Magnetic field II

Plan Motion of charge particle in electric and magnetic fields Some applications of magnetic fields

Force due to magnetic field Recap………

Work done by F B Magnetic forces can only alter the direction Recap………

Lorentz force Recap………

Combined E and B fields Acts on any particle, whether moving or in rest Acts on moving particle only

Motion of charge particle in the crossed B and E fields

Particle for which v = E/B, passes un deflected. Particles with other fields are deflected. If

Calculation of e/m for electron

Motion of charged particle in constant uniform Electric field Neglecting gravity A Parabolic path

Substituting

Constant uniform Magnetic field B does not change the speed It changes direction of motion Thus particle should move in a circle, if moves in a plane perpendicular to B.

xx xx x x x x xxxx xxxxx x x x xx x xx x x xx x x x x x x x FBFB

Angular frequency xx xx x x x x xxxx xxxxx x x x xx x xx x x xx x x x x x x x FBFB xx xx x x x x xxxx xxxxx x x x xx x xx x x xx x x x x x x x FBFB

Applications of magnetic fields

Application I- Mass spectrometer R m To separate the ionized atoms

Application II - Cyclotron E. O. Lawerence (1930)

Worlds largest cyclotron

This is at TRIUMF (CANARA) Accelerates protons to energies up to 520 MeV Diameter of machine = 18 m During the course of acceleration proton travels 45 km

Magnetic Mirror Non uniform magnetic field Strong B Weak B

The Hall effect Provides a way to determine sign and density of charge carriers. conductor w

If electrons are majority charge carriers EHEH E B E conductor

V H If the electrons are majority charge carriers + - conductor

Density of charge carriers

Convention If the voltage of lower terminal is negative, electrons are the majority charge carriers. If the voltage of lower terminal is positive, holes are the majority charge carriers.

Show that, in terms of hall electric field E H, and the current density j, the number of charge carriers per unit volume is given by

Show that the ratio of hall electric field to the electric field is given by

A metal strip 10 cm long, 1 cm wide and 1mm thick moves with constant speed v through a magnetic field of 1mT perpendicular to the strip. A potential difference of 4 V is measured between the points x and y across the strip. Calculate the speed v V d is the velocity of strip now V d = 0.4 m/s

A strip of copper 150 m thick is placed in a magnetic field B = 0.65 T perpendicular to the plane of the strip. A current 23 A is setup in the strip. What hall potential difference will appear across the width of the strip if there were 8.5 x electrons/m 3 ?