Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A metal rod m long turns about one end, in a plane at right angles to a uniform field of T. It makes turns each second. Find the speed of the free end, and the emf between the ends of the rod. What is the potential difference between the middle of the rod and the pivot?
A rod of length that moves at speed at right angles to the field has . On rails with a total resistance , , the force on the rod is , and the power is . 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 .
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.
Step 1. The angular speed. . The speed of the free end is .
Step 2. The emf. .
Step 3. The middle point. The part from the pivot to the middle has length m. So .
Answer: m/s, V and V.
Check. The potential difference grows as the square of the distance from the pivot. Half the length gives a quarter of the emf: V.
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