Lecture 13 - Force on a current-carrying wire Every charge...

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Force on a current-carrying wire • Every charge q ii the wire moving at the constant drift velocity v D will experience a force f B =q v D × B . Now just count up the moving charges. If the wire has length L and cross sectional area A, this can be written as N=nAL, where n is the number density of the charge carriers. • The total force is then F B =N f B =L(Anq v D B . Recognize s the current density J and nq s JA the current n D as the current density J, and Anq v D as JA the current. • The force on the wire is then F B =IL u × B , where u is a unit vector that points in the direction of the current flow. L B u v D n A I=JA=(nqvD)A F B
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orce on a current loop or circuit Force on a current loop or circuit •Current very often flows in complete circuits. The force on such a circuit from a constant magnetic field is zero! •The easy way to see this is that for every piece of wire in a ircuit carrying current I to the right, for example, there must circuit carrying current I to the right, for example, there must be another piece carrying the current to the left in a complete circuit. These two pieces will experience magnetic rces that cancel forces that cancel. •More formally, we can write the magnetic force as r r his is zero because the sum of displacements around a [ ] B r d I F B r × = •This is zero because the sum of displacements around a closed path must be zero.
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cute observation A cute observation • In a constant B-field, the force on any piece of wire in a plane that does not cross itself is just F B =IDB t × B , where D is the distance between the ends of the wire, and t is a nit vector that points from the end where the current unit vector that points from the end where the current comes in to the end where it goes out.
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Lecture 13 - Force on a current-carrying wire Every charge...

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