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Physics II PHY 202/222
Magnetism
452 South Anderson Road
Rock Hill, SC 29730
www.yorktech.com
Magnetism– Test 5Beiser Chapters 27
MC: odd, SP: 5 – 17 odd
Beiser Chapters 28
MC: odd, SP: 1 – 19 odd
Beiser Chapters 29
SP: 3Browne Chapter 26-29 for PHY 222 Students
26: 1,5,9
27: 2,
28: 7
29: 1, 2
Beiser p.319
Chapter 27 – Magnetism
Beiser p.319
Magnets
When we think of magnets we either consider permanent magnets or magnetic effects of moving charge. Since permanent magnets come from moving charge, we consider moving charge first.
Beiser p.319
Magnetic Fields
Unit of magnetic field is the Tesla where
1 T = 1 N/Am = 1 Weber/m2 = 10,000 Gauss
The field around a strong permanent magnet is 0.1 T. An MRI is from 0.2 to 1.5 T. A junkyard electromagnet for lifting cars is 1 T.
Beiser p.320
Magnetic Field of a Straight Current
6
IB
2 s
where 1.257 10 Tm / A
Every current in a wire generates a magnetic field.
Point the thumb of your right hand in the direction of the current, and your curled fingers will point in the direction of the field.
The magnitude at a distance s from the wire is given by the formula:
Beiser p.321
Magnetic Field of a LoopA current in a loop of wire generates a magnetic field.
Point the fingers of your right hand in the direction of the current, and your thumb will point in the direction of the field inside the coil.
The magnitude of the field inside the loop is given by the formula:
IB single loop
2rNI
B many loopsL
Beiser p.322
Earth Magnetism
The Earth has a magnetic field due to currents of molten material in the core.
The magnitude is around
3 x 10 -5 T
Beiser p.323
Magnetic Force on a Moving Charge
A charge Q moving in a magnetic field B with velocity v will experience force F.
In the picture, the charge is moving to the right in a magnetic field into the screen. The magnitude of the force is given by
The force will be upwards as follows:
Put the thumb of your right hand in the direction of v. Put your fingers in the direction of B. Curl fingers up. Force will be in direction of fingers for a positve charge, and opposite for a negative charge.
v
Magnetic field into screen
F
B
+QF QvBsin
Beiser p.323
Magnetic Force on a Current
F = I L B
v
Magnetic field into screen
F
B
Wire
+Q
I
L – Length of wire in magnetic field
The force will be upwards as follows:Put the thumb of your right hand in the direction of I. Put your fingers in the direction of B. Curl fingers up. Force will be in direction of fingers.
Beiser p.324
Force Between two Currents
o 1 2I IF
L 2 s
L
s
If currents are in opposite directions, the force is repulsive; same attractive.
Beiser p.327
Ferromagnetism
27.6
27.10
27.12
27.14
27.16
Beiser p.335
Chapter 28 – Electromagnetic Induction
Beiser p.335
Electromagnetic Induction
A current is produced if:
•If a conductor is moved in a magnetic field
•If a magnet is moved near a wire, especially a coil of wire
•A magnetic field changes near a conductor/coil.
Induced EMF V Blv For a straight conductor moving perpendicular to a magnetic field.
Beiser p.335,6
Faraday’s Law
BAInduced EMF V N N
t t
For a magnet moving in a coil:
Lenz’s Law: an induced current is always in the direction so that it’s own magnetic field opposes the effect that created it.
Hence the negative sign above.
Beiser p.337
Transformers
1 1 1 2
2 2 2 1
V N I N
V N I N
N1 N2
Beiser p.339
Self Induction
ISelf Induced EMF V L
t
A change in current in a conductor causes a change in magnetic field.
A change in magnetic field causes an self-induced emf.
Where L is the inductance of the circuit component.
For a solenoid:
2N AL
Inductors in Combination
1 2 3
1 2 3
L L L L ... inductors in series
1 1 1 1... inductors in parallel
L L L L
Beiser p.341
Energy of an Inductor
21W LI
2
Beiser p.341-3
Time Constants and Current
When a switch in an inductive circuit is closed, the current builds up to it’s full value according to the formula:
t / T0I I 1 e Where the time constant, T = L / R.
28.4
28.6
28.8
28.10
28.12
28.14
28.16
28.18
28.20
Beiser p.350
Chapter 29 – Alternating Current Circuits
Beiser p.350
Alternating Current
DC Direct Current
V = constant
AC Alternating Current
V = Vmax sin ωt
I= Imax sin ωt
Generators
Generator: Move the coil, electricity out. Motor: Electricity in, motion out.
Split ring commutator
Slip rings
Beiser p.350
Effective Values
Since the average AC voltage V = Vmax sin ωt is zero, we need a way to be able to calculate its capacity to do work. So we use the “effective value” or root-mean-square (rms) value.
maxeff max
maxeff max
VV .707 V
2I
I .707 I2
Beiser p.353
Phase Angle
ELI – ICEIn an AC circuit with only an inductor (L) the voltage (E) leads the (I) current by 900.
In an AC circuit with only an capacitor (C) the current (I) leads the voltage (E) by 900.
In AC circuits with both inductors and capacitors you would have to find the phase angle as shown in the book.
Maxwell’s Equations
0
B
E0 0 0
QE dA
B dA 0
dE ds
dtd
B ds Idt
Browne p.343
Gauss’s Law for electricity: Electric fields come from charges
Gauss’s Law for Magnetism: There are no magnetic charges/monopoles. Any “ball” has the same B out as in: sum =0
Faraday’s Law: Change in magnetic field makes electricity.
Ampere’s Law: Change in electric field makes magnetism.
ΔE → ΔB → ΔE → … propagates through space as light or other EM waves. WOW!