1. Sources of Magnetic Fields
Moving point charge:
Bits of current: I
also
Permeability constant
Biot-Savart Law
The magnetic field “circulates” around the wire.

2. Magnetic field due to a current loop
Principle of superposition:
At the center,
On axis generally,

3. Magnetic Field At Center of Circular Arc Current
I runs clockwise in the closed loop wires below:
What is B at center?

4. Circular Loop Current as a Magnetic Dipole
if |x|>>R
In fact,
On electric dipole axis

5. READING QUIZ 1
Which of the following statements about static
magnetic fields is correct?
A| Magnetic fields lines end and begin in magnetic charges
called monopoles.
B| The magnetic flux through a closed surface can have a
non-zero value.
C| Magnetic field lines are closed loops which link
(surround) currents.
D| Ampere’s law contradicts the Biot-Savart law.

6. Gauss’s Law for Magnetism
sources
Gauss’s Law
Gauss’s Law for Magnetism
No sources

7. Magnetic field of a solenoid
A constant magnetic field could be produced by an infinite sheet of current. In practice, however, it is easier and more convenient to use a solenoid. R
A solenoid is defined by a current I flowing through a wire that is wrapped n turns per unit length on a cylinder of radius R and length L.
Stretched-out solenoid

8. Magnetic field of a solenoid (continued)
Contribution to B at origin from length dx
# turns in length dx
one turn
(or for L>>R)
(half at ends)

9. Solenoid’s B field synopsis
// to axis
Long solenoid (R<<L):
B inside solenoid
B outside solenoid
nearly zero
(not very close to the ends or wires)
Bar magnet’s B field
Solenoid’s B field

10. PHYS 241 – Warm-Up Quiz 2
A circular current loop lies in the plane perpendicular to this sheet with its axis along the x-direction, and produces magnetic field B as shown. What is the direction of the current at the top end of this loop?
a. Out of the sheet
b. Into the sheet
c. Along +x axis
d. Along -x axis
e. Current is zero. x

11. Magnetic field of a Straight Currenty I
Infinite straight current

12. Two Parallel Currents
The ampere is defined to be the constant parallel currents that will produce the force between them of x 10-7 N per meter when 1 m apart.
Definition of charge 1 C (1 A for 1 Sec)

13. Two Perpendicular Currents
FB 1,2 I1
FB2,1 B I2 I3
FB 1,3

14. DOCCAM 2

15. Force on a Moving Charge near a Current
(b)
(c) I
q>0 B
Magnetic Force
(a)
(b)
zero
(c)

16. Ampere’s Law in Magnetostatics
Biot-Savart’s Law can be used to derive another relation: Ampere’s Law
The path integral of the dot product of magnetic field and unit vector along a closed loop, Amperian loop, is proportional to the net current encircled by the loop,
Choosing a direction of
integration.
A current is positive if it
flows along the RHR normal
direction of the Amperian
loop, as defined by the
direction of integration.

17. Example: Magnetic field of a long wire
outside the wire
inside the wire

18. Example: A Non-Uniform Current Distribution
Long, hollow cylindrical current of current density:
Insider the cylinder, the total current encircled by the Amperian loop is

19. Ampere’s Law applied to a solenoid
// to axis
Long solenoid (a<<L):
B inside solenoid
B outside solenoid
nearly zero
(not very close to the ends or wires)
Ampere’s Law:
n windings per unit length
B = μO n h I n = N/l

20. Limitations of Ampere’s Lawq -q
Not enough symmetry
Ampere’s Law needs correction!

21. PHYS 241 – 10:30 Quiz 3
A circular current loop lies on the xy-plane as shown,
where the current is clockwise as seen from the positive z-axis. What is the direction of the B field at point A? z
a. Along +x axis
b. Along +y axis
c. Along +z axis
d. Along -z axis
e. Along -x axis y I x A

22. PHYS 241 – 11:30 Quiz 3
A circular current loop lies on the xy-plane as shown, where the current is clockwise as seen from the positive z-axis. What is the direction of the B field at point A? z
a. Along +x axis
b. Along +y axis
c. Along +z axis
d. Along -z axis
e. Along - x axis y I x A

23. PHYS241 - Quiz C
A circular current loop lies on the xy-plane as shown, where the current is clockwise as seen from the positive z-axis. What is the direction of the B field at point A? z
a. Along +x axis
b. Along +y axis
c. Along +z axis
d. Along z axis
e. Along  x axis y I A x