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Equipotential lines (fields) question?
For a while I have had some questions on how equipotential lines work in fields in physics. I understand that all points on the line have the same potential and that the lines are at right angles to the field lines but what I don't understand is why:
1) When a field is not uniform and the mass/charge is spherical why are the lines more close to one another the closer to the mass charge we are and then become more and more spaced out? Theoretically, shouldn't there be infinite equipotential lines for every possible distance from the mass/charge?
2) Also why when there are two masses close to one another the equipotential lines sort of merge and end up becoming the same the farther away we move from the masses?
2 Answers
- nebLv 75 years agoFavorite Answer
1) Yes, there are an infinite number of equipotential lines. The potential (e.g, electrical potential) falls off continuously as a function of r. The potential is a scalar field, and the so called gradient is derived from the scalar potential. The gradient measures the rate of change in the potential perpendicular to the equipotential line. The gradient depends on 1/r^2 and generally pictorially they show the changes as denser equipotentials to show the magnitude of the gradient is larger at smaller values of r.
2) Intuitively, you should be able to picture two closely spaced charges or masses from a long distance. The distinction between the two get smaller and smaller as you get farther away and ultimately they will just look like a point mass with double the mass or double the charge.
- StephenLv 45 years ago
1
For a point charge, the potential is V = kQ/r
For example suppose kQ =6 then
V = 6/r
r = 6/V
The V=6 volts equipotential is at r= 6/6 =1m
The V=5 volts equipotential is at r= 6/5 = 1.2m
The V=4 volts equipotential is at r= 6/4 = 1.5m
The V=3 volts equipotential is at r= 6/3 = 2m
etc.
You can see the gap between equipotentials 1V different increases as we go outwards.
For any given distance, there is only 1 value of equipotential
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When you are a long way from the mass or charge, the gap between them becomes unimportant. E.g. if the charges, q each, are 1cm apart and you are 1 million metres away, you 'see' a single charge of 2q. The 1cm gap is negligible and the field is virtually the same as that from a single 2q charge.