Electric Potential Energy Problem

In summary, the problem involves a fixed charge of -4.00 µC and a moving particle with a mass of 2.50 × 10–3 kg and charge of -3.00 µC. The particle is fired from a horizontal distance of 55.0 cm with an initial speed of 15.0 m/s towards the fixed charge. The question asks for the distance the particle travels before it stops and begins to return back. To solve this, the equation for kinetic energy is used to find the initial kinetic energy of the particle. Then, using the equation for potential energy and the relationship between potential energy and electric field, the final potential energy is calculated. By subtracting the two, the change in potential energy is
  • #1
mlostrac
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Homework Statement


A charge of –4.00 µC is fixed in place. From a horizontal distance of
55.0 cm, a particle of mass 2.50 × 10–3 kg and charge –3.00 µC is fired with an
initial speed of 15.0 m/s directly toward the fixed charge. How far does the
particle travel before it stops and begins to return back?

Homework Equations


KE = 1/2 mv^2
Pba = -W = -qEd
F = kQ1Q2/r^2

The Attempt at a Solution


1) Found the Kinetic energy of the moving particle :
KE = 1/2mv^2
= 1/2 (2.5x10^-3)(15)^2
= 0.281 J

2) Set the value I found for KE to PE and used the Potential Energy eqn:
PE = -qEd

Since E = kQ/d^2

PE = -qd(kQ/d^2)

Therefore: d = -qkQ/PE

d = 0.38 m

I'm not sure if I did that right. But the answer I came up with looks like it could work. Any help would be appreciated!
 
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  • #2
You should not be finding [tex]\Delta[/tex]PE that way.
[tex]\Delta[/tex]PE = -qEd only if E is constant. But E is not constant here.

Write down V at the initial point and the final point.
How is PE related to V?
Then subtract the two to find [tex]\Delta[/tex]PE.

:)
 

1. What is electric potential energy?

Electric potential energy is a form of energy that a charged particle possesses by virtue of its position in an electric field. It is measured in joules (J) and is a measure of the work required to move a charged particle from one point to another in an electric field.

2. How is electric potential energy calculated?

The electric potential energy of a charged particle is calculated by multiplying its charge (q) by the electric potential (V) at its location. This can be expressed as U = qV, where U is the electric potential energy in joules (J), q is the charge in coulombs (C), and V is the electric potential in volts (V).

3. What is the difference between electric potential and electric potential energy?

Electric potential (V) is a measure of the electric potential energy (U) per unit charge (q) at a given point in an electric field. It is often referred to as voltage and is measured in volts (V). Electric potential energy, on the other hand, is a measure of the energy that a charged particle possesses by virtue of its position in an electric field, and is measured in joules (J).

4. How does the distance between charged particles affect electric potential energy?

The electric potential energy between two charged particles is directly proportional to the magnitude of their charges and inversely proportional to the distance between them. This means that as the distance between charged particles increases, their electric potential energy decreases, and vice versa.

5. What are some real-life applications of electric potential energy?

Electric potential energy has many real-life applications, including powering electronic devices, such as cell phones and computers, through the use of batteries and capacitors. It is also used in power plants to generate electricity, and in electric motors to convert electrical energy into mechanical energy.

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