Electric potential of point charge

[pyninja]

Homework Statement

A charged particle is fixed in place at the origin. A second particle of charge $$+10^{-6}$$ C is released from rest from very far away ($$\approx (\infty, 0)$$). The second particle passes the point (9 m, 0) with a kinetic energy of 1.0 J.

Find the electric potential due to the fixed charged particle at the point (9 m, 0).

Homework Equations

$$F = \frac{q_1q_2}{r^2} = ma$$
$$V = \frac{1}{4\pi\epsilon_0} \frac{q_1}{r}$$

The Attempt at a Solution

We need to the find the charge of the fixed particle to apply the formula for V... I tried using conservation of energy, but it seems to me that the initial potential energy and kinetic energy are both 0. Not sure what I'm doing wrong there...

 

[madah12]

ok why don't you use foruma U= Q*delta V if as you say the total energy is zero then U2 = -K2

 

[pyninja]

ok why don't you use foruma U= Q*delta V if as you say the total energy is zero then U2 = -K2

Oh, for some reason I thought the energy has to be positive, haha.

So then I get $$q_1 = -\frac{k r}{q_2}$$.

And $$V = -\frac{k^2}{q_2}$$?

(where $$k = \frac{1}{4\pi\epsilon_0}$$)

Thanks for your help!

 

[madah12]

Only kinetic energy has to be positive.

 

[rwisz]

I would approach this problem by first understanding the concept of electric potential. Electric potential is a measure of the potential energy per unit charge at a point in an electric field. It is a scalar quantity and is given by the equation V = kQ/r, where k is the Coulomb's constant, Q is the charge of the particle, and r is the distance from the particle to the point where the potential is being measured.

In this problem, we are given the charge of the second particle (+10^-6 C) and its kinetic energy (1.0 J). However, we are not given the charge of the fixed particle. To find the electric potential at the point (9 m, 0), we need to first calculate the force between the two particles using Coulomb's law, F = kQ1Q2/r^2. From there, we can use the fact that the electric potential is equal to the work done per unit charge, V = W/q. In this case, the work done would be the change in kinetic energy (1.0 J) as the particle moves from infinity to (9 m, 0). Therefore, we can write the equation:

V = (1.0 J)/(10^-6 C)

Solving for V, we get an electric potential of 1.0 x 10^6 volts at the point (9 m, 0). This means that the fixed particle has a charge of +1.0 x 10^-6 C.

In conclusion, to find the electric potential at a point due to a point charge, we need to first calculate the force between the two particles, then use the equation V = W/q to find the electric potential. This approach is based on the fundamental principles of Coulomb's law and the definition of electric potential.