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Problem:

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 1.91 cm from the wire it has a speed 2.80E+5 m/s, going away from the wire. When it is at a new distance of 4.01 cm, its speed is 3.20E+6 m/s. What is the charge density of the wire?

Alright so this is how I approached it but didn't get it right:

The difference in kinetic energy at two given distances should be equal to the opposite difference in potential energy ([tex]\Delta[/tex]K = -[tex]\Delta[/tex]U), which when divided by the given charge of the particle should give the potential difference. Right? ([tex]\Delta[/tex]U = q*[tex]\Delta[/tex]V)

The potential difference is equal to -E*d where d is the distance between the two given points and E is the electric field of the wire given by: lambda/2*pi*epsilon*r.

With these you should be able to solve for lambda but I keep getting the answer wrong and I think its because I'm using the wrong r in the equation for the electric field. I thought r should be the distance from the wire to the farthest given point but I wasn't sure...

Can anyone help?

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 1.91 cm from the wire it has a speed 2.80E+5 m/s, going away from the wire. When it is at a new distance of 4.01 cm, its speed is 3.20E+6 m/s. What is the charge density of the wire?

Alright so this is how I approached it but didn't get it right:

The difference in kinetic energy at two given distances should be equal to the opposite difference in potential energy ([tex]\Delta[/tex]K = -[tex]\Delta[/tex]U), which when divided by the given charge of the particle should give the potential difference. Right? ([tex]\Delta[/tex]U = q*[tex]\Delta[/tex]V)

The potential difference is equal to -E*d where d is the distance between the two given points and E is the electric field of the wire given by: lambda/2*pi*epsilon*r.

With these you should be able to solve for lambda but I keep getting the answer wrong and I think its because I'm using the wrong r in the equation for the electric field. I thought r should be the distance from the wire to the farthest given point but I wasn't sure...

Can anyone help?

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