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AP Unit III D1. Magnetic Fields

• Students should understand the force experienced by a charged particle in a magnetic field, so they can

• (a) Calculate the magnitude and direction of the force in terms of q, v, and B, and explain why the magnetic force can do no work.

• (b) Deduce the direction of a magnetic field from information about the force experienced by charged particles moving through that field.

• (c) Describe the paths of charged particles moving in uniform magnetic fields.

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• (d) Derive and apply the formula for the radius of the circular path of a charge that moves perpendicular to a uniform magnetic field.

• (e) Describe under what conditions particles will move with constant velocity through crossed electric and magnetic fields.

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Magnetic Fields

• Magnetic Field Strength B = magnetic flux / area A

• B= /A.

• B is measured in Teslas (T), magnetic flux is measured in Webers (Wb), and Area is measured in m2

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• The magnetic field around a bar magnet is spider shape

• The direction of the field lines is from North to South (the direction the north pole of a magnet would go in if placed in the field.)

• The magnetic field around a current carrying wire B = 0 I /2 a where 0 is the magnetic permeability of free space or vacuum permeability = 4 x 10-7 (T · m) / A

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Magnetic Field in a loop of current carrying wire.

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Magnetic field around single current carrying wire

Magnetic field around loop of current carrying wire

Current I

I

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• x x

• x x x

• x x x x x

• x x x

• x x

x means magnetic field arrows going INTO paper towards direction of North

If current goes counterclockwise then this side is north pole of electromagnet

If current goes clockwise then this side is south pole of electromagnet

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Magnetic Force _ The Motor Effect

• The magnetic force on a wire is given by F=BILsin

• The magnetic force on a charge is given by F = Bqv

• The direction of the force is given by the right hand rule for conventional current (positive charges)

• X means magnetic field going into the page means magnetic field coming out of the page.

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Direction of force on a positive charge (Fig 19-7 p629)

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• A charge entering a magnetic field will describe a circle.

• Magnetic force = centripetal force

• Bqv = mv2/r

• Calculate v for an electron describing 12 cm radius circle in magnetic field 4 x 10-4 T.

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• Bev = mv2/r

• v= rBe/m

• v= 12 x 10-2 x 4 x 10-4 x 1.6 x 10-19/ 3.31 x 10-34

• v=

If the particle moves under constant velocity under crossed electric and magnetic fields the electrical and magnetic forces are equal and opposite. Eq = Bqv

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• This effect is used in particle accelerators to determine the mass of an unknown particle.

• The charged particle is accelerated into a known magnetic field. The radius of path it describes tells us the mass since Bqv = mv2/r them m = Bqr/v.

• x x x x x• x x x x x

r

v

Bq

If the particle is not charged it can be accelerated into a particle which is.

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Crossed magnetic and electric fields

• x x x x x x x x

• x x x x x x x x

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What is magnitude of charge on particle and which direction will it move in ? Homework Questions: AP U III D 1Q1-10p652 all.

V= 2000V

d = 0.5 cm

B = .007 T