Homework #2
Conceptual Solution

1. (b). The electric field has the greatest magnitude when the equipotential plot is steepest; that is, where the potential is changing most rapidly with distance, so that the equipotential curves are densest. Here this occurs at point I.

2. (d). The electron's potential energy is given by EPE = qV; since its charge q is negative, its potential energy is positive where the potential is negative. The greatest, or most positive, electron potential energy occurs for the smallest, or most negative, potential, which occurs on the -70 V contour at H.
3. (d) Since the question didn't specify a potential difference from B to E, or from E to B, it just asks the magnitude of between points B and E. Since B is at potential 10 V, and E is at potential -40 V, the potential difference is just |10 V - -40 V| = 50 V.
4. (b) The electric field points perpendicular to the equipotentials, in the direction of decreasing potential. At B, the potential decreases toward the left, or toward D.
5. (c) The work done by the electric force in moving a charge between two points is . This question asks for the work required to move a charge between two points, which means external work done against the electric force. This (work against the electric force) is minus work by the electric force, given above. Thus we have

   

   We have moving from A to E, with

   

   Thus

   

   The fact that this sign is positive means an external agent had to do work to move the charge in a direction opposed by the electric force. This makes sense here, since the negative charge moved toward decreasing potential, and the electric force pushes it toward increasing potential.

6. (e) Note that work done by the electric field during a particle's motion obeys ; that is, it depends only on the final and initial potential energies, and not on the details of the path chosen. Here the particle begins and ends with the same electric potential, and hence the same electric potential energy. Thus no work is done (either by or against the electric force). One could calculate separately the work done from B to D, then add to the work from D to C, but these two are guaranteed to cancel to give net work zero.
7. (d) Again, the electric field points perpendicular to the equipotentials, in the direction of decreasing potential. At F, this direction is to the left, toward point H and away from point E. A positive charge feels an electric force which points along the direction of , so that it moves along , away from point E.
8. (e) Near A, the equipotential curves are evenly spaced, meaning that the potential descends at constant steepness from right to left throughout the area. This constant steepness means that the electric field is constant. For constant electric field, we know that ; that is, the electric field points toward decreasing potential, so that the potential drops an amount Es as we move a distance s along the field lines. Thus the potential drop of 40 V as we move 0.4 m along the field lines indicates an electric field magnitude .

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