1 answer

A charge of 24.9 ?C is located at (4.39 m, 6.08 m), and a charge of...

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?


Answers

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:

.

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