At what point on the x-axis is the Electric Potential zero?

[Minhtran1092]

Homework Statement

A 13.0nC charge is at x = 0cm and a -1.1nC charge is at 6cm. At what point or points on the x-axis is the electric potential zero?

Let X₀ be a position on the x-axis
Let V₁ be the electrical potential at a point due to the 13nC charge
Let V₂ be the electrical potential at a point due to the -1.1nC charge

Homework Equations

V=k(q)*(1/r); k = Coulomb's constant, q = source charge for which at distance 'r' away, the electrical potential is V volts.

The Attempt at a Solution

There are three possible positions for which the electrical potential is 0:
1) To the left of the 13nC charge
2) Between 13nC charge and -1.1nC charge
3) To the right of the -1.1nC charge

For 1), I took the net voltage: V₁ + V₂ = 0 which is:
K(13E-9)*(X₀) + K(-1.1E-9)*(X₀) = 0, respectively. Simplifying the sum of two fractional terms, I only needed to find the X₀ that would make the numerator 0 and thus obtain the X₀ for which net Voltage is 0.

I applied similar calculation procedures for 2) and 3). My results were that X₀ = -.0655m, .05532m, .07109m, 1) to 3) respectively.

Attached is a diagram of the problem solving approach I took.

 

[Redbelly98]

Welcome to Physics Forums.

Homework Statement

A 13.0nC charge is at x = 0cm and a -1.1nC charge is at 6cm. At what point or points on the x-axis is the electric potential zero?

Let X₀ be a position on the x-axis
Let V₁ be the electrical potential at a point due to the 13nC charge
Let V₂ be the electrical potential at a point due to the -1.1nC charge

Homework Equations

V=k(q)*(1/r); k = Coulomb's constant, q = source charge for which at distance 'r' away, the electrical potential is V volts.

The Attempt at a Solution

There are three possible positions for which the electrical potential is 0:
1) To the left of the 13nC charge
2) Between 13nC charge and -1.1nC charge
3) To the right of the -1.1nC charge

For 1), I took the net voltage: V₁ + V₂ = 0 which is:
K(13E-9)*(X₀) + K(-1.1E-9)*(X₀) = 0, respectively. Simplifying the sum of two fractional terms, I only needed to find the X₀ that would make the numerator 0 and thus obtain the X₀ for which net Voltage is 0.

I'm a little confused by what you did here. It's not clear what X₀ is, and I don't see any fractional terms in your equation -- though I agree that there should be.

Also, for the electric potential, it is not necessary to break the solution process up into three regions. Unlike the electric field, the potential does not "flip sign" when going from one side of a point charge to the other. So you can just set

V₁ + V₂ = 0​

and solve for all x everywhere at once.

I applied similar calculation procedures for 2) and 3). My results were that X₀ = -.0655m, .05532m, .07109m, 1) to 3) respectively.

Attached is a diagram of the problem solving approach I took.