Current induced in rotating conductor in Magnetic Field

2 replies · 4K views · last reply
Jimmeh
Messages
9
Reaction score
0

Homework Statement


Printed homework problem: a 2cm conductor parallel to the z axis rotates at 30cm radius at 1600 rev/min, with radial field B = 1.5 a_r T; asks induced voltage and which end is the anode.



Homework Equations


[itex]l = 0.02 m[/itex]

[itex]r = 0.3 m[/itex]

[itex]E = \frac{-d\phi}{dt}[/itex]

[itex]\phi = BA[/itex]


The Attempt at a Solution


[itex]A = \pi 0.32^2 - \pi 0.3^2 = 0.0124\pi[/itex] ...Area "cut" by conductor

[itex]\phi = 1.5a_r0.0124\pi = 0.0186\pi a_r[/itex] ...change in flux in one revolution

[itex]1600 rev/min = 1600 rev/ 60 seconds = 1 rev / \frac{60}{1600} seconds[/itex]

[itex]E = \frac{-0.0186\pi a_r}{\frac{60}{1600}}[/itex]

[itex]E = -0.496\pi a_r V[/itex]

I'd just like someone to verify this please, and also I'm not sure about which end would be the anode. I think it'd be the end closest the origin, since the magnetic field is in the outward radial direction, [itex]a_r[/itex], the emf induced is in the [itex]-a_r[/itex] direction, and thus current would be flowing towards the origin, but I'm not sure if I went about handling the direction vectors the right way.
 
Attachments
  • Printed homework problem: a conductor 2cm long rotates parallel to the z axis at 30cm radius at 1600 rev/min; find the induced voltage for radial field B = 1.5 a_r T, and which end is the anode.
    thing.jpg
    20.7 KB · Views: 577
Anyone? The exam's tomorrow, I'd just like a quick verification...

Thanks
 
It sounds like an inadequate description of the motion. 30 cm from the origin in what direction? And, what is the axis of rotation?

My hunch (without knowing the above information) is that the electric and magnetic forces on a test charge Q in the wire would have to be equal in magnitude, opposite in direction.