\cdot\frac{40\cdot10^{-9}\cdot30\cdot10^{-9}}{(\sqrt{0.2^2+0.1^2})^2}=0.000216\ (N)$

$\tan\alpha=-\frac{0.1}{0.2}=-0.5\to \alpha=153.435°$ (relative to the positive direction of the x-axis)

$F_x=0.000216\cdot\cos153.435°=-1.93\cdot10^{-4}\ (N)$

$F_y=0.000216\cdot\sin153.435°=0.96\cdot10^{-4}\ (N)$

$\vec F_{p-n}=-1.93\cdot10^{-4}\ \vec i+0.96\cdot10^{-4}\ \vec j$

(b)

$\vec F_{n-p}=-\vec F_{p-n}$

$\tan\alpha=-\frac{0.1}{0.2}=-0.5\to \alpha=-26.56°$ (relative to the positive direction of the x-axis)

$\vec F_{n-p}=1.93\cdot10^{-4}\ \vec i-0.96\cdot10^{-4}\ \vec j$