Question

3 charges each of 20micro coulomb are placed along a straight line. successive charges being 2metre apart from each other. calculate the force on the charges at the right end​

Answer 1

Answer:

Forces between charges obey Coulomb’s law:

F⃗ 12=kq1q2r2r^12

Here the “12” subscript on the force means the force on 1 exerted by 2 and on the unit vector it means “from the object exerting the force (2) to the object feeling the force (1).” r is the distance between the two objects

This is a 1D problem, so the unit vector isn’t so complicated, we could just call it i^ , but I generally prefer to rewrite this in a more friendly to use fashion as:

F⃗ 12=kq1q2r3r⃗ 12

The reason for this is that most students I find have difficulty with unit vectors, particularly in more than 1 dimension, which the meaning of r⃗ 12 is clear - you are giving someone directions on how to walk from 2 (the object exerting the force) to 1 (the object feeling the force).

The only other piece of information you need to know is that forces add. So if you want the force on the right hand object you need to calculate the force from the left hand object (which is 4 m away) and add it to the force from the middle object (which is 2 m away). Since all the charges are positive and in a line, both those forces are to the right (repulsive) and just add in magnitude. Since this sounds like it may be a homework problem I’ll leave the rest of the work(plugging in the numbers) as an exercise for the reader.