Two electrons are a distance r apart, the first electron exerts a force F on the second electron. a) What force does the second electron exert on the first? b) In terms of r, at what distance is the force that the first electron exerts on the second F/9?
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This question is on electric forces between charged particles. A useful equation to consider is Coulomb's law:
F=k(Q1Q2)/R2
Where k is the Coulomb's law constant:
k~9.0x109Nm2/C2
Q is the charge on each particle in Coulombs, R is the distance in metres and F is the force in Newtons.
a) This part is a simple application of Newton's third law, as the first electron is exerting a repulsive force F on the second, the second must also be exerting a repulsive force F on the first. (Every force has an equal and opposite reaction force!)
b) This section requires you to look at Coulomb's law. It is what is known as an inverse square law, this effectively means the force decreases proportionally to the square of the distance, so for the force to have decreased by a factor of 9, the distance must have increased by a factor of the square root of nine, this equals 3, so the new distance is 3r. Nothing else in the equation changes, so they all other terms can be treated as constants and ignored.
This can be seen more explicitly by mathematically manipulating Coulomb's law, however I find it easier and more useful to instead find the answer by just thinking about the underlying link between force and distance in this equation, this means you develop a proper understanding of the inverse square relationship.
