1. Two questions:
(1) How to find the force, F on the electric charge, Q excreted by the field E and/or B?
(2) How fields E and/or B can be created?
Maxwell’s equations
Gauss’s law for electric field
Electric charges create electric field:
Gauss’s law for magnetic field
Magnetic charges do not exist:
For one not moving (v<<c) charge:
Amperes law
Electric current creates magnetic field:
Faraday’s law
(Will be discussed later)
(As we will see later,
this law should be extended)

2. 7. Ampere’s law. (Sources of magnetic field)
Iout
Iin
Iin
Iout
2) Applications of Ampere’s law
(AL can be used to calculate the magnetic field in situations with a high degree of symmetry)
a) Long straight conductor I r
Example1:
I = 10A
r = 0.02 m
B - ?

3. Example2: Two long parallel wires are 4. 0 cm apart
Example2: Two long parallel wires are 4.0 cm apart. Each wire carries the current
10 A in the same direction. Find the magnetic field halfway between the wires. I I r r
Example3: Two long parallel wires are 4.0 cm apart. Each wire carries the current
10 A in the opposite direction. Find the magnetic field halfway between the wires. I I r r

4. b) Long cylindrical conductor

5. N – number of loops (or turns)
c) Field inside a solenoid B
N – number of loops (or turns)
encircled by our path l
Example 1:
Example 2: The magnetic field inside an air filled solenoid is B. The area of the solenoid is doubled, keeping the current flowing through the solenoid and the number of turns per unit length unchanged. Find the magnetic field inside the new solenoid.
Answer: Magnetic field inside a solenoid is independent from the area!

6. Example 3: A long solenoid has 100 turns/cm and carries current I
Example 3: A long solenoid has 100 turns/cm and carries current I. An electron
moves within the solenoid in a circle of radius 2.30 cm perpendicular to the
solenoid axis. The speed of the electron is 1.40*107 m/s. Find the current in
the solenoid.

7. Magnetic field lines always form a closed loops!
Long straight conductor
Inside long cylindrical conductor (r<R)
Inside solenoid
Inside toroidal solenoid (toroid)
Magnetic field lines always form a closed loops!

8. 3) Force between two parallel wires
4) Definition of the Ampere