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I have learned that the right hand screw rule works for your thumb being in the direction of conventional current (positive to negative potential) but also that the right hand screw rule is used for a negatively charged particle placed in a magnetic field. Isn’t there a contradiction here?

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    $\begingroup$ Different right hand rules (and left hand rules) exist for different circumstances and the way you want to interpret things, and usually the people teaching them aren't specific enough about it. It's best just to forget the right hand rules altogether and learn the equation each one comes from, then apply the right hand rule according to the equation, like the Lorentz Force Equation. And when looking such equations do not forget that q is negative when the moving charge is an electron. $\endgroup$
    – DKNguyen
    Commented Apr 22, 2021 at 20:46
  • $\begingroup$ The circumstances of the question are unclear....what are these 2 right-handed screw rules, and how are they applied? $\endgroup$
    – JEB
    Commented Apr 22, 2021 at 20:58

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The only strictly correct answer here is that there is one "right-hand-rule" (RHR) from which all others are to be derived. This is the rule for determining the direction of a cross-product of two vectors. The statement of this rule is that to find the directionality of $vec A\times \vec B$, you first point your finders in the direction of $\vec A$, curl them in the direction of $\vec B$, and then the direction your thumb points is the direction of the cross product (orthogonal to both $\vec A$ and $\vec B$).

Every other rule you will come across will be a special case of this as determined by the equations governing whatever you're looking at. For a first example, take the Lorentz force (for zero electric field since that has no bearing on the current discussion) for a point charge $q$: $$ \vec F=q\vec v\times \vec B. $$ Given $\vec v$, $\vec B$, and $q$, the RHR I described will tell you the direction of $\vec v\times \vec B$. That is all. If $q$ is positive, then $\vec F$ will point in the same direction the RHR found for $\vec v\times\vec B$. If it is negative, then the negative sign will negate the direction so $\vec F$ will point the other way. There are not two different rules for positive and negative charges, there is only the rule determining the direction of the cross-product and the Lorentz force law itself.

The same statements apply to finding the direction of the magnetic field itself about a wire (see the Biot-Savart law). But OP seems to be asking about forces, so I'll leave it here.

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