A charge of +2.00 μC is at the origin and a charge of –3.00 μC is on the y axis at y = 40.0 cm . (a) What is the potential at point a, which is on the x axis at x = 40.0 cm ? (b) What is the potential difference V b − V a when point b is at (40.0 cm, 30.0 cm)? (c) How much work is required to move an electron at rest from point a to rest at point b?

a) Potential in A: -2700 V

b) Potential difference: -26,800 V

c) Work:

Explanation:

a)

The electric potential at a distance r from a single-point charge is given by:

where

is the Coulomb's constant

q is the charge

r is the distance from the charge

In this problem, we have a system of two charges, so the total potential at a certain point will be given by the algebraic sum of the two potentials.

Charge 1 is

and is located at the origin (x=0, y=0)

Charge 2 is

and is located at (x=0, y = 0.40 m)

Point A is located at (x = 0.40 m, y = 0)

The distance of point A from charge 1 is

So the potential due to charge 2 is

The distance of point A from charge 2 is

So the potential due to charge 1 is

Therefore, the net potential at point A is

b)

Here we have to calculate the net potential at point B, located at

(x = 0.40 m, y = 0.30 m)

The distance of charge 1 from point B is

So the potential due to charge 1 at point B is

The distance of charge 2 from point B is

So the potential due to charge 2 at point B is

Therefore, the net potential at point B is

So the potential difference is

c)

The work required to move a charged particle across a potential difference is equal to its change of electric potential energy, and it is given by

where

q is the charge of the particle

is the potential difference

In this problem, we have:

is the charge of the electron

is the potential difference

Therefore, the work required on the electron is