Archive for October 5, 2014

A Problem of Wires on the Rails

Posted in Cute Problems with tags , , , on October 5, 2014 by telescoper

It’s been a long time since I posted a cute physics problem so here’s one about magnetism for your edification and/or amusement.

Two long wires are laid flat on a pair of parallel rails perpendicular to the wires. The spacing d between the rails is large compared with x, the distance between the wires. Both wires and rails are made of material which has a resistance ρ per unit length. A magnetic flux density B is applied perpendicular to the rectangle formed by the rails and the wires. One wire is moved along the rails with uniform speed v while the other is held stationary. Derive a formula to show how the force on the stationary wire varies with x and use it to show that the force vanishes for a value of x approximately equal to μ0v/4πρ.

Give a physical interpretation of this result.

HINT: Think about the current induced in the wires…

 

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