CA2 POLYTECH PHYSICS
PART 1
FIELDS
Throughout the problem, we will neglect the weight of the particles in front of other forces and the
laws of mechanics. We consider the separation of isotopes Xenon (Xe) using a spectrograph
129 +¿ ¿ x +¿
Dempster. An ionization chamber produces ions positive 54 Xe and X 52e ¿ . These ions are
accelerated between two parallel metal plates P1 and P2 then subjected to the action of a magnetic
field, which allows them to be separated.
P1 P2
Beam of ions
O
O1 O2
u B
e = 1.6 x 10-19 C,
We give: elementary electric charge:
mp = mass of the proton = 1.67 x 10-27 kg
mn = neutron mass = 1.67 x10-27 kg
1. Acceleration of ions. Ions pass through the plate P 1 in O1 without initial speed. They are then
subjected, between P 1 and P2 , at an accelerating voltage U = 1000V.
1.1. In what direction should this tension be established?
1.2. Show that the kinetic energy, acquired by the ions as they pass through the P2 plate in O2 , is
independent of the isotope considered and calculate its value in joules.
129 +¿ ¿
1.3. Calculate the speed v acquired by the ions 54 Xe in O2 . We will assimilate the mass of the ion to
the sum of masses of its nucleons.
129 +¿ ¿
1.4. Express, as a function of x and v , the acquired speed v’ by io ns 54 Xe in O2 .
2. Separation of ions. The ions, animated by the speeds v And v’ calculated above, penetrate into O in
a region where a uniform perpendicular magnetic field ⃗ B prevails in the plane of the figure. We recall
⃗
that the electromagnetic force F acting on a charge q animated by a speed ⃗v is normal to the plane
defined by ⃗v and ⃗ B and such that the trihedral ⃗v , ⃗
B, ⃗
F is direct. The magnitude of the force is given
by f = qvB when ⃗v and ⃗ B are orthogonal.
2.1. We are interested in the movement of ions. Show that it is flat, circular and uniform. Give the
expression of the radius of curvature R . Calculate R For B = 0.1T.
129 +¿ ¿ x +¿
2.2. Ions 54 Xe and X 52e ¿ describe a semicircle before falling on a photographic plate,
respectively in A and B.We measure the distance AB = 8mm. Deduce the value of x ( B = 0.1T).
Part 2
OSCILLATIONS
MECHANICAL OSCILLATONS
2. A compound pendulum consists of a homogeneous disk (D) fixed to a rod OA, with negligible mass
and length l, whose end O coincides with the center of the disk and the end A carries a ball (B), with
mass M, which can be considered as a point. The disk has a mass M' = 2M and a radius r = l/3. The
pendulum can oscillate without friction around a horizontal axis (∆), perpendicular at O to the plane of
the disk.
2.1. Express, in terms of M and l, the moment of inertia of the pendulum with respect to the axis (∆).
A.N. M = 100 g; l = 60 cm.
2.2. The pendulum is displaced from its stable equilibrium position by a very small angle θ 0 = 0.1 rad
and released without initial velocity. Show that its oscillations are sinusoidal. What is the value of the
angular velocity at the passage through the equilibrium position knowing that θ 0 = 0.1 rad?
2.3. Now we displace the pendulum from its stable equilibrium position by an angle of π/2 rad and
release it without initial velocity. Calculate its angular velocity at the passage through the equilibrium
position. Deduce the velocity of the ball (B). g = 10 m s−2.
Between two points A and B, we apply a sinusoidal voltage of form U=Umsin(wt) of frequency 50
ELECTRICAL OSCILLATORS
Hz
3.1. a thermal conductor of resistance R = 100 Ω is placed between A and B and crossed by a current
of intensity 1.2A. deduce the numerical value of UM and the expression for U(t).
3.2 an inductor of negligible resistance is placed alone between A and B and crossed by a current of
intensity 1.2A
3.2.1 what is the inductance of the coil
3.2.2 give the expression for current i(t)
3.3. we now mount in series a capacitor c = 10µF and the inductor coil aforementioned between A and
B
3.3.1 what is the current intensity in the circuit
3.3.2 what is the potential difference between each element
3.3.3; draw the Fresnel vector diagram for theses p.ds
3.3;.4 what is the power consumed by the circuit
3.3.5. what is the value of the capacitance if we required maximum current value. In this case, what is
the value of the instantaneous current as a time function i(t)
PART 3
LIGHT
Wave Phenomena
1. What is called the wavelength of a wave?
2. Using the Young slit device, we obtain in monochromatic light, an interference pattern bright on a
screen placed parallel at the plane of the slots F 1 and F 2 and at the distance D = 2m from this plane.
The distance separating the secondary slits is has = 1.8mm. The wavelength of the illuminating
radiation is λ = 540nm. What are:
2.1. the nature of the fringe of order p = - 4.5 ?
2.2. the distance between the middle of this fringe and the middle of the central fringe?
