An electron with a kinetic energy of 22.5eV moves into a region of uniform magne

Question

An electron with a kinetic energy of 22.5eV moves into a region of uniform magnetic field B of magnitude 4.55 x 10-4 T. The angle between the directions of B and the electron's velocity is 65.5 (degrees).

a.) What is the radius and pitch of the electron's trajectory? Provide a sketch of the orbit including the velocity & magnetic field vectors & projections of velocity along appropriate perpendicular directions.

b.) What is the period of revolution?

c.) What will happen to the pitch & radius if electron's energy decreases to 16.5 eV?

d.) How will trajectory change, if for the initially given energy, the magnetic field is increased to 4.55 mT?

e.) How will trajectory change if a proton with the same energy as the initially given electron is entering the initially given field at the same angle?

Explanation / Answer

a)

kinetic energy KE = (1/2)*m*v^2 = 22.5 eV

1 eV = 1.6*10^-19 J

(1/2)*9.1*10^-31*v^2 = 22.5*1.6*10^-19

v = 2.81*10^6 m/s

magneitc force Fb = centripetal force

q*B*v*sintheta = m*(v*sintheta)^2/r

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

r = 9.11*10^-31*2.81*10^6*sin65.5/(1.6*10^-19*4.55*10^-4)

r = 0.032 m

pitch = vx*T = v*costheta*2*pi*r/(v*sintheta)

pitch = 2*pi*r/tantheta

pitch = 2*pi*0.032/tan65.5 = 0.092 m

=================

(b)

time period T = 2*pi*r/(v*sintheta)

T = 2*pi*0.032/(2.81*10^6*sin65.5)

T = 7.86*10^-8 s <<<<<-answer

======================

(c)

kinetic energy KE = (1/2)*m*v^2 = 22.5 eV

1 eV = 1.6*10^-19 J

(1/2)*9.1*10^-31*v^2 = 16.5*1.6*10^-19

v = 2.41*10^6 m/s

magneitc force Fb = centripetal force

q*B*v*sintheta = m*(v*sintheta)^2/r

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

r = 9.11*10^-31*2.41*10^6*sin65.5/(1.6*10^-19*4.55*10^-4)

r = 0.0274 m

pitch = vx*T = v*costheta*2*pi*r/(v*sintheta)

pitch = 2*pi*r/tantheta

pitch = 2*pi*0.0274/tan65.5 = 0.0784 m

========================

(d)

kinetic energy KE = (1/2)*m*v^2 = 22.5 eV

1 eV = 1.6*10^-19 J

(1/2)*9.1*10^-31*v^2 = 22.5*1.6*10^-19

v = 2.81*10^6 m/s

magneitc force Fb = centripetal force

q*B*v*sintheta = m*(v*sintheta)^2/r

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

r = 9.11*10^-31*2.81*10^6*sin65.5/(1.6*10^-19*4.55*10^-3)

r = 0.0032 m

pitch = vx*T = v*costheta*2*pi*r/(v*sintheta)

pitch = 2*pi*r/tantheta

pitch = 2*pi*0.0032/tan65.5 = 0.0092 m

======================

(e)

kinetic energy KE = (1/2)*m*v^2 = 22.5 eV

1 eV = 1.6*10^-19 J

(1/2)*9.1*10^-31*v^2 = 22.5*1.6*10^-19

v = 2.81*10^6 m/s

magneitc force Fb = centripetal force

q*B*v*sintheta = m*(v*sintheta)^2/r

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

r = 1.67*10^-27*2.81*10^6*sin65.5/(1.6*10^-19*4.55*10^-4)

r = 58.6 m

pitch = vx*T = v*costheta*2*pi*r/(v*sintheta)

pitch = 2*pi*r/tantheta

pitch = 2*pi*58.6/tan65.5 = 168 m

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