The figure shows a homo polar generator, which has a solid conducting disk as ro

Question

The figure shows a homo polar generator, which has a solid conducting disk as rotor and which is rotated by a motor (not shown). Conducting brushes connect this emf device to a circuit through which the device drives current. The device can produce a greater emf than wire loop rotors because they can spin at a much higher angular speed without rupturing. The disk has radius R = 0.260 m and rotation frequency f = 4200 Hz, and the device is in a uniform magnetic field of magnitude B = 52.0 mT that is perpendicular to the disk. As the disk is rotated, conduction electrons along the conducting path (dashed line) are forced to move through the magnetic field. (a) For the indicated rotation, is the magnetic force on those electrons up or down in the figure? (b) Is the magnitude of that force greater at the rim or near the center of the disk? (c) What is the work per unit charge done by that force in moving charge along the radial line, between the rim and the center? (d) What, then, is the emf of the device? (e) If the current is 51.0 A, what is the power at which electrical energy is being produced?

Explanation / Answer

a) as the current flows down so , the electrons must be moving up

b) magnetic force is given by q* *v*B

where r is the distance from the centre ,

v is the velocity.

now , for a constant angular velocity ,

v = sqrt (w*r)

hence magnetic force becomes,

F=q* B*sqrt( wr)

hence with higher radius the force increases.

c) work done per charge = Force * dispacement

so work done = intergral of B* sqrt( w) * r0.5 dr from 0 to R

= 3.378 r1.5 ] 00.26

=0.746 J

d) emf is given by B* r *v

=B* r* sqrt (w*r)

=52x10-3 * 0.26 * sqrt( (2*pi* 4200)* 0.26)

= 1.119 V

e) power = V* I

= 1.119 V * 51 A= 57.11 W

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