Sapling Learning Two solenoids are nested coaxially such that their magnetic fie

Question

Sapling Learning Two solenoids are nested coaxially such that their magnetic fields point ln opposite directions. Treet the solenoids as ideal. The outer one has a radius of 20 mm, and the radius of the Inner solendid is 10 mm, The length, of tums, and cument of the outer solenoid are, respectively, 20.3 cm, 533 tums, and For the inner the speed, v. should a proton be traveling, inside the apparatus and perpendicular to the magnetic At if it is field, are 18.1 cm, and to orbit the axis of the solenoids at a radius of 5.79 mm? Number m/ s And at what speed, V2, for an orbital radius of 14.7 mm? Number m/s O Previous ® Gve up s view solution Check Answer 0 Ned Ext Hint

Explanation / Answer

The required force is equal to m v^2/r

Which is provided by the magnetic force.

The magnetic force = q v cross B = q v B

Since these two forces are equal, then qvB = mv^2/r

qBr = mv

v = qrB/m

1)

Magnetic field = mu n I

The net magnetic field inside the inner coil = mu n1 I1 - mu n2 I2 = 4pi*10^-7(533*4.31/0.203-309*1.93/0.181) = 0.01 T

v1 = 1.6*10^-19*5.79*10^-3*0.01/(1.67*10^-27) = 5547.30539 m/s

2)

The net magnetic field inside the inner coil = mu n1 I1 = 4pi*10^-7(533*4.31/0.203) = 0.0142 T

v1 = 1.6*10^-19*14.7*10^-3*0.0142/(1.67*10^-27) = 19999.0419 m/s

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