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 Fx 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.
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)]
Fx = k[Q2/(a2 + x2)]cos(θ),
where θ is the angle betwen the force F and the x axis.
Fx = k[Q2/(a2 + x2)][x/√(a2 + x2)] for positive values of x, and
Fx = - 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,
Barron's AP Physics B