Electric Potential and Kinetic Energy

[jakey]

Homework Statement

Two identical +9.5e-6C point charges are initially 3.5 cm from each other. If they are released at the same instant from rest, how fast will each be moving when they are very far from each other? Assume they have identical masses of 1.0mg.

Homework Equations

im not sure with this though but i used D(KE) + D(PE) = 0 where D=delta

The Attempt at a Solution

i used the above equation to solve for v. i kinda considered the problem by taking 1 point charge. however, i can't get the right answer...

 

[Doc Al]

i kinda considered the problem by taking 1 point charge.

What do you mean by that?

There are two point charges. Make sure you consider the total change in KE of both of them.

 

[thomate1]

I would approach this problem by first identifying the relevant equations and principles in play. The key equations here are the electric potential energy equation (U = kQq/r) and the kinetic energy equation (KE = 1/2mv^2).

Based on the given information, we know that the two charges are initially 3.5 cm apart and have identical masses of 1.0mg. We also know that they have the same charge of +9.5e-6C.

To solve for the final velocity, we can use the conservation of energy principle, which states that the total energy of a system remains constant. This means that the initial potential energy (U) must equal the final kinetic energy (KE) when the charges are very far apart.

We can set up the following equation:

U initial = KE final

Using the electric potential energy equation, we can calculate the initial potential energy:

U initial = (k)(9.5e-6C)^2/0.035m = 0.0000125 J

Since the charges are initially at rest, the initial kinetic energy is zero.

0.0000125 J = 1/2(0.001kg)(v)^2

Solving for v, we get v = 0.5 m/s.

Therefore, when the charges are very far apart, they will be moving at a speed of 0.5 m/s. This is a simplified calculation, as it does not take into account factors such as the direction of motion and the influence of external forces. However, it provides a basic understanding of the relationship between electric potential and kinetic energy in this scenario.