1) A cyclotron used to accelerate alpha particles (m = 6.65 × 10-27kg , q 3.2 x
ID: 1794044 • Letter: 1
Question
1) A cyclotron used to accelerate alpha particles (m = 6.65 × 10-27kg , q 3.2 x 10-19C) has a radius of 0.7 m and a magnetic field of 2.3 T. (a) What is the period of revolution of the alpha particles? (b) What is their maximum classical kinetic energy? 2) The Superconducting magnet for the experimental MRI studies at a laboratory is a 1 m long solenoid of 60 cm diameter, producing a field of 5 T. The current energizing the device is 250 A. a) How many turns of this 250 A superconductor are in this magnet? b) What is the inductance of the magnet? 3) A coil with length of 11 cm and a cross-section of 2.3 cm2 is connected in series with a 8.0k resistor. A 42.0 V battery is applied across the two devices, and the current reaches a value of 3.20 mA after 6.00 ms. (a) Find the inductance of the coil. (b) How much energy is stored in the coil at the same moment? (c) What is the energy density inside the coil?Explanation / Answer
1)
given, m = 6.65*10^-27 kg
q = 3.2*10^-19 C
r = 0.7 m
B = 2.3 T
a. period of revolution = 2*pi*r/v
but qvB = mv^2/r
hence
v = qBr/m
T = 2*pi*r*m/qBr = 2*pi*m/qB
T = 5.677*10^-8 s
b. maximum classical kinetic energy = 0.5mV^2
V = qBR/m
KE = 1.9957*10^-11 J = 124.732 MeV
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