Download 1. In a rectangular area shown in the figure uniform magnetic field of

1. In a rectangular area shown in the figure uniform magnetic field of B = 0.5 T
perpendicular to the plane of the paper is present. A proton is arriving at the
boundary of the magnetic field with constant velocity of v = 107 m/s perpendicular
to the magnetic field. The mass and the charge of the proton are me = 1.67 ×
10−27 kg and Qp = 1.6 × 10−19 C, respectively. d = 0.3 m.
a.) What kind of motion will the proton have in the
presence of uniform magnetic field? Make a plot
in the figure! How much distance does the proton
cover in the magnetic field
v0
b.) Where will the electron leave the area where the
magnetic field is present?
c.) How large will the speed of the proton leaving the
magnetic field? How much work has been done by
the magnetic field on the particle?
d
d.) Give the minimum of the velocity the proton needs
to leave the rectangular area on the right side!
2. A charged particle is moving on a straight line with constant velocity of v = 100 m/s
in the presence of uniform electric and magnetic field. The components of the electric
~ = (100 N/C, 0, 0), ~v = (0, 100 m/s, 0).
field and velocity vectors are E
a.) Give the smallest value of the magnetic field and the corresponding direction!
b.) Give the direction of the magnetic field if its magnitude is B = 2 T !
c.) Solve the problem if the components of the velocity vector are ~v = (0, 60 m/s, 80, m/s)
3. A proton and a deuteron are moving in the presence of uniform magnetic field. Their
velocities are perpendicular to the magnetic field and they have the same kinetic
energy but the mass of a deuteron is twice as large as the mass of a proton. How
large is the ratio of the radii of their motion?
4. A charged particle with a mass of m = 0.001 kg and with a charge of Q = 10−3 C is
moving in the presence of uniform magnetic field. The initial velocity of the particle
~ = (0.4 T, 0, 0.3 T ).
is ~v = (8 m/s, 6 m/s, 0) and the magnetic field is B
a.) What kind of motion will the particle have?
b.) Which component of the velocity will not change during the motion?
c.) Give the shortest time when the particle will have the same velocity as the
initial velocity!
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