# Charge Density of wire with potential difference

• Nexest
In summary, the problem involves a charged particle moving away from a fixed wire at different distances and speeds. To find the charge density of the wire, one must use the relation \DeltaK = -\DeltaU and \DeltaU = q*\DeltaV, where \DeltaV is the potential difference. However, the electric field in this case is not uniform, so the simplified equation V = -Ed cannot be used. Instead, one must integrate the electric field as a function of distance to find the potential difference. The "d" in the equation represents a differential.
Nexest
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 ($$\Delta$$K = -$$\Delta$$U), which when divided by the given charge of the particle should give the potential difference. Right? ($$\Delta$$U = q*$$\Delta$$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?

Last edited:
Without showing your work, I would guess you may be finding the potential incorrectly. It looks like you are treating E as a constant with the expression V=-E*d. Recall,

$$V=-\int \mbox{Edr}$$

where r is the perpendicular distance from the wire. Your approach to the problem appears correct.

Yes I think I found my problem, I can't use the simplified V = -Ed equation because E is not a uniform electric field in this case.

Can you please explain it in more detail ? How do you calculate the potential difference then if you can't consider it a uniforn electric field ? and what is d ?

*unicorn* said:
Can you please explain it in more detail ? How do you calculate the potential difference then if you can't consider it a uniforn electric field ? and what is d ?
I'm guessing you don't know calculus. chrisk explained it. You must integrate the electric field as a function of distance. The "d" means "differential". If you don't know calculus, then I don't expect you will have any idea what this means.

ok.. nevermind.. i got it.. thanks !

## 1. What is charge density?

Charge density is a measure of the amount of electric charge per unit volume of a material. It is typically expressed in units of coulombs per meter cubed (C/m³).

## 2. How is charge density related to potential difference?

The charge density of a wire is directly proportional to the potential difference applied across it. This means that as the potential difference increases, the charge density also increases, and vice versa.

## 3. What is the formula for calculating charge density?

The formula for charge density is ρ = Q/V, where ρ is the charge density, Q is the amount of charge, and V is the volume of the material.

## 4. How does charge density affect the flow of current in a wire?

Charge density plays a significant role in determining the flow of current in a wire. A higher charge density means there is a greater concentration of charges in the wire, which leads to a stronger electric field and a faster flow of current.

## 5. How does the charge density of a wire affect its resistance?

The charge density of a wire is directly proportional to its resistance. This means that as the charge density increases, the resistance also increases. This is because a higher charge density results in more collisions between the charges and the atoms of the material, making it more difficult for the charges to flow through the wire.

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