Fa05-MT2-Luk-Soln - Solution to Midterm II Problem 1 Part(a...

Solution to Midterm II Problem 1
Part (a)
Our two spheres have the same charge on them. What this means is that they
will experience a repulsive force between them. Eventually these two spheres
will reach static equilibrium at some angle from the vertical. This situation is
depicted graphically below.
L
l
L
m,q m,q
θ
F
F
F
T
el
g
θ
Our condition for static equilibrium is that the sum of the forces in both the
horizontal and the vertical direction must be zero.
Σ F
x
= 0 and Σ F
y
= 0
To apply these to our problem consider a free body diagram for one of the
spheres. As we can see in the diagram we have three forces acting on each of
the spheres. One is the gravitational force pointing down, one is the electric
force felt because the two charges are near each other, and the last is the tension
in the string. We introduce the angle θ to be the angle between the vertical and
the string. We can see then that our equilibrium conditions now read:
F
T
cos θ = F
g
= mg and F
T
sin θ = F
el
=
q 2
4 πepsilon1
0
l
2