Announcements

• WebAssign HW Set 6 due this Friday• Problems cover material from Chapters 19

• Prof. Kumar tea and cookies today from 5 – 6 pm in room 2165

• mine are 2 - 3 pm Thursday, room 2265• also, can schedule by appointment

• Exam 1 statistics

QUESTIONS? PLEASE ASK!

•Average: 14.43• Standard deviation: 3.44

From last time Magnets and earth’s magnetic field

Magnetic Fields:

Units are T = N/A.m Use right hand rule to determine

direction of force

Force on a wire: F = B I L sin θ

Torque on a Current Loop Torque = B I A N sin

Applies to any shape loop N is the number of turns in the coil Torque has a maximum value of

NBIA (when = 90°) Torque is zero when the field is

parallel to the plane of the loop

Magnetic Moment = IAN is a vector Torque can be written as = B sin

Example Problem 19.31

A long piece of wire with a mass of 0.100 kg and a length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hinged along a horizontal side, carrying a 3.40 A current, and is placed in a vertical magnetic field of 0.010 T. (a) Determine the angle that plane of the coil makes with the vertical when the coil is in equilibrium. (b) Find the torque acting on the coil due to the magnetic force at equilibrium

Electric Motor

electric motor - converts electrical energy to mechanical energy

The mechanical energy is in the form of rotational kinetic energy

An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field

Electric Motor

Torque acting on the loop will rotate the loop to smaller values of θ until the torque becomes 0 at θ = 0°

If the loop turns past this point and the current remains in the same direction, the torque reverses and turns the loop in the opposite direction

Bad!!

Electric Motor

So, we need to be clever…

To provide continuous rotation in one direction, the current in the loop must periodically reverse

In AC motors, this reversal naturally occurs

In DC motors, a split-ring commutator and brushes are used

Actual motors would contain many current loops and commutators

Force on a Charged Particle in a Magnetic Field

Consider a particle moving in an external magnetic field so that its velocity is perpendicular to the field

The force is always directed toward the center of the circular path

The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle

Force on a Charged Particle

Equating the magnetic and centripetal forces:

Solving for r:

r is proportional to the momentum of the particle and inversely proportional to the magnetic fieldSometimes called the cyclotron equation

Particle Moving in an External Magnetic Field

If the particle’s velocity is not perpendicular to the field, the path followed by the particle is a spiral The spiral path is

called a helix

Example Problem 19.42

A cosmic ray proton in interstellar space has an energy of 10 MeV and executes a circular orbit having a radius equal to that of Mercury’s orbit around the Sun (5.8 x 1010 m). What is the magnetic field in that region of space?

Solution to 19.31

Solution to 19.42