The Magnetic Field

The force on a charge q moving with a velocity The magnitude of the force

left-hand rule right-hand rule

Motion in magnetic field 1) Uniform, 2) Uniform, 3) Nonuniform

The angular velocity

The angular velocity (cyclotron frequency ) does not depend on velocity! The force is always perpendicular to velocity, so it cannot change the magnitude of the velocity, only its direction. The work done by the magnetic force is zero! Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed.

Electron motion in a microwave oven A magnetron in a microwave oven emits electromagnetic waves with frequency f=2450 MHz. What magnetic field strength is required for electrons to move in circular paths with this frequency?

Using Crossed and Fields Velocity selector independent of the mass of the particle!

Mass spectrometer

Thomson’s e/m experiment 1897: Cavendish Laboratory in Cambridge, England

Current carrying wires 1820 Hans Christian Oersted Hans Christian Ørsted

Gauss’s Law The total flux of electric field out of any closed surface is equal to the charge contained inside the surface divided by.

Conductors and insulators Charges reside at the surface of the conductor Conductor E=

Electric field of a ball of charge Q Electric field outside of a charged sphere is exactly the same as the electric field produced by a point charge, located at the center of the sphere, with charge equal to the total charge on the sphere.

Insulating sphere with charge Q uniformly spread throughout the volume A E r A

Conducting sphere with charge Q A E r V r A

A Charged, Thin Sheet of Insulating Material

A field in a cavity of a conductor Faraday’s cage

Electric field near a surface of a conductor a

The capacitance is: Spherical capacitor; Cylindrical capacitor

Capacitors in series: Capacitors in parallel: If the capacitors were initially uncharged,

Current Density Consider current flowing in a homogeneous wire with cross sectional area A. for j =Const only!

Current, Ohm’s Law, Etc.

For steady state situation 1.Kirchhoff’s junction rule: The algebraic sum of the currents into any junction is zero. 2.Kirchhoff’s loop rule: The algebraic sum of the potential differences in any loop must be zero.

Joule’s Law

Resistors in parallel: Resistors in series: