A long conducting cylindrical rod is inside a long conducting enclosure with a s

Question

A long conducting cylindrical rod is inside a long conducting enclosure with a square cross-section as shown to the right.

The rod is maintained at a potential of +5000 volts with respect to the square which is grounded (V=0). The contour lines are equipotentials at V = +4000, +3000, +2000, and +1000 volts.

Select a response for each statement below. (Use 'N', North, towards top of page (+y dir), and 'E', East, to the right (+x dir), 'NE' for in between 'N' and 'E', etc.)
TrueFalseNNEESESSWWNWThe y-component of the E-field at 4 is negative.
TrueFalseNNEESESSWWNWThe direction of the force on a small (-) charge at 9 is ....
TrueFalseNNEESESSWWNWThe direction of the force on a small (+) charge at 9 is ....
TrueFalseNNEESESSWWNWThe direction of the E-field at 5 is ....
TrueFalseNNEESESSWWNWThe magnitude of the E-field at 4 is greater than that at 7
TrueFalseNNEESESSWWNWThe y-component of the E-field at 7 is zero.
TrueFalseNNEESESSWWNWThe E-field at 6 is zero

Calculate the work which would be required to move a charge Q = -73.5 nC from '5' to '8'.

Explanation / Answer

1. False. The E field is directed NW so the y-component is positive.

2. N. Straight up.

3. S. Straight down.

4. SW (at point 5)

5. False. The equipotentials are closer together at point 7 so the voltage change per meter is greater there.

6. True. The field is pointed directly in the positive x direction there.

7. The potential difference between points 5 and 8 is 2000 v, so it will take (-73.5 nC)(2000 V) = -1.47 * 10-4 J of work. The sign is negative, which is correct since the force is attractive and an external force will do negative work moving the particle.

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