Coulomb - expanding (forces must balance, so that charges...

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Coulomb’s Law Example (2-dimensions) Consider 3 charges placed in the shape of an equilateral triangle. Each vertex carries an equal charge: q 1 = q 2 = q 3 = - q (negative) and the side length is d . Forces on each charge are repulsive (triangle wants to expand). Magnitude of forces are all equal: F 13 = F 31 = F 12 = F 21 = F 23 = F 32 = K q 2 d 2 ! F 12 But note that directions of the forces are not always the same. Where can we add a fourth charge q 4 so that all charges are at rest? By symmetry, we expect the location of a positive fourth charge to be at the center of the triangle. But we need to determine the amount of charge needed to keep the triangle from
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Unformatted text preview: expanding (forces must balance, so that charges are static). For particle 1: 12 13 14 F + F + F = (condition for forces to balance at equilibrium) Note that this is a vector equation, and the forces must separately balance in the x and y directions. In component notation, these forces are: F 12 = ! F 12 cos60 ! i ! F 12 sin60 ! j F 13 = ! F 13 i F 14 = F 14 cos30 ! i + F 14 sin30 ! j So balancing each component of the forces gives: i : ! F 12 cos60 ! ! F 13 + F 14 cos30 ! =...
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This document was uploaded on 11/01/2011 for the course PHY PHY2049 at Broward College.

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