Question

A charge of 24.9 ?C is located at (4.39 m, 6.08 m), and a charge of -11.9 ?C is located at (-4.58 m, 6.83 m). What charge must be located at (2.24 m, -2.92 m) if the electric potential is to be zero at the origin?

Answer 1

Let be:

$Q_1=24.9\mu C$

$P_1=(4.39, 6.08)$

$Q_2=-11.9\mu C$

$P_2=(-4.58, 6.83)$

$Q_3=?$

$P_3=(2.24, -2.92)$

The distances from every point to the origin are calculated by using the distance between two points formula, where (x, y) is one point and (0,0) is the other:

$r=\sqrt{x^2+y^2}$

Then:

$r_1=7.499m$

$r_2=8.22m$

$r_3=3.68m$

The potential due to the three charges at the origin is:

$V=k(\frac{Q_1}{r_1}+\frac{Q_2}{r_2}+\frac{Q_3}{r_3})$

$k(\frac{Q_1}{r_1}+\frac{Q_2}{r_2}+\frac{Q_3}{r_3})=0$

$Q_3=r_3[-\frac{Q_1}{r_1}-\frac{Q_2}{r_2}]$

$Q_3=-6.89\mu C$

The potential at the origin due to the three charges is: