A thin rod of length H has a uniform linear charge density ? and lies along the

Question

A thin rod of length H has a uniform linear charge density ? and lies along the y-axis. The lower end of the rod is located a distance D above the origin. We wish to find the electric field, due to this rod, at the origin.
Now suppose the lower half of the rod is negatively charged, while the upper half contains an equal amount of positive charge. What would be the direction of the electric field at the origin in this case? Furthermore, if a negative test charge were released from rest at the origin, would it move in the direction of increasing or decreasing electric potential? (No calculation needed, think qualitatively)

Explanation / Answer

note the negative charge is closer to the origin than the positive charge, so electric field at the origin sue to negative charge is dominant, then the direction of the field is +y direction. if a negative test charge were released from rest at the origin, it would move in the direction of increasing electric potential, so the electric potential energy of the electron would decrease.

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