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(8%) Problem 9: A proton moves in a circular path of the same radius as a cosmic

ID: 1866118 • Letter: #

Question

(8%) Problem 9: A proton moves in a circular path of the same radius as a cosmic ray electron moving at 8.5 x 102 m/s to the Earth's magnetic field at an altitude where the field strength is 1.0 x 10-ST. 25% Part (a) what will the speed of the proton be in mis? as 25% Part (b) What would the radius of the path be in meters if the proton had the same speed as the electron? ?? ? 25% Part (c) what would the radius be in meters if the proton had the same kinetic energy as the electron? 25% Part (d) What would the radius be in meters if the proton had the same momentum as the electron?

Explanation / Answer

a) radius of path of electron, r = m*v/(B*q)

= 9.1*10^-31*8.5*10^6/(1*10^-5*1.6*10^-19)

= 4.83 m

proton speed, v = ?

use, r = m*v/(B*q)

==> v = B*q*r/m

= 1*10^-5*1.6*10^-19*4.83/(1.67*10^-27)

= 4.63*10^3 m/s <<<<<<<<<<--------------------------Answer

b) r = m*v/(B*q)

= 1.67*10^-27*8.5*10^6/(1*10^-5*1.6*10^-19)

= 8.87*10^3 m or 8.87 km <<<<<<<<<<--------------------------Answer

c) KE_proton = KE_electron

(1/2)*mp*vp^2 = (1/2)*me*ve^2

vp = ve*sqrt(me/mp)

= 8.5*10^6*sqrt(9.1*10^-31/(1.67*10^-27))

= 1.98*10^5 m/s

r = m*vp/(B*q)

= 1.67*10^-27*1.98*10^5/(1*10^-5*1.6*10^-19)

= 207 m <<<<<<<<<<--------------------------Answer

d)

P_proton = P_electron

mp*vp = me*ve

vp = ve*(me/mp)

= 8.5*10^6(9.1*10^-31/(1.67*10^-27))

= 4631 m/s

r = m*vp/(B*q)

= 1.67*10^-27*4631/(1*10^-5*1.6*10^-19)

= 4.83 m <<<<<<<<<<--------------------------Answer