Problem 1: Suspended Charges (20 points) Two charges of identical mass m, one wi

Question

Problem 1: Suspended Charges (20 points) Two charges of identical mass m, one with charge q and the other with charge 51, hang from strings of length L from a common point. Assume that the charge q in relation to the mass m is such that any angle you're looking for is very small, and find an approximate expression for the angle that each charge makes with respect to the vertical. Check (show us!) that the units work out, and that the limiting behavior for large mass, large length, and/or small q are sensible.

Explanation / Answer

Given,

m1 = m2 = m ; length l

q1 = q and q2 = 2q

Let T be the tension in the string

In y direction:

T sin(theta) = F(electric)

T sin(theta) = q E (1)

In x direction:

T cos(theta) = F(gravity)

T cos(theta) = mg (2)

(1)/(2)

tan(theta) = qE/mg

theta = tan^-1(qE/mg)

So for q,

theta = tan^-1(qE/mg)

for 2q

theta = tan^-1(2qE/mg)

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