Two charged rods, each with net charge -Qo, are held in place as shown in the diagram below
a) A small test charge -qo travels from point X toi point Y along the circular arc shown.
i. Draw an arrow at each point (X and Y) to show the direction of the electric force on the test charge at that point.
ii. Is the work done on the charge by the electric field positive, negative, or zero?
iii. Is the electric potential difference positive negative or zero?
b) The test charge is launched from point X with initial speed vo and is observed to pass through point Y. Is the speed of the test charge at point Y greater than, less than or equal to vo?
V = (delta PE)/q
W = Fd
The Attempt at a Solution
a) i. The electric force at X is pointing at southwest direction and force at Y is pointing at North direction
ii. Positive. W = Fd. For the rod on the left, the force exerted on the object is 0, so the rod has no effect on the test charge. However, the rod on the right exerts a positive force on the test charge. This is because the force direction from the rod and the displacement are pointing at the same direction
iii. Negative. The difference in electric energy is positive because point X is closer to the negative rods than point Y. And since V = (delta PE)/q. Delta PE is positive and q is negative, so the electric potential difference must come out to be negative.
b) Greater than. -PE = KE. If electric potential energy is negative, then KE must be positive. Thus, greater velocity
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