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Re: Electrostatics problem



The "proofs" I have seen here so far have been flawed, incomplete, or
overly difficult. Allow me to propose an exceedingly simple geometric
argument:

Adopting Bob's notation, i.e.,

T1,T2 = angles of the strings from the vertical
F = the coulomb force magnitude.

1. Note that the strings and the line joining the masses form an
isosceles triangle. Call the two equal angles T3.

2. Draw vector force triangles for each mass recognizing the
equality of the two electrostatic forces and the two
gravitational forces and recognizing the angle T3 at the
vertices formed by the electrostatic and tension forces.

3. From the triangle of forces for body 1, the law of sines says:

sinT1/F = sinT3/mg

From the triangle of forces for body 2, the law of sines says:

sinT2/F = sinT3/mg

With only the most obvious added assumption that T1 and T2 are both acute,
it can be ssen by inspection that T1 = T2.

QED?

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm