- #1
mr_sparxx
- 29
- 4
Homework Statement
Three particles with the same charge q are hold together by three strings of the same length l forming an equilateral triangle. The tension in each string is:
a) ## \frac {K q^2 cos 60º}{l^2}##
b)## \frac {K q^2 cos 30º}{l^2}##
c)## \frac {K q^2 sin 60º}{l^2}## or
d)## \frac {K q^2 sin 30º}{l^2}##
It is a multiple choice question.
Homework Equations
Coulomb's law for electrostatic force: ## F = \frac {K q_1 q_2}{d_{12}^2} ##
The Attempt at a Solution
Well, numbering the charges from 1 to 3, we get that the total force acting on the third charge is the sum of the tensions plus the sum of the elecrostatic forces:
$$ \vec F = \vec T_{13} + \vec T_{23} + \vec F_{13} + \vec F_{23} = 0 $$
Furthermore, the symmetry of the problem implies that:
$$ T_{13} = T_{23} = T_{12} $$
$$ F_{13} = F_{23} = F_{12} $$
So, in the two directions where forces lie
$$ \vec T_{13} = - \vec F_{13} $$
$$ \vec T_{23} = - \vec F_{23} $$
And, therefore
$$ T_{13} = F_{13} = \frac {K q^2}{l^2} $$
The tension in the other strings is exactly the same.
I am unable to see my mistake, simple as it may be...
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