Magnetic Fields

Information
Exam and numerical answers are on Moodle
All students have labs today and onwards; inductance experiment is “functional”
NO use of mobile phones or music in labs
Arrive on time for labs:Students arriving late for labs will get reduced marks. Students arriving 15 or more minutes late will not be allowed top do a lab, and will get a zero mark.

Magnetism
Sources of magnetism
Moving charges
…atomic dipoles…permanent magnets
Magnetic field B
Detect by placing moving charge q at each point
F = qv x B
This is the definition of B.

Magnetic field B
F = qvBsinθ gives the magnitude, while the direction is found either with the right-hand-rule or Fleming’s-left-hand-rule.
Direction and magnitude by vector product: F = qv×B
Force is always perpendicular to the plane defined by v and B
Units Tesla (T) or Webers per m2 (Wb m-2)
If charge q is negative force is
in opposite direction

F = qv×B
(Force a
+ve charge experiences )
( qv, or moving charge)
( B, or Mag. Field)

Example 1
A proton moving at 1.00 x 108 ms-1 enters a region where the magnetic field is 0.500 T
Evaluate the magnitude of the force on the proton if the angle between the velocity of the proton and the field is
a) 00 b)900 c) 450 d) 300
What is the direction of the force?
B
v

Charged particle moving in region of uniform magnetic field:
eg A proton is moving as shown in the B field which is directed out of the plane of the screen/paper

Force on current carrying wire
Suppose q passes a point in the wire in time t then current i=q/t . If speed of q is v then in time t it moves L=vt
Thus qv=iL
so F = qv x B
becomes
F = iL x B

Example 2
A straight 0.400 m length of wire carries a current of 2.00 A. It is placed in a B field of 0.250 T as shown. The angle between the wire and the field is 300
What is the magnitude and direction of the force on the wire?
B
I

Visualising a magnetic field
Magnetic “lines of force”
Flux: total number of lines passing through an area.
The flux density gives the magnitude of B field. This is the number of lines passing through unit area placed normally to the lines. Units: Wb m-2 equivalent to Tesla
Direction of the magnetic field is the direction of a tangent to a field line
Magnetic dipole aligns with field line

Field due to a straight current carrying wire

where μ0 is the permeability of free space and is defined to be exactly
μ0 = 4π x 10-7 kg m s-2 A2 (or Hm-1)
approx value μ0 = 1.26 x 10-6 Hm-1
Field due to current carrying wire is given by:

Example 3
A long straight wire is perpendicular to a uniform magnetic field of strength
2.00 x 10-5 T. If the wire carries a current of 1.00 A what is the total magnetic field at points A and B in the diagram?
Sketch the field lines which represent the resultant field near the wire

Force between two current carrying wires
Wire 2 is in the field B1 due to wire 1
= F1 on 2 /L =
Therefore
1
2
Consider force on wire 2
attractive
If two long parallel wires 1 m apart carry the same current, and the magnetic force per unit length on each wire is 2 x 10-7 N/m, then the current is defined to be 1 A.

Example 4
Two long, straight, parallel wires are 3.00 cm apart. I1 = 3.00 A and
I2 = 5.00 A in opposite directions.
(a) Find B field strength at point P
(b) At what point, besides infinity, is the B field strength zero?
P

LECTURE CHECK LIST
LECTURE 31 Magnetic Fields
READING Adams and Allday: 5.14, 5.15, 5.16
Serway ch. 19.1-19.3
At the end of this lecture you should:
Understand how a magnetic field is defined implicitly by the Lorentz force
Be able to calculate the magnitude and direction of the force on a conductor of length, l, carrying current, I, in a magnetic field of field strength, B
Know the formula for the field strength due to a long straight wire carrying current, I, at a distance, r, from the wire
Understand how the definition of the ampere arises and be able to give the definition
Understand the concept of field lines for a magnetic field

Fields due to coil and solenoid

Field due to wires in solenoid

Magnetic fields due to permanent magnet
Iron filings scattered near short bar magnet
Field lines due to solenoid (long coil of wire carrying current)

Earth’s magnetic field

Circular Path of charge moving perpendicularly to B field
Therefore:

Velocity selector

Mass spectrometer

Cathode Ray Oscilloscope

Cathode Ray Oscilloscope

Time-base voltage

LECTURE CHECK LIST
LECTURE 27 Magnetic Fields
READING Adams and Allday: 5.14, 5.15, 5.16
At the end of this lecture you should:
Understand how a magnetic field is defined implicitly by the Lorentz force
Be able to calculate the magnitude and direction of the force on a conductor of length, l, carrying current, I, in a magnetic field of field strength, B
Know the formula for the field strength due to a long straight wire carrying current, I, at a distance, a, from the wire
Understand how the definition of the ampere arises and be able to give the definition
Understand the concept of field lines for a magnetic field
Know the formula for the magnetic field strength due to a solenoid and be able to perform calculations using that formula
Have an understanding of the form of the Earth’s magnetic field and understand that this field resolves into two components