Miscellaneous

 

      Motion of a charge in a nonuniform magnetic field (magnetic bottle)

 

  A charge moving in a magnetic field is subjected to the Lorentz force.

  In this case we have a nonuniform field, less intense in the centre and more intense on the sides. The situation is similar to that of the Earth's magnetic field, in which the maximum magnitude is at the poles and the minimum magnitude at the equator.

  In this case we have a nonuniform field, less intense in the centre and more intense on the sides. The situation is similar to that of the Earths magnetic field, in which the maximum magnitude is at the poles and the minimum magnitude at the equator.

  The charge moving in a helical movement is blocked in the zone with major magnitude. The same happens to the charged particles that arrive from space toward the Earth. These concentrate in some zones called Van Allen belts.

 

  On the tool bar it is possible to vary the field magnitude (represented by the field lines) and the speed of the charge.

  Button  allows drawing the trajectory.

  By clicking on button  it is possible to start a new simulation con with new features.

 

 

 

 

 

      Parabolic antenna

 

  In this simulation an antenna has the form of a paraboloid of rotation.

  By putting a source of spherical waves on the focal point of the antenna, these are reflected by the antenna under the form of plane waves.

  Vice versa, once they are reflected the plane waves converge on to the focal point of the antenna.

 

  On the tool bar it is possible to choose between the receiving antenna and the transmitting antenna.

  With button    we can temporarily hide the wave fronts.

  Click on  to obtain rays.

  By clicking on button   it is possible to start a new simulation.

 

 

 

 

 

      Doppler (simulation)

 

  The Doppler effect is seen through the wave fronts.

  In the case of a still source, the circles, which indicate the wave fronts have radii with a difference between them of a half wavelength.

  If the point source moves with a certain speed, the circles are not concentric. The distances between the wave fronts are smaller in direction of the motion and larger in the opposite direction. Considering the link between frequency and wavelength this indicates respectively a higher frequency and a slower frequency.

 

  On the tool bar it is possible to choose the speed of the source.

  The speed of the propagation of the wave is prefixed.

  By clicking on button it is possible to start a new simulation with new features.

 

 

 

 

 

      Doppler (comparison between waves)

 

  The simulation happens considering the screen as a strip of paper in uniform motion from left to right. A pencil writes on the paper and draws a sinusoid with a harmonic oscillation perpendicular to the motion.

  The wavelength changes both on the basis of the frequency of the oscillation of the pencil (source) and on the basis of the drifting speed of the paper (speed of the medium of propagation). It can also change if the pencil moves in respect to the medium of propagation.

  The simulation shows two sources S (still) and S' (mobile) in the centre of the screen; while the observers are indicated with O and O' on the right of the screen.

 

  Buttons  allow the source S' to standby, to go away or come near the observer O'.

  Button  allows sending a signal with the waves (changing the phase) to show that the speed of the waves emitted by the still source and the moving source is always the same.

  The mobile source automatically stops at the ends of the screen.

 

 

 

 

 

    Frequency

 

  The frequency is the number of oscillation in the unit of time. It is measured in Hertz (Hz).

 

 

 

 

 

    Wavelenght

 

  The wavelength is the minimum distance between two points of the medium of propagation that vibrate in phase. Actually, it is the distance travelled by the wave in a period.

  where
  1. v is the speed of propagation of the wave,
  2. T is the period of oscillation of the source,
  3. f is the frequency of oscillation of the source.

  In graph amplitude of oscillation versus distance of the source, the wavelength is represented by the distance between two crests or two troughs.

 

 

 

 

 

    Wave fronts

 

  The wave fronts are formed by the points that belong to the same line or to the same surface that vibrate in phase.

 

 

 

 

 

    Difference of phase

 

  The difference of phase between two sinusoidal quantities which vibrate with the same frequency, is the minimum time expressed in grades or radians, taken between the instants in which both the increasing or decreasing quantities assume the zero value.

   We can have particular cases when = 0° (in phase), = 180° (in phase opposition).

 

 

 

 

 

    Amplitude

 

  The amplitude of the oscillation represents the maximum displacement of the mobile from the centre of oscillation, i.e. from its equilibrium position.

 

 

 

 

 

    Vector

 

  A vector is a quantity characterized by the fact that has a direction and a magnitude.

  It is represented by an oriented segment in which:

  • The direction is given by the line the segment is part and by the parallels.
  • The magnitude is given by the length of the arrow once a scale has been introduced.

 

 

 

 

 

    Vectorial product

 

  The vector product a between two vectors b and c is a vector that has its direction normal to the plane formed by the two vectors. The course is given by the rule of the right hand, according to which by disposing the thumb in the course of b and the other fingers in the course of c the course of a is that which exits from the palm of the hand. The magnitude is given by |a| = |b| * |c| * sin where is the angle formed by the two vectors. The magnitude is represented by the surface of a parallelogram that has the two vectors as its consecutive sides. The vector product is not commutative, i.e. if the order of the factors is changed the result (the course) changes.

 

 

 

 

 

    Lorentz force

 

  The Lorentz force that acts on a charged particle moving in a magnetic field is given by the vectorial product

 where
  1. q is the charge,
  2. v the velocity,
  3. B the magnitude of the magnetic field.

  The magnitude of the force is given by F = q v B sin , where is the angle formed by the velocity and by the field. The direction of the force is perpendicular to the plane formed by the v and B vectors.