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Magnetic field II

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

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Force due to magnetic field Recap………

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

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Lorentz force Recap………

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

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Motion of charge particle in the crossed B and E fields

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

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Calculation of e/m for electron

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

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Substituting

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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.

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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

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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

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Applications of magnetic fields

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

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

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Worlds largest cyclotron

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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

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Magnetic Mirror Non uniform magnetic field Strong B Weak B

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

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If electrons are majority charge carriers + + + + + + - - - - - - - - EHEH E B E conductor

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

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Density of charge carriers

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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.

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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

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

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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

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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 10 28 electrons/m 3 ?

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