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## 16 February 2011

### How much justification is enough for Right Hand Rules?

An electron moves to the right into a uniform magnetic field, as shown in the diagram.  The question: What is the direction of the force on the electron?  Justify your answer.

The student reasonably asks, how much justification is enough?

"The electron is moving right, so I point the fingers of my right hand to the right.  The magnetic field is down the page, so I put my right palm toward the bottom of the page and curl my fingers.  I extend my thumb, which now points into the page - that would be the direction of the force on a positive charge.  Since this is an electron, I flip the direction of the force, so the electron is forced out of the page."  -- Too much.  We don't need a dissertation.  On a test, one might have just a minute or so to solve this kind of problem.  It's unreasonable to expect a student to provide this level of detail about such a simple problem, especially as the student becomes so proficient that this problem is easy.

"Out of the page -- first right hand rule."  -- Not enough.  There are three right hand rules, which are all taught differently in different physics classes.  And even then, saying that a right hand rule applies isn't much beyond stating a bare answer.  Of COURSE a right hand rule applies -- it's a magnetism question!

"Out of the page.  Use the RHR for the force on a moving charge.  Point right, curl down the page, flip the thumb because the charge is negative." -- Just right.  The right hand rule in use is identified unambiguously.  ("The right hand rule associated with F = qvB would have been good, too.)  The mechanics of the rule are stated clearly but in a shorthand.  Anyone reading this justification would recognize that this student understands why the force on this charge is out of the page.