Calculating Work on a Charged Particle in an Electric Field

In summary, the problem involves two charges, one with a charge of -2.0*10^-3 C and the other with a charge of -6.0*10^-3 C. The question asks how much work must be done on the first charge to move it from a distance of 0.2 m to 0.9 m away from the second charge. Using the equations for electric force and work, the incorrect solution is calculated to be 694285.7143 N. However, the correct solution can be found by using the potential method and calculating the potential difference between the two distances, and then using the equation W=qV. The correct solution is -4.2*10^5.
  • #1
Dillion
39
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Homework Statement


A -2.0*10^-3 C charge is 0.2 m away from a -6.0*10^-3 C charge. How much work is must be done on the first charge to move it to a distance of 0.9m?

Homework Equations


F = qs*qt*k/r^2

W = F * d* cos theta

The Attempt at a Solution


(-2.0*10^-3)(-6.0*10^-3)(9*10^9)/0.2^2
=2700000 N
(-2.0*10^-3)(-6.0*10^-3)(9*10^9)/0.7^2
=220408.1633 N

W = 2700000N * .2 = 540000
W = 220408.1633 * .7 = 154285.7143

The sum of those is 694285.7143This is obviously not right because the answer is supposed to be -4.2*10^5
 
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  • #2
I think It is easy to use potential method, first calculate the potential difference 0.2m to 0.9m due to the second charge,
the use the eqn, W=qV
 

1. What is work done on a particle?

Work done on a particle is a measure of the energy transferred to or from the particle. It is calculated by multiplying the force acting on the particle by the displacement of the particle in the direction of the force.

2. How is work done on a particle calculated?

The work done on a particle can be calculated using the equation W = F * d, where W is the work done, F is the force acting on the particle, and d is the displacement of the particle.

3. What is the unit of measurement for work done on a particle?

The unit of measurement for work done on a particle is joules (J). This is the same unit used to measure energy.

4. Can work done on a particle be negative?

Yes, work done on a particle can be negative. This occurs when the force and displacement are in opposite directions, meaning the energy is being transferred away from the particle.

5. How does work done on a particle relate to the particle's kinetic energy?

According to the work-energy theorem, the work done on a particle is equal to the change in the particle's kinetic energy. This means that work done can either increase or decrease the particle's kinetic energy, depending on the direction of the force and displacement.

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