Magnetism (sec. 27.1) Magnetic field (sec. 27.2) Magnetic field lines and magnetic flux (sec. 27.3) Motion of charges in a B field (sec. 27.4) Applications - moving charged particles (sec. 27.5) Magnetic force on conductor with current (sec. 27.6) Force and torque on a current loop (sec. 27.7) Direct current motor(sec. 27.8) The Hall effect(sec. 27.9) Magnetic Field & Forces Ch. 27 C 2012 J. F. Becker

Learning Goals - we will learn: ch 27 The nature of the force that a moving charged particle experiences in a magnetic field. How to analyze the motion of a charged particle in a magnetic field. How to analyze and calculate the magnetic forces on current-carrying conductors and loops.

Forces between bar magnets (or permanent magnets )

Earth’s magnetic field (Note the N-S poles of the bar magnet!)

The Van Allen radiation belts around the Earth

Magnetic force acting on a moving (+) charge

Compass over a horizontal current-carrying wire

Magnetic field lines associated with a permanent magnet, coil, iron-core electromagnet, current in wire, current loop

MAGNETIC FLUX through an area element dA

F = q v x B Orbit of a charged particle in a uniform magnetic field is a circle, so F = qvB = m(v 2 /R) and R = m v / q B

Velocity selector for charged particles uses perpendicular E and B fields q v B = q E v = E / B

Mass spectrometer uses a velocity selector to produce particles with uniform speed. And from R = m v / q B we get q / m = v / B R

A charged particle moves through a region of space that has both a uniform electric field and a uniform magnetic field. In order for the particle to move through this region at a constant velocity, Q27.10 A. the electric and magnetic fields must point in the same direction. B. the electric and magnetic fields must point in opposite directions. C. the electric and magnetic fields must point in perpendicular directions. D. The answer depends on the sign of the particle’s electric charge.

Force on a moving positive charge in a current-carrying conductor: F = I L x B L I I For vector direction use “RIGHT HAND RULE”

Magnetic force on a straight wire carrying current I in a magnetic field B Right hand rule F = I L x B

Magnetic field B, length L, and force F vectors for a straight wire carrying a current I

Components of a loudspeaker F = I L x B

Forces on the sides of a current-carrying loop in a uniform magnetic field. This is how a motor works!

Right hand rule determines the direction of the magnetic moment (  ) of a current-carrying loop

Torque (  x B) on this solenoid in a uniform magnetic field is into the screen thus rotating the solenoid clockwise

Current loops in a non-uniform B field

Atomic magnetic moments in an iron bar (a) unmagnetized (b) magnetized (c) torgue on a bar magnet in a B field

Bar magnet attracts an unmagnetized piece of iron; the B field gives rise to a net magnetic moment in the object

A simple DC motor

The Hall effect – forces on charge carriers in a conductor in a B field. With a simple voltage measurement we can determine whether the “charge carriers” are positive or negative.

A linear motor

Electromagnetic pump

See Review C 2012 J. F. Becker