Question 16
(a) State what is meant by a magnetic field. [2]
(b) A charged particle of mass m and charge +q is
travelling with velocity v in a vacuum.
It enters a region of uniform magnetic field of flux
density B, as shown in Fig. 5.1.
Fig. 5.1
The magnetic field is normal to the direction of motion
of the particle. The path of the
particle in the field is the arc of a
circle of radius r.
(i) Explain why the path of the particle in the field is the
arc of a circle. [2]
(ii) Show that the radius r is given
by the expression
r = mv / Bq
[2]
(c) A thin metal foil is placed in the magnetic field in (b).
A second charged particle enters the region of the
magnetic field. It loses kinetic energy
as it passes through the foil. The particle follows the
path shown in Fig. 5.2.
Fig. 5.2
(i) On Fig. 5.2, mark with an arrow the direction of travel
of the particle. [1]
(ii) The path of the particle has different
radii on each side of the foil.
The radii are 7.4 cm and 5.7 cm.
Determine the ratio
final momentum of
particle
initial momentum of
particle
for the particle as it passes through the foil. [2]
Reference: Past Exam Paper – June 2011 Paper 41 Q5
Solution:
(a) A
magnetic field is a region (of space) where there is a force on a moving charge.
(b)
(i) The force
on the particle is (always) normal to the velocity / direction of travel. The speed
of the particle is constant.
(ii)
{The magnetic force
provides the centripetal force.}
mv2 / r = Bqv
{Make r the subject of
formula.}
Radius r = mv / Bq
(c)
(i) The direction
is from ‘bottom to top’ of the diagram
{From Fig 5.2, we can
observe that the path is NOT the arc of a circle as in Fig 5.1.
We are 2 options for the direction
of the path: either from right to left or from bottom to top of the diagram.
As the charged particle
passes through the coil, it loses some kinetic energy. Its speed v decreases
and so, the radius of the path also decreases (since r = mv / Bq). In the
diagram, this reduction can be observed as we pass through the foil from the
bottom to top and NOT from right to left along the path.}
(ii)
The radius is proportional
to momentum.
{r = mv / Bq
mv = p where p is the momentum.
r = p / Bq
B (same field) and q (same
particle) are constant.
So, the momentum p (= mv)
is directly proportional to r.
Ratio = final momentum /
initial momentum
Ratio = final radius /
initial radius}
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