Two horizontal parallel conducting rods are connected such that a conducting crossbar free to slide along them

Question:

Two horizontal parallel conducting rods are connected such that a conducting crossbar free to slide along them has a constant current \(I\) running through it (Figure P27.34). The rods are separated by a distance \(\ell\) and are in an external uniform magnetic field of magnitude \(B\) directed out of the page. The crossbar has a length \(\ell\) and mass \(m\).

(a) In which direction does the crossbar move?

(b) If there is a coefficient of static friction \(\mu_{s}\) between rods and crossbar, what is the minimum current \(I_{0}\) necessary for the crossbar to move?

Data from Figure P27.34

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