Which Point Requires the Most Work to Reach in an Electric Field?

[Soaring Crane]

Homework Statement

The work required to bring a negatively charged body from very far to either of the points indicated in the figure is greatest for point _____.

a. point A

b. point B

c. point C

d. point D

e. point E

Homework Equations

U = q_0*V or W (a-b) = (q*q_0)/(4*pi*epsilon_0)*[(1/r_a) -(1/r_b)]

The Attempt at a Solution

The negatively charged particle is moving against the electric field. As indicated by the equipotential lines, the electric field is strongest near the positive charge, so the potential V is greatest near the positive charge. If V is greatest at E, then won't the work at this point be greatest? (Or did I reverse it since a negative charge is involved and q*q_0 is negative?)

Thanks.

 

[anathema]

Hello,

You are correct that the work required to bring a negatively charged body from very far to a specific point is greatest when the potential at that point is highest. However, in this case, the potential at point E is actually the lowest (since it is closest to the negative charge) and therefore, the work required to bring the negatively charged body to point E would be the least.

Therefore, the correct answer is point A. This is because point A is farthest from the negative charge and therefore has the highest potential, requiring the most work to bring the negatively charged body to that point.

I hope this helps clarify things for you! Let me know if you have any other questions.

 

[m2003]

Your reasoning is correct. Since the electric field is strongest near the positive charge, the potential is greatest near the positive charge. The work required to bring a negatively charged body from very far to a point with a high potential is greater than the work required to bring it to a point with a lower potential. Therefore, the work is greatest at point E, where the potential is highest.