Download PROBLEMA A-1 An electron is emitted in the x direction with velocity

PROBLEMA A-1
An electron is emitted in the x direction with velocity v. At the time t=0 the electron
enters into a parallel plate empty capacitor (squared plates of side l and separation
distance h) exactly at half height of the separation between the plates. The plates are
electrically charged with a surface charge density . At a distance d from the end of the
capacitor the is a screen S. Neglecting the sides effects:
1) calculate the maximum value max of the surface density charge for which the
electron does not hit the plates.
2) Determine, in the case max, the y coordinate of the point where the electron
hits the screen.
3) Discuss the dependence of the arrival time of the electron on the screen S as a
function of the surface density charge on the plates of the capacitor.
PROBLEMA A-2
A conductive bar of mass M=10g slides without friction along two
parallel vertical conductive rails divided by a distance L=15cm
and joined at their top by a resistance R=50. The bar is always
electrically connected with the rails and all the device is inside a
magnetic field B=2T with entering sense into the drawing plane.
Calculate the induced current into the coil when the bar falls with
velocity v=2.0 ms-1.
Calculate the forces acting on the bar at the same time.
Which is the maximum velocity v0 that can be reached by the bar
during its fall?
DOMANDA A
Discuss the main properties of the static electric field.
PROBLEMA B-1
A spherical capacitor is made by an internal conductor of radius r1 = 3 cm and an
external one of radius r2 = 5 cm. The space between the conductors is partially, from
r=r1 to r=r0=4 cm, filled by a linear, homogeneous and isotropic dielectric with
permittivity r = 3. The conductors are maintained at the potential difference V=15 V.
Calculate the electric field E and the field D as a function of the distance r from the
center of the spherical capacitor. Calculate the polarization charges and their spatial
location.
Calculate the electrostatic energy of the capacitor with and without the dielectric
between the conductors. Compare the energy difference with the work of the power
supply during the extraction of the dielectric (with constant potential).
PROBLEMA B-2
A circular coil of area =15 cm2 and resistance R=50 is located inside a spatially
uniform magnetic field B=10-2 T, with direction perpendicular to the plane of the coil
and with entering sense (looking from the top). The magnetic field is gradually reduced
from the initial value B0 with a time dependence B(t)=B0 e-t (=100 s-1). Calculate
the expression of the induced current, mentioning the rotation sense. The forces acting
on this current make the coil expanding or narrowing? Calculate the total electrical
charge in the time interval required to reduce the magnetic field from B0 to zero.
DOMANDA B
Discuss how have to be modified the Maxwell's equation when we are dealing with time
dependent electric and magnetic fields.
PROBLEMA C-1
An indefinite wire conductor is flown by a current i1
= 3A and a rectangular coil by a current i2 = 5A like is
shown in the figure. Two sides of the coil are parallel
to the wire and have length a=10 cm, the others two
sides are perpendicular to the wire and have length
b=3cm. The coil is located at a distance c=2cm from
the wire.
a) Calculate the interaction between the wire and the
coil.
b) Calculate the mutual inductance coefficient.
c) Assuming that the coil is not flown by current, but is moving away perpendicularly
from the wire with velocity v. Determine the expression of the induced fem.
PROBLEMA C-2
A full, metallic sphere of radius R has an electrical charge +2Q. An empty sphere of
radius 3R is located in a position concentric respect to the first one and has an electrical
charge -Q. Determine the expressions of the electric field as a function of the distance r
from the center of the spheres.
Calculate the electrical potential difference between the two spheres.
In a second time the two spheres are connected between them and to a third sphere (not
concentric with firsts two) of radius 2R and with charge +4Q. Discuss the distribution of
the electrical charges after having performed the connections.
DOMANDA C
Discuss the different behavior of conductive and isolating materials in presence of an
electric field.