Question

A point charge of +3 C is located at the origin of a coordinate system and a second point charge of -6 C is at x = 1.0 m. At what point on the x-axis is the electrical potential zero?

Answer 1

Answer:

The point at which the electrical potential is zero is x = +0.33 m.

Explanation:

By definition the electrical potential is:

$V_{E} = \frac{K*q}{r}$

Where:

K: is Coulomb's constant = 9x10⁹ N*m²/C²

q: is the charge

r: is the distance

The point at which the electrical potential is zero can be calculated as follows:

$V_{1} + V_{2} = 0$

$K(\frac{q_{1}}{r_{1}} + \frac{q_{2}}{r_{2}}) = 0$    (1)

q₁ is the first charge = +3 mC

r₁ is the distance from the point to the first charge  

q₂ is the first charge = -6 mC

r₂ is the distance from the point to the second charge    

By replacing r₁ = 1 - r₂ into equation (1) we have:

$K(\frac{q_{1}}{1 - r_{2}} + \frac{q_{2}}{r_{2}}) = 0$   (2)

By solving equation (2) for r₂:

$r_{2} = \frac{q_{1}}{q_{1} - q_{2}} = \frac{3 mC}{3 mC - (-6 mC)} = +0.33 m$

                 

Therefore, the point at which the electrical potential is zero is x = +0.33 m.

I hope it helps you!