A metal rod 30 cm long slides at 3.0 m/s along two rails, in a field of 0.45 T at right angles to…

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A metal rod $30$ cm long slides at $3.0$ m/s along two rails, in a field of $0.45$ T at right angles to the plane of the rails. The rod and the rails, together with a resistor, have a total resistance of $0.90\ \Omega$ . Find the emf, the current, the force that you must apply to keep the speed steady, and the power that you supply.

Need a reminder? The key ideaShow

A rod of length $l$ that moves at speed $v$ at right angles to the field $B$ has $\varepsilon = Blv$ . On rails with a total resistance $R$ , $I = \varepsilon/R$ , the force on the rod is $F = BIl$ , and the power is $P = Fv = I^2R$ . A tilted field counts only by its part at right angles to the rod and to its velocity. A rod that turns about one end has $\varepsilon = \tfrac{1}{2}B\omega l^2$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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