Finding charge density of a wire

In summary, a particle with a charge of +2e and mass of 6.70E-27 kg moves away from a fixed long charged straight wire. Its speed increases from 2.20E+5 m/s to 4.00E+6 m/s as it moves from a distance of 1.61 cm to 4.01 cm. The potential energy lost by the particle is equal to its change in kinetic energy, which can be found by integrating the electric field along a line. The electric field is related to the electrostatic potential V, which can be used to find the charge density of the wire. To find the appropriate line to integrate along, one should consider how the charge is moving away from the
  • #1
hanagasumi
11
0
1. Consider a long charged straight wire that lies fixed and a particle of charge +2e and mass 6.70E-27 kg. When the particle is at a distance 1.61 cm from the wire it has a speed 2.20E+5 m/s, going away from the wire. When it is at a new distance of 4.01 cm, its speed is 4.00E+6 m/s.



2. What is the charge density of the wire?



3. I attempted to do this question but had no idea how would I approach this, I thought:
1) I find total KE by using 1/2(mv^2+mv'^2), and this KE is equivalent to the -U of the system,
2)I know that dU=Q*dV
3) dV= - (integral) E*ds, but I'm not sure which distance I should use.
4)I know that E=lambda/(2pi*r*e0)

Then I have no idea how should I interconnect my information, and I'm confused if about the change in KE and U, and the actualy KE and U. Also, if we are supposed to integrate this, I don't know how to define the upper and lower limit for the function.

Can anyone please help me? I'm really confused on how to do this question.


Thank you very much in advance!
 
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  • #2
In this case the potential energy lost by the charge will be equal to its change in kinetic energy.

You know the electric field due to a long straight wire, it might help you to find the electrostatic potential V. You've written down how it relates to E, it means integrating the E field along a line.

What do you think would be an appropriate line to integrate along? Think about how the charge is moving away from the wire! (It starts a some distance 'a' away from the wire, then is found again a new distance 'b' away).
 
  • #3
JesseC said:
In this case the potential energy lost by the charge will be equal to its change in kinetic energy.

You know the electric field due to a long straight wire, it might help you to find the electrostatic potential V. You've written down how it relates to E, it means integrating the E field along a line.

What do you think would be an appropriate line to integrate along? Think about how the charge is moving away from the wire! (It starts a some distance 'a' away from the wire, then is found again a new distance 'b' away).

Thank you so much! I'm kind of getting this now, I'll go try it again.
 

1. What is charge density?

Charge density is a measure of how much electric charge is present per unit volume of a material. It is typically denoted by the symbol ρ (rho) and has units of coulombs per cubic meter.

2. How do you find the charge density of a wire?

To find the charge density of a wire, you need to know the total charge on the wire and its length. Then, you can use the formula ρ = Q/L, where Q is the charge and L is the length of the wire. This will give you the charge density in coulombs per meter.

3. What factors affect the charge density of a wire?

The charge density of a wire is affected by the amount of charge on the wire, the length of the wire, and the type of material the wire is made of. Materials with higher conductivity will have a higher charge density than materials with lower conductivity.

4. How does charge density relate to electric fields?

Charge density is directly related to the strength of the electric field in a material. The higher the charge density, the stronger the electric field will be. This is because a higher charge density means there are more charges present to interact with the electric field.

5. Can the charge density of a wire change?

Yes, the charge density of a wire can change if the amount of charge or the length of the wire changes. Additionally, the charge density can also change if the wire is made of a different material with a different conductivity. However, the total charge on the wire will always remain constant, as charge is conserved.

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