Two charged rods each with net charge Qo are held in place a

Two charged rods, each with net charge -Q_o are held in place as shown in the top view diagram below. A small test charge -q_o travels from point X to point Y along the circular arc shown. Draw an arrow on the diagram at each point (X and Y) to show the direaction of the electric force on the test charge at that point. Explain why you drew the arrows as you did. Is the work done on the charge by the electric field positive, negative, or zero? Explain. Is the electric potential difference deltaV_xr positive, negative, or zero? Explain. The test charge is launched from point X with an initial speed v_0 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 v_a? Explain your reasoning.

Solution

a]i]

The below uploaded image gives the direction of E , here a net negative charge moves from point X to Y , So direction of E is towards the arc since the direction of E originates from positive charge and ends in negative charge.

The electric force at X is pointing at southwest direction and force at Y is pointing at North direction

ii]

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

Hence work done is positive.

iii]

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.

Potential is negative.

b]

-PE = KE. If electric potential energy is negative, then KE must be positive. Thus, greater velocity