Relationship between density of energy and magnetic force

AI Thread Summary
The discussion focuses on the relationship between energy density in a magnetic field and magnetic force, specifically using the formula F = q v X B. The energy density of a magnetic field is given by the equation (B_0)² / (2μ). To find the magnetic force from a known energy density, one can solve for B using the energy density formula and then substitute that value into the force equation. This approach allows for calculating the magnitude of the magnetic force based on energy density. Understanding this relationship is crucial for applications in electromagnetism and physics.
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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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