Quick Clarification on Work in Electric Field: Negative or Positive?

[betterfuture]

Work done by an electric field on a test charge is negative or positive?

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[theonlytycrane]

The work will be done by an electric force, and will be positive.

 

[betterfuture]

and so the work done is the change in PE, so basically PE becomes (-)?

W=-ΔPE

 

[theonlytycrane]

There are some different energy formulas out there, but I use Work (conservative force) = -deltaPE

deltaPE is negative as a charge accelerates through the E-field, and work is positive.

Another way to look at it is W = F * d. The electrical force will be in the direction that the charge accelerates, making Work positive.

 

[betterfuture]

Just corrected my post. I meant the same. I just don't get why U is negative in the equation for V=-U/q. You know, when determining what potential an electron will naturally flow and what potential a proton will flow? Any ideas here?

 

[theonlytycrane]

The signs get kind of funky, but here's a simple example that might help.

Say we have a positive source-charge +q. The E-field from this source-charge points away from it, in the direction that a positive test charge would go.

If we drop a positive test charge into the near vicinity, it will move away from the source-charge (like charges repel). U = k * q(source) * q(test) / r. The "r" term gets bigger as the test charge moves away, and the test charge decreases potential energy as it moves.

If we drop a negative test charge into the near vicinity, it will move towards the source-charge (opposite charges attract). This time U = k * q(source) * -q(test) / r. The negative sign makes it so that as r gets smaller, U gets more negative. The test charge decreases in potential energy as it moves closer to the source-charge.

Charges always move from higher to lower electrical potential energy, but the direction may differ depending on the sign of the charge.