Need help with Magnetic Force (Calculus)

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Discussion Overview

The discussion revolves around the magnetic force as described by the formula F=qv x B, focusing on the orientation of the force vector in relation to the velocity and magnetic field vectors. Participants explore the implications of the right-hand rule, the nature of orthogonality in vector relationships, and the arbitrary choices involved in defining directions in magnetic fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that while the force vector is orthogonal to both velocity and magnetic field vectors, there are two possible directions for the force vector, raising questions about why one direction is chosen over the other.
  • Another participant clarifies that the right-hand rule is a mnemonic for determining directions when the vectors are orthogonal, but emphasizes that the vectors do not need to be orthogonal for the cross product to be computed.
  • Some participants argue that the choice of using the right-hand rule or left-hand rule is arbitrary, as long as the same rule is applied consistently throughout calculations.
  • There is a suggestion that the definition of the magnetic field direction is arbitrary, and changing the definition could lead to different signs in calculations.
  • One participant expresses that the form of the equation itself may not have a definitive explanation, suggesting that it reflects a fundamental aspect of nature.

Areas of Agreement / Disagreement

Participants generally agree that the choice of direction in the context of magnetic forces is arbitrary and that different conventions (right-hand vs. left-hand rules) can be used. However, there is no consensus on the deeper implications of why the equation takes its specific form or the nature of the magnetic force itself.

Contextual Notes

Participants acknowledge that the discussion involves assumptions about the definitions of vectors and coordinate systems, and the implications of these choices are not fully resolved.

ohshiznit422
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Ok, so. The formula is F=qv x B, meaning that the force vector is an orthogonal vector equal to the cross product of vectors qv and B. There are, however, 2 orthogonal vectors, in each direction. The thing I am having trouble understanding is why is one direction chosen over the other. I understand that this is demonstrated in the right hand rule, but the magnetic forces do not orient themselves in such a way just because that's the shape of my hand.
 
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There is no reason \vec{v} and \vec{B} need to be orthogonal, but \vec{F} is gaurenteed to be orthogonal to both. The right hand rule is just an easy way to remember the directions the vectors will point in in the special case when
\vec{v} and \vec{B} are orthogonal. If they aren't, then you have to actually do the work of computing the cross product.
 
I understand that the force vector will always be orthogonal, but there are 2 directions it can choose. For example, if qv is in the positive x direction, along the x axis, and b is in the positive y direction, along the y axis, the force vector can exist in either the positive OR negative z direction. I'm asking why the force aligns to any particular direction, and how it does so.
 
It is just an arbitrary decision.

The bottom line is that we could use the left hand rule or the right hand rule in any calculation we want, as long as we use the same rule consistently.
 
The definition of the magnetic field direction is arbitrary - with a reversed definition, it would be a left-hand rule.
Swapping the sign of F or v would be possible mathematically, too, but I think this would be quite unintuitive.
 
Yea, it's because, arbitrarily, we choose to use a right-handed cooridnate system. If you used a left-handed system, things would have different signs.

If you want to ask the question of why the equation has that form at all, then you're asking something which probably has no answer - that's the way nature is.
 

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