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Two 0.78-m-long conducting rods are rotating at the same speedin opposite direct

ID: 1677772 • Letter: T

Question

Two 0.78-m-long conducting rods are rotating at the same speedin opposite directions, and both are perpendicular to a 4.0-Tmagnetic field. As the drawing shows, the ends of these rods cometo within 1.0 mm of each other as they rotate. Moreover, the fixedends about which the rods are rotating are connected by a wire, sothese ends are at the same electric potential. If a potentialdifference of 5.6 x 103 V is required to cause a 1.0-mmspark in air, what is the angular speed (in rad/s) of the rods whena spark jumps across the gap?

Two 0.78-m-long conducting rods are rotating at the same speedin opposite directions, and both are perpendicular to a 4.0-Tmagnetic field. As the drawing shows, the ends of these rods cometo within 1.0 mm of each other as they rotate. Moreover, the fixedends about which the rods are rotating are connected by a wire, sothese ends are at the same electric potential. If a potentialdifference of 5.6 x 103 V is required to cause a 1.0-mmspark in air, what is the angular speed (in rad/s) of the rods whena spark jumps across the gap?

Explanation / Answer

The magnitude of the emf across the rod is      V= B L^2 From the above equation is given as      = V / B L^2         = 5.6x10^3 /(4)(0.78)^2        = 2301 rad /s
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