Good afternoon! I'm stumped with this question here.

Q: An electron starts from rest 32.5 cm from a fixed point charge with Q=-0.125μC. How fast will the electron be moving when it is very far away?

I got an answer of 5.54 * 10^-16 J, but apparently it is incorrect. Please help! Thanks!

The PE available is : kQ/r=9e9 (.125e-6)/.325=3462 joules

1/2 m v^2=PE
v= sqrt(2*3462/(.325*9.1e-31)) = I dont get your answer, or even near it.

Paste this in your google search window sqrt(2*3462/(.325*9.1e-31)) =

Oh. So we're first using the Voltage formula to find the voltage given k is a constant, and we have Q and r. Then, we plug in the voltage into the 1/2mv^2 formula. Now I'm confused though -- what is the PE?

P.S. Isn't there also another formula: 1/2 m v^2 = KE? I don't have the PE one but I have a KE one on my notebook here.

when you move a charge to a new location, it has potential energy, the same amount of work that was done to get it that. In the case of a charge , that work moving is kQ/r, and that is its potential energy. If it moves from there, back into new position, the work done converts to KEnergy.

if you move a box up in a gravitational field you do work, mgh. At the end, it has PE mgh. If you release it, 1/2 mv^2. If you start a repelling charge, at some r, the work done on it by the electric field gives it KE. Work is energy, energy is work. Anyway, PE comes for potential theory (which comes in many forms: electrical, gravitational, nuclear) which can be converted to KE.

Voltage is potential energy per unit charge:

see:
http://www.studyphysics.ca/2007/30/06_forces_fields/12_voltage.pdf

Ohhhhh... I see.

Thanks! :)

Good afternoon! It seems like you're mixing up the units a bit. The answer you provided, 5.54 * 10^-16 J, seems to be a measure of energy (joules), rather than speed or velocity.

To find the speed of the electron when it's far away, we can use the principle of conservation of energy. The initial potential energy is equal to the final kinetic energy.

So let's convert the charge Q from microcoulombs to coulombs (μC to C). We have Q = -0.125μC = -0.125 * 10^-6 C.

Using the potential energy formula, PE = k * |Q| / r, where k is Coulomb's constant and r is the distance between the charges, we can calculate the initial potential energy.

PE = k * |Q| / r = (9 * 10^9 Nm^2/C^2) * |-0.125 * 10^-6 C| / 0.325 m

Now, to find the final kinetic energy, we can use the equation KE = 0.5 * m * v^2, where m is the mass of the electron and v is its velocity.

Since the problem states that the electron starts from rest, its initial kinetic energy is zero. So we can set the initial potential energy equal to the final kinetic energy:

PE = KE

Solving for v, we get:

v = sqrt(2 * PE / m)

But since the electron is very far away, it will have negligible kinetic energy. Therefore, v will be very close to zero.

Good afternoon! I can help you with that. It seems like you're trying to determine the speed of an electron when it is very far away from a fixed point charge. However, the answer you provided, 5.54 * 10^-16 J, is actually an energy value, not a speed value. Let's go through the steps to calculate the correct answer.

To solve this problem, you can use the principle of conservation of energy. The initial potential energy of the electron will be converted into kinetic energy as it moves away from the fixed point charge.

Here's the approach to solve this problem:

1. Determine the initial potential energy (U_initial) of the electron at a distance of 32.5 cm from the fixed point charge.

The formula for potential energy between two point charges is given by:

U = (k * |Q1 * Q2|) / r

Where:
k is the electrostatic constant (8.99 * 10^9 Nm^2/C^2)
Q1 and Q2 are the charges (in coulombs) of the two point charges
r is the distance between the two charges

In this case, Q1 is the charge of the electron (1.60 * 10^-19C), Q2 is the charge of the fixed point charge (-0.125 * 10^-6C), and r is 32.5 cm (or 0.325 m). Plug these values into the formula to calculate the initial potential energy (U_initial).

2. Determine the final kinetic energy (K_final) when the electron is very far away.

At a very large distance, the potential energy becomes almost zero because the charge difference becomes negligible. Therefore, all the initial potential energy will be converted into kinetic energy. This allows us to set U_initial equal to K_final.

K_final = U_initial

3. Calculate the final speed (v_final) of the electron using the kinetic energy formula:

K = (1/2) * m * v^2

Where:
K is the kinetic energy
m is the mass of the electron (9.11 * 10^-31 kg)
v is the final velocity (speed) of the electron

Rearrange the formula to solve for v:

v_final = √(2 * K_final / m)

Substituting K_final from step 2, plug in the values and calculate v_final.

Following these steps will give you the correct answer for the speed of the electron when it is very far away.