Question about right hand rule (magnetism)

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SUMMARY

The right-hand rule (RHR) is applicable for determining the direction of the magnetic field, force, and current, regardless of whether the vectors are orthogonal. The formula for magnetic force on a charged particle, F = qvB sin(theta), illustrates that the angle theta can vary, meaning the vectors do not need to be at 90 degrees. In practical scenarios, such as a current-carrying wire, the force acting on the wire can be at any angle, but only the component of the force that is orthogonal to the current contributes to the magnetic field. This understanding expands the application of the RHR beyond strict orthogonality.

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  • Knowledge of the Lorentz force law
  • Basic concepts of magnetic fields and forces
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Is the right hand rule for determining the direction of the magnetic field, force, and current only used when the aforementioned vectors are orthogonal to each other? Or, can the RHR be used in other cases as well?
 
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When aren't they orthogonal?
 
They're not always orthogonal I think. The formula for the magnetic force on a charged particle:
F = qvB sin(theta). The sin is the angle between the velocity vector of the charged particle and the magnetic field, and it doesn't have to be 90.
 
Example: A wire with current going through it has a force applied to it which makes it move. The force could be at any angle but only the portion of the force which is orthogonal to the current will make a magnetic field (which is orthogonal to both the current and the portion of force which is orthogonal to the current.

I hope that makes sense.
 

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