**31. ssm Two 0.68-m-long conducting rods are rotating at the same speed in opposite directions, and both are perpendicular to a 4.7-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 4.5 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?

 

w1183

 

The effective area the bar creates for magnetic flux is pL2 for each revolution or period

 

 

We drop minus sign again it is related to polarity and N is 1 here.  Period relates to angular speed as

 

 

Since the rods swing in opposite directions their free ends are going to be at oppositely signed polarities

 

Solve for ω

 

 

 

 

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This page last updated on June 24, 2018