A solenoid is formed by winding 100 [m] of copper wire such that the solenoid ha

Question

A solenoid is formed by winding 100 [m] of copper wire such that the solenoid has n = 1000 turns per meter. The copper wire is cylindrical, has a radius of r = 1 [mm] (one millimeter) and the resistivity of copper is rho = 1.72 times 10 [Ohm m]. The mass of a proton is approximately 1.67 times 10 [kg]. For what value of the current will the solenoid produce a magnetic field of magnitude 5 [T] Do you need to specify where in the solenoid the magnetic field takes this value? How much power is dissipated as heat in the solenoid? You may assume an ideal current source provides the current you calculated in part to the wire. This hints at why superconducting coils are advantageous in creating strong magnetic fields. A proton is moving at 1% the speed of light (3 times 106 [m/s]) perpendicular to the magnetic field m the solenoid and undergoes uniform circular motion. What is the radius of the proton's trajectory?

Explanation / Answer

a) B=oni (where n is turns per length)

     5=4x10-7*i*1000

    i=3978.87A (that's a LOT of current)

b) P=i2R (where R=L/A)

R=1.72x10-8*100/(x(1mm)2)

=0.547

P=8.67MW

c)r=mv/qB

    =9.1x10-31*3x106/(1.6x10-19*5)

   =3.41m (3.41x10-6 m)

(check my calculations for current.. I have a feeling it's waay too much)

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