PhysicsLAB AP Free Response Question
2010 C1 E&M

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A charge +Q is uniformly distributed over a quarter circle of radius R, as shown above. Points A, B, and C are located as shown, with A and C located symmetrically relative to the x-axis. Express all algebraic answers in terms of the given quantities and fundamental constants.
 
 
(a) Rank the magnitude of the electric potential at points A, B, and C from greatest to least, with number 1 being greatest. If two points have the same potential, give them the same ranking.
 
 
Justify your rankings.
 

Point P is at the origin, as shown below, and is the center of curvature of the charge distribution.
 
 (b) Determine an expression for the electric potential at point P due to the charge Q.

 (c) A positive point charge q with mass m is placed at point P and released from rest. Derive an expression for the speed of the point charge when it is very far from the origin.

 
(d) On the dot representing point P below, indicate the direction of the electric field at point P due to the charge Q.
 

 (e) Derive an expression for the magnitude of the electric field at point P.




 
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