Lorentz force. Hall effect. Movement of a charge in a magnetic field.
Lorentz force
A positive electric charge q moving at a speed v from a magnetic field with induction B is affected by a force F. Similarly, a negative electric charge q moving at a speed v from a magnetic field with induction B is affected by a force F. The force acting on moving electric charges is called the Lorentz force. The Lorentz force is always perpendicular to the velocity of the charged particle. Therefore, it only changes the direction of this speed without changing its module. The direction of the Lorentz force is determined by the rule of the left hand: if the palm of the left hand is positioned so that the vector B enters it, and the four outstretched fingers are placed in the direction of the positive charge, then the bent thumb will show the direction of the Lorentz force. The Lorentz force vector is equal to the product of the magnitude of the electric charge q by the vector product of the charge velocity vector and the magnetic induction vector. The module of the Lawrence force vector is equal to the product of the magnitude of the electric charge and its velocity, the magnetic induction, and the sine of the angle Alpha. Alpha angle between velocity vector v and magnetic induction vector B
Movement of a charge in a magnetic field
1 A charge moves along a magnetic field. The speed v of the charge is parallel to the direction of the magnetic field B - A charged particle moves in a magnetic field along the lines of magnetic induction (the angle alpha between the vectors v and B is 0 or pi). In this case, the Lorentz force is zero. The magnetic field does not act on the particle, and it moves uniformly and in a straight line.
2 The speed v of the charge is perpendicular to the direction of the magnetic field B - A charged particle moves in a magnetic field perpendicular to the lines of magnetic induction (angle alpha Pi in half). The particle will move along a circle of radius R with centripetal acceleration a with index h. The Lorentz force is constant in absolute value and normal to the particle trajectory. Normal acceleration is determined by the formula speed squared divided by the radius of the circle. From Newton's second law, we obtain the radius of the circle and the period of rotation.
3 A charged particle moves at an angle alpha to the lines of magnetic induction. The motion of a particle can be represented as the sum of two motions: uniform rectilinear motion along the field and uniform motion along a circle in a plane perpendicular to the field. The total motion will be a spiral motion, the axis of which is parallel to the magnetic field.The pitch of the helix h is equal to the product of the parallel component of the velocity v times the period T. We determine the period of rotation of the particle T and the radius of the circle R. And we obtain the final formula for the pitch of the helix h.
hall effect
The Hall effect is the occurrence of an electric field in a current-carrying conductor or semiconductor when it is placed in a magnetic field.Let a metal plate with current and linear dimensions a and d and current carriers by electrons be located in a magnetic field B. The vector B is perpendicular to the current density vector J. The Lorentz force leads to an increase in the concentration of current carriers - electrons - at the upper edge of the plate. In this case, the upper edge will be charged negatively, and the lower edge positively. Stationary distribution of charges will be achieved when the action of the electric field thus created balances the Lorentz force
An electric field is established in the conductor with the intensity vector E equal to the product of the Hall constant R and the vector product of the magnetic induction vector B and the current density vector J. The Hall effect is a consequence of the influence of the Lorentz force on the movement of current carriers. The transverse or Hall potential difference delta phi is equal to the product of the Hall constant R and the ratio of the product of the current strength I in the plate to the magnetic induction B to the width of the metal plate d, where R is the Hall constant equal to one divided by the electron charge and the concentration of electrons in the plate.