How to Calculate Work Required for Moving a Charge in 2D Electric Field

In summary, the conversation discusses a 2D problem involving calculating the work required to move a charge from infinity to a specific point. The electric field and potential are also mentioned, and the topic of parametrization is brought up as a possible solution. It is confirmed that a parametrization can be used, as long as the path is continuous and differentiable. The final integral form for calculating the work is provided.
  • #1
linda300
61
3
Hey,

I've been working on this problem, it starts by asking for the potential, then from that the electric field, and finally it asks to calculate the work required to move a charge from infinite to the point it was originally.

It's a 2D problem so the electric field was E = (Ex,Ey) and the location of the particle is at (a, b).

W = ∫F . dl

and F = qE = q (Ex,Ey),

My question is, how do i integrate both x,y in the vector seperately from infinity to a or b?

Do I first do the only the Ex component and set y=b, then to work calculated from that add the work calculated using the Ey component and setting x=a ?

Or use parametrization ψ(x) = 1/t(a,b) 0<t<1 so infinity initially and (a,b) at t=1

then do ∫F(ψ) . -1/t^2(a,b) between 0 and 1,

I'm just unsure if your allowed to have a parametrization like that, which involve infinity since should be continuously differentiable. But in this case I want it to be infinity initially
 
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  • #2
and then (a,b) at t=1.Thanks in advance for any help Yes, you can use a parametrization like that, as long as the path from infinity to (a, b) is continuous and differentiable. The integral would be of the form W = ∫F(ψ(t))*(-1/t^2(a,b))dtwhere F(ψ(t)) is the force field at the point (a, b). Integrating with respect to t should give you the total work required.
 

What is the formula for calculating work required for moving a charge in a 2D electric field?

The formula for calculating work required for moving a charge in a 2D electric field is W = qEd, where W is the work in Joules, q is the magnitude of the charge in Coulombs, E is the strength of the electric field in Newtons/Coulomb, and d is the distance moved in meters.

What is the unit of measurement for work in the context of 2D electric fields?

The unit of measurement for work in the context of 2D electric fields is Joules (J).

How do I determine the direction of the work when calculating it for a 2D electric field?

The direction of the work is determined by the direction of the electric field. If the charge is moving in the same direction as the electric field, the work is positive. If the charge is moving in the opposite direction of the electric field, the work is negative.

Can I use the same formula to calculate work for moving a charge in a 3D electric field?

No, the formula for calculating work in a 2D electric field is specific to that context. In a 3D electric field, the formula is W = qEcosθd, where θ is the angle between the direction of the electric field and the direction of the charge's movement.

What is the significance of calculating work in a 2D electric field?

Calculating work in a 2D electric field helps us understand the amount of energy required to move a charge in a specific direction in the presence of an electric field. It also allows us to analyze and predict the behavior of charged particles in various electric fields.

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