How does the conservation of electrostatic energy work?

In summary, the problem involves calculating the velocity of a proton at position (6,0) when it was released from position (5,0), given that there is a charge of +2.5 micro coulomb at the origin and a +3.5 micro coulomb at (3,0). Using the equations E0=Ef and PE=KE, we can calculate the net work required to move the proton and set it equal to its kinetic energy. The correct approach involves calculating the work required to move the proton against each charge and adding them together, using the correct formula for the distance between the proton and the charge at (3,0). The resulting velocity is 1.1E6.
  • #1
Coderhk
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A charge of +2.5 micro coulomb is at the origin and a +3.5 micro coulomb is at the point (3,0). What is the velocity of a proton when it is at (6,0) if it was released at (5,0).
My solution:
$$E_0=E_f$$
$$PE=KE$$
$$Since...Work = -PE$$
I can calculate the work it takes to move the proton from (6,0) to (5,0) multiply that by negative one and set that equal to the kinetic energy.
To calculate the net work and I can calculate the work required to move the proton against each charge and add them together.
$$W=\sum\int{dw}=(\int_6^5{\frac{kq_1}{r^2}dr})+\int_6^5{\frac{kq_2}{r^2}dr}=-k(\frac{q_1+q_2}{30})$$
$$k(\frac{q_1+q_2}{30})=\frac{1}{2}mv^2$$
$$v=\sqrt{k(\frac{q_1+q_2}{15m})}$$
$$v=1.46E15$$
However my answer seems to be incorrect.How should I approach this question instead?
Correct answer is 1.1E6
 
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  • #2
If q2 is the charge standing at (3,0) then the denominator in the second integral is wrong, should be ##(r-3)^2##. Also you should multiply both integrals by the charge of the proton.
 
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FAQ: How does the conservation of electrostatic energy work?

What is electrostatic energy?

Electrostatic energy is the potential energy that exists between two or more charged particles due to their attraction or repulsion to one another.

How does conservation of electrostatic energy work?

The law of conservation of electrostatic energy states that in a closed system, the total amount of electrostatic energy remains constant. This means that the energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

What factors affect the conservation of electrostatic energy?

The conservation of electrostatic energy is affected by the distance between charged particles, the magnitude of their charges, and the medium in which they are located. These factors determine the strength of the electrostatic force between the particles and therefore, the amount of potential energy they possess.

How is electrostatic energy conserved in everyday life?

Electrostatic energy conservation can be observed in everyday life through various examples such as rubbing a balloon on hair to create static electricity, lightning strikes, and the attraction between opposite charges in a battery.

What are some practical applications of electrostatic energy conservation?

Electrostatic energy conservation has many practical applications, including in electronic devices, industrial processes, and medical procedures. It is also used in the development of renewable energy sources such as wind turbines and solar panels.

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