Example of AP Physics B Free Response Problem

The figure above shows two point charges each of charge -Q.
a) Write an expression for the magnitude of the force on the charge placed on the x axis in terms of a, b, Q and fundamental constants.
b) Write an expression for the electrical potential in the origin due to both charges.
c) On the axis below sketch the horizontal component F_x on the B charge as it is moving along the x axis.

d) The B charge is moved from the x axis to the y axis. Sketch the force F on the B charge as it is moved along the y axis.




Answer:
a) The distance between the particles is √(a² + b²).
F = k[QQ/(a² + b²)]
F = kQ²/(a² + b²)

b) V = k(-Q)/a + k(-Q)/b = -kQ(1/a + 1/b)

c) F = k[QQ/(a² + x²)]
F_x = k[Q²/(a² + x²)]cos(θ),
where θ is the angle betwen the force F and the x axis.
F_x = k[Q²/(a² + x²)][x/√(a² + x²)] for positive values of x, and
F_x = - k[Q²/(a² + x²)][x/√(a² + x²)] for negative values of x.
Using a graphic calculator we can sketch the shape of the force as a function of x.


d) F = kQ²/(y-a)² if y > a and,
F = - kQ²/(y-a)² if y < a and,

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Barron's AP Physics B