Two 0.91-m-long conducting rods are rotating at the same speed in opposite direc

Question

Two 0.91-m-long conducting rods are rotating at the same speed in opposite directions, and both are perpendicular to a 5.3-T magnetic field. As the drawing shows, the ends of these rods come to within 1.0 mm of each other as they rotate. Moreover, the fixed ends about which the rods are rotating are connected by a wire, so these ends are at the same electric potential. If a potential difference of 3.5 x 103 V is required to cause a 1.0-mm spark in air, what is the angular speed (in rad/s) of the rods when a spark jumps across the gap?

Explanation / Answer

We know that electromagnetic force is given by:

EMF = B*v*L

v = EMF/(B*L)

Using given values:

v = 3.5*10^3/(5.3*0.91)

v = 725.68 m/sec

Now angular speed is given by:

w = v/r

w = 725.68/0.91

w = 797.45 rad/sec

Please Upvote. Let me know if you have any doubt.

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