Positive charge +Q is uniformly distributed on the upper half of a rod and a negative charge -Q is uniformly distributed on the lower half.What is the direction of the electric field at point P, on the perpendicular bisector of the rod?
A)" $\uparrow$ "
B)" $\downarrow$ "
C)" $\leftarrow$ "
D)" $\rightarrow$ "
E) ""

Question

Positive charge +Q is uniformly distributed on the upper half of a rod and a negative charge -Q is uniformly distributed on the lower half.What is the direction of the electric field at point P, on the perpendicular bisector of the rod? 
A)" $\uparrow$ " 
B)" $\downarrow$ " 
C)" $\leftarrow$ " 
D)" $\rightarrow$ " 
E) ""

Quizplus · Accepted Answer

Since the charges are uniformly distributed, the electric field at point P due to the top half of the rod cancels out with the electric field due to the bottom half of the rod along the horizontal direction, leaving only the vertical component of the electric field. By symmetry, the vertical components of the electric field due to the top and bottom halves of the rod are equal in magnitude, but opposite in direction, so they cancel out. Therefore, there is no electric field along the vertical direction (i.e. perpendicular to the rod), and the correct direction of the electric field at point P is downward, which is represented by the arrow pointing downwards () in choice B.

Positive Charge +Q Is Uniformly Distributed on the Upper Half ↑\uparrow↑

Positive Charge +Q Is Uniformly Distributed on the Upper Half $\uparrow$