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