Electrostatic forces and the principle of superposition

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Discussion Overview

The discussion revolves around the principle of superposition in electrostatics, exploring its implications and definitions. Participants also touch on the nature of quantized and conserved physical quantities, as well as a related phenomenon of static electricity experienced when walking on a carpet.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants explain that the principle of superposition means the total effect from multiple charges is the sum of the effects from each charge considered separately, applicable in linear systems.
  • One participant questions the definition of a linear system, noting that the force is not a linear function of distance to a charge.
  • Another participant clarifies that they refer to linear force and provides a mathematical definition of linearity in the context of operators.
  • There is a discussion about the careful consideration of distances when calculating forces from multiple charges, emphasizing the need for clear diagrams.
  • Some participants mention that electrostatics and electrodynamics are typically linear systems, while noting exceptions in nonlinear materials and other fields like fluid mechanics.
  • A participant raises a question about the cause of static electricity experienced when walking on a carpet and how it might be prevented.
  • Definitions of quantized and conserved quantities are provided, with quantization referring to discrete measurable values and conservation indicating quantities that remain unchanged over time.

Areas of Agreement / Disagreement

Participants express differing views on the definition of linear systems in the context of electrostatics, indicating that there is no consensus on this aspect. The discussion remains unresolved regarding the nuances of linearity and its implications for electrostatic forces.

Contextual Notes

Participants highlight the complexity of defining linear systems and the conditions under which electrostatic forces can be considered linear. There are also references to the limitations of linearity in other physical contexts, such as fluid mechanics and nonlinear materials.

anam89
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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.
 
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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.
 
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?
 
Homework questions?
 
Andy Resnick said:
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
 
yes, i mean linear force.
 
kamerling said:
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.
 

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