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In flemming's left hand rule, thumb represents the direction of motion/ magnetic force, index is magnetic field and middle finger is current while in right hand rule of magnetism, thumb represents magnetic force, index is direction of current and middle finger is magnetic field. Why is the role for index and middle finger reversed in, what it seems like, the same conditions. What am I not understanding here?

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3 Answers 3

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These rules come straightforwardly from the Lorentz force equation: $$\vec F=q\left(\vec v\times\vec B\right)$$ where $\vec F$ is along the of motion/magnetic force, $q\vec v$ is along the direction of current (or opposite, depending on sigh of q) and $\vec B$ is along the magnetic field.

From this we can see that $\vec F$ will be along the direction perpendicular to both current and field in such a way that when we curl our right hand from the direction of $\vec v$ to that of $\vec B$, our thumb points in the direction of $\vec F$.

However, if we do the same with our left hand, our left thumb will point in the direction opposite to that of the right thumb! This is because the left hand is not exactly the same as the right hand but a reflection of the right hand. To see why this is important, consider your hand and reflection of your hand in a mirror. What this means is that for both hands, up/down is up/down, left/right is left/right, but in/out is out/in! And this is exactly why our force (thumb) was pointing in the wrong direction.

The left and right-hand rules in physics have the same fingers representing the same things. The left-hand is used because a × b = - b × a. As the charge of an electron is negative the right-hand rule would point in the opposite direction.

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  • $\begingroup$ So basically, flemming's left hand rule and right hand palm rule are variations for finding out the same thing(s)? $\endgroup$
    – Agam Gupta
    Commented Mar 1, 2020 at 15:34
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Fleming's two rules are very similar, but they must not be confused. When a current causes motion (like in a d.c. motor), Fleming's left hand rule applies. When motion causes current (like in a generator), Fleming's right hand rule applies. Since these two phenomena are the exact opposite from each other, it makes sense that direction of current would be opposite from each other.

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To add to Dhruv Kapu's answer, if the rules were not opposite then we could easily make electrically-driven perpetual motion machines.

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