Magnetic fields

• When current passes through a wire or other long current carrying conductor, a magnetic field is induced around the wire.
• The field lines around a wire form concentric rings around it, the direction of which can be found using the right hand grip rule - do a thumbs up in the direction of the (conventional) current and the direction of the fingers is the direction of the field.
• The magnetic flux density is the strength of the field, measured in Tesla.
• When a current carrying wire is placed in a magnetic field, the component of the wire that is perpendicular to the field experiences a force from the field.
• When a current carrying wire is perpendicular to a field, the equation for the force exerted on it by the field is F=BIL.
• Fleming's left hand rule shows the direction the force on a current carrying wire in a magnetic field experiences. Put the thumb up, the first finger out straight and the second finger perpendicular to the palm. The thumb is the direction of the force, the first finger is the direction of the field and the second finger is the direction of the current. Think FBI.
• The direction of magnetic field on a magnet is from its north pole to its south pole.
• A force acts on charged particles moving in a magnetic field, which is why a force is exerted on a current carrying wire because it contains moving electrons.
• The equation for force acting on a charged particle moving in a magnetic field is F=BQv.
• To adapt Fleming's left hand rule for a single charge, consider that the direction of current is the direction a free positive charge would go. Thus if the charge is negative, reverse the direction.
• The force exerted on a charge in a magnetic field is always perpendicular to the motion of travel, and thus charged particles follow a circular path.
• To find the radius of the circular motion of a charged particle in a magnetic field, combine the formulas for force for magnetic field (F=BQv) and circular motion (F=mv^2/r).
• The equation for radius of the circular motion of a charged particle in a magnetic field is r=mv/BQ.
• A cyclotron accelerates charged particles, and is used to produce ion beams for radiotherapy and radioactive tracers.
• A cyclotron is formed of two semi-circular electrodes called Dees, with a uniform magnetic field acting perpendicular to the plane of the electrodes and a high frequency alternating voltage applied between the electrodes.
• In a cyclotron, charged particles move from the centre of one of the Dees and are deflected in a circular path by the magnetic field. Here, the particles' speed is constant. When the particles reach the edge of the Dee, they are accelerated across the gap by the electric field, increasing their speed but also the radius of their path so they cross the other dee in the same time. The alternating electric field changes direction, accelerating the particles to the original dee. This process repeats until the particles reach the required speed and exit the cyclotron.
• Magnetic flux, measured in Weber, is the perpendicular magnetic field density in a certain area, and its equation is flux=BA.
• Magnetic flux linkage, measured in Weber turns, is the magnetic flux in a coil of wire and the equation is linkage=BAN where N is the number of turns.