Relationship between density of energy and magnetic force

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Discussion Overview

The discussion revolves around the relationship between the density of energy stored in a magnetic field and the magnetic force. Participants explore theoretical connections and mathematical formulations related to this topic.

Discussion Character

  • Exploratory, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks about the relationship between energy density in a magnetic field and magnetic force.
  • Another participant provides the Lorentz force equation, suggesting a need to look up the energy density of a magnetic field.
  • A participant states the formula for energy density in a magnetic field as ((B_0)^{2}) / (2\mu) and seeks a direct formula linking energy density to magnetic force.
  • Another reply suggests solving for B from the energy density and substituting it into the force expression, noting that only the magnitude can be determined.

Areas of Agreement / Disagreement

Participants have not reached a consensus on a direct relationship or formula linking energy density and magnetic force, and multiple approaches are presented without resolution.

Contextual Notes

Participants reference specific formulas and concepts but do not clarify assumptions or dependencies on definitions, leaving some mathematical steps unresolved.

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What is the relationship between density of energy stored in a magnetic field and the magnetic force?
 
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F = q v X B

Homework: Look up the energy density of a magnetic field.
 
The energy of a density field is ((B_0)^{2}) / (2\mu). I am looking for a direct formula as such linking these two. Let's say I have the value for density of energy, how can we find the magnetic force?
 
Solve the energy density for B. Then substitute that into the expression for F. Note, you will only be able to solve for the magnitude.
 

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