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A proton, with a charge of +e (= + 1.6 x 10^19 C), and a mass of 1.7 x 10^-27 kg

ID: 2006048 • Letter: A

Question

A proton, with a charge of +e (= + 1.6 x 10^19 C), and a mass of 1.7 x 10^-27 kg, is accelerated from rest through a potential difference of 10,000 volts, then enters a region where there is a uniform magnetic field of 0.5 Teslas in a direction perpendicular to the velocity of the proton. As shown below, the proton makes a "U turn", and leaves the magnetic field region in the opposite direction from its initial velocity.

A) What is the speed of the proton as it enters the magnetic field region?
B) What is the speed of the proton as it leaves the magnetic field region?
C) What is the magnitude of the magnetic force on the proton while it is in the magnetic field region?
D) What is the radius of the half-circle that the proton makes in the magnetic field region?
E) How long is the proton in the magnetic field region?
F) If the magnetic field is increased to 5 Teslas, how do the answers to parts a-e change?

Explanation / Answer

Given: (a) charge of the proton = q = +1.6x10-19 C mass of the proton = m = 1.7 x 10-27 kg acclelerates through the potential = V = 10,000 volt acc. to conservation of energy electrical energy appliedto the proton is equal to its Kinetic energy   q V = 1/2 mv2 thus,  v =( 2 q V / m )                 = (2 x 1.6x10-19x 10,000x /1.7x10-27)                  = 137.19x 104                     = 1.3719 x106 m/s (b)           when it leaves from the magnetic field                    the velocity of the proton is                         v = 1.3719x106 (remains constant as in electric field ) (c)           Magnetic force acting on the proton is                 F = q v B                      = (1.6x10-19)(1.3719x106)(0.5)                       =  1.09752 x10-13 N (d)            radious of the half circle that the proton makes in the magnetic field                   is r = mv /B q = (1.7 x 10-27 )(1.3719x106) /(0.5) (1.6x10-19)                                            = 2.9125 x 10-2 m (e)                 time for which proton is in the magnetiv field is                      T = 2r / v = 2 (3.14)(2.9125 x 10-2 ) / ( 1.3719x106 )                                          = 13.33 x 10-8 sec (f)               If B change to = 5 T        then ,          (a)      doesn't change              (e)      doesn't change            (Note: both will not depends upon the B value)         (f)               If B change to = 5 T        then ,          (a)      doesn't change              (e)      doesn't change            (Note: both will not depends upon the B value)                                     

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