Two solenoids are nested coaxially such that their magnetic fields point in oppo

Question

Two solenoids are nested coaxially such that their magnetic fields point in opposite directions. Treat the solenoids as ideal. The outer one has a radius of 20 mm, and the radius of the inner solenoid is 10 mm. The length, number of turns, and current of the outer solenoid are, respectively, 21.9 cm, 585 turns, and 4.03 A. For the inner solenoid the corresponding quantities are 18.7 cm, 365 turns, and 1.79 A. At what speed, V_1, should a proton be traveling, inside the apparatus and perpendicular to the magnetic field, if it is to orbit the axis of the solenoids at a radius of 5.81 mm? v_1 = And at what speed, V_2 for an orbital radius of 16.3 mm? v_1 =

Explanation / Answer

Magnetic field due to outer solenoid , B1 = u*N1*I1/L1

= 1.26*10^-6*585*4.03/0.21

= 0.0136 T

And the magnetic field due to inner solenoid ,

B2 = 1.26*10^-6*365*1.79/0.187

= 0.0044 T

So, net magnetic field , Bnet = 0.0136 - 0.0044 = 0.0092 T

For circular motion, mv^2/R = qvB

So, v = qBR/m = 1.6*10^-19*0.0092*5.81*10^-3/(1.67*10^-27)

= 5121 m/s

Now, for orbital radius 16.3 mm:

v = 1.6*10^-19*0.0092*(16.3*10^-3)/(1.67*10^-27)

= 14367 m/s

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