Work required to move a charge through an electric field (3D)

In summary, the problem involves finding the work required to move a 6nC charge through an electric field, given the initial point, total length moved, and unit path length vector. The charge is moving in a straight line in the direction specified by the vector. The final position is not necessary to determine, as the distance traveled and starting point are known.
  • #1
GAtechie291
1
0

Homework Statement


"This problem regards the work required to move a 6nC charge through an electric field given by

E =
wolframalpha-20110921163646221.gif


Initial point is at (2,-2,3)

Total length the charge is being moved = 2µm

Unit path length vector: a_l = -6/7 * a_x + 3/7 * a_y + 2/7 * a_z



Homework Equations


W = -Q * integral(E dL, from init position --> final position)


The Attempt at a Solution



I'm having trouble setting up this integral because I'm not sure how to determine the final position given the initial position and the distance traveled. Or is that not necessary?
 
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  • #2
I think the charge is moving in a straight line in the direction given by the above,

"Unit path length vector: a_l = -6/7 * a_x + 3/7 * a_y + 2/7 * a_z"

You know the distance traveled and the starting point.

Good luck!
 

FAQ: Work required to move a charge through an electric field (3D)

What is the formula for calculating the work required to move a charge through an electric field?

The formula for calculating the work required to move a charge through an electric field is W = qEd, where W is the work in joules, q is the charge in coulombs, E is the electric field strength in newtons per coulomb, and d is the displacement in meters.

How does the direction of the electric field affect the work required to move a charge?

The direction of the electric field can either aid or oppose the movement of a charged particle, depending on the direction of the electric field and the direction of the particle's movement. If the electric field and the particle's movement are in the same direction, the work required will be positive. If they are in opposite directions, the work required will be negative.

How is the work required to move a charge through an electric field affected by the magnitude of the electric field?

The work required to move a charge through an electric field is directly proportional to the magnitude of the electric field. This means that as the electric field strength increases, the work required to move the charge will also increase.

Does the work required to move a charge through an electric field depend on the charge of the particle?

Yes, the work required to move a charge through an electric field is directly proportional to the charge of the particle. This means that a particle with a larger charge will require more work to move through the same electric field compared to a particle with a smaller charge.

Can the work required to move a charge through an electric field be negative?

Yes, the work required to move a charge through an electric field can be negative. This occurs when the direction of the electric field is opposite to the direction of the particle's movement, resulting in a negative value for work.

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