Work on a charge inside a Variable Electric Field

AI Thread Summary
The discussion centers on calculating the work done to move a point charge in a variable electric field described by E = (5.04x + 84.2) x 10^4 i N/C. The user initially calculated the change in potential energy (ΔU) and found it to be -30.62 J, leading to confusion about the sign of the work done. Clarifications indicate that a negative change in potential energy implies positive work done on the charge, resulting in a final work value of 30 J. The conversation emphasizes the importance of correctly interpreting the relationship between potential energy and work in electric fields. The conclusion confirms that the original calculations were correct, with the electric field exerting a force in the positive x direction.
Alan I
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Homework Statement


A variable electric field permeates all space:

E= (5.04x+ 84.2)x104i where x is in meters and E is in N/C

How much work is done to move point charge q = 8.03 μC at constant velocity along the x-axis from point A at (3.63 m,0) to (7.67 m,0)? The sign will indicate who does the work.

NOTE: This requires integration!

Homework Equations


ΔU=-q∫Eds

The Attempt at a Solution


Δu=-(8.03x10-6x104∫(5.04X+84.2)dx
-(8.03x10-2)*[5.04X2/2+84.2X]3.637.67
=-30.62J

Are the limits wrong or the integral itself? Any hints would be greatly appreciated!
 
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You have written the change in potential energy. If the change in potential energy is negative, the work on the charge is positive. Compare with computing the work as the line integral of the force.
 
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Likes Alan I
Orodruin said:
You have written the change in potential energy. If the change in potential energy is negative, the work on the charge is positive. Compare with computing the work as the line integral of the force.

OK I think I got it. So the mistake was the sign bc ΔU=-W=-∫F*dl , so since I got ΔU=-30J ⇒ W=30J.
 
I think the original answer is correct. The E field imparts a force in the +x direction on the charge so the work done ON the charge is negative.
 
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