Electrostatic forces and the principle of superposition

[anam89]

1. Explain what is meant by statement that electrostatic forces obey the principle of superposition?
2. what does it mean to say that physical quantityis (a) quantized or (b) conserved.

 

[Andy Resnick]

The prinicple of superposition means that effects from multiple sources (charge, for example) is simply the sum of effects from each source, considered separately. It holds for linear systems.

A physical quantity is quantized if measured values can only take on discrete values- energies of bound electrons, for example. A conserved quantity is one that does not change over time.

 

[anam89]

question

when we walk briskly across a carpet, you often experience a sparkon touching a door knob.what causes this?and how might it be prevented?

 

[dst]

Homework questions?

 

[kamerling]

The prinicple of superposition means that effects from multiple sources (charge, for example) is simply the sum of effects from each source, considered separately. It holds for linear systems.

I wonder what exactly you mean with a linear system here. The force isn't a linear function of the distance to a charge

 

[anam89]

yes, i mean linear force.

 

[Andy Resnick]

I wonder what exactly you mean with a linear system here. The force isn't a linear function of the distance to a charge

That's a good point. A system characterized by an operator S{} defined as: S{f} = g, where f is the input is considered linear iff

S{a1f1+a2f2} = S{a1f1}+S{a2f2} = a1 S{f1} + a2 S{f2} = a1g1+a2g2. (the a's are constants)

So, for electrostatic force, S{r} = e1*e2/r^2 or whatever. Now for three charges (or two stationary and 1 test charge) we have to be careful to keep track of which r we mean: r1 is the test-charge 1 distance, r2 the test-charge 2 distance. But if you draw a diagram, you can see that the resultant force on the test charge is equal to the summed forces from each of the 2 fixed charges.

Electrostatics and electrodynamics are *usually* linear systems. Nonlinear materials are those that, for example, have a refractive index that varies with intensity. Or performs frequency mixing.

Stress and strain relationships in continuum mechanics are linear only in the limit of infinitesimal deformations. Fluid mechanics is intrinsically nonlinear.