Electric Potential between two point charges

[ryanverbena]

Homework Statement

Two point charges Q1 = +5.00 nC and Q2 = −3.00 nC, are separated by 35.0 cm.
(a) What is the electric potential at a point midway between the charges?
(b) How much energy is required to bring an electron, located at infinity, to this midway
point?

Homework Equations

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The Attempt at a Solution

PE = ke x q1q2/r

 

[Doc Al]

What's the formula for the electric potential at some distance from a point charge?

 

[Moetasim]

(a) The electric potential at a point midway between the two charges can be calculated by finding the electric potential due to each charge individually and then adding them together. Using the equation for electric potential, we have:

V1 = k x Q1/r = (9 x 10^9 Nm^2/C^2) x (5.00 x 10^-9 C)/(0.175 m) = 2.57 x 10^5 V
V2 = k x Q2/r = (9 x 10^9 Nm^2/C^2) x (-3.00 x 10^-9 C)/(0.175 m) = -1.54 x 10^5 V
Therefore, the electric potential at the midway point is:
V = V1 + V2 = (2.57 x 10^5 V) + (-1.54 x 10^5 V) = 1.03 x 10^5 V

(b) The amount of energy required to bring an electron from infinity to the midway point can be calculated using the equation for electric potential energy:
PE = qV
where q is the charge of the electron (1.6 x 10^-19 C) and V is the electric potential at the midway point (1.03 x 10^5 V). Therefore, the energy required is:
PE = (1.6 x 10^-19 C) x (1.03 x 10^5 V) = 1.65 x 10^-14 J

In summary, the electric potential at the midway point between the two charges is 1.03 x 10^5 V and the energy required to bring an electron from infinity to this point is 1.65 x 10^-14 J.