Magnetic field in vacuum

Circulation and flow of the magnetic field induction vector in vacuum.

Vakuumdagi magnit maydon induksiya vektorining sirkulyasiyasi va oqimi

Plan – (reja)

1. Ampere’s Law: A Solenoid

(Amper qonuni solenoidda)

2. Ampere’s Law: A Toroid

(Amper qonuni Toroidda)

3. Magnetic Flux

(Magnit oqimi)

4. Gauss’law in Magnetic field

(Magnit maydonda Gauss qonuni)

5. Magnetic flux and Gauss’ Law in magnetics

(Magnitlarda Gauss qonuni va magnit oqim)

Ampere’s Law: A Solenoid (Amper qonuni: Solenoidda)

Number of wires: (N/L)d
What is on sides?
B outside is very small
(solenoid)
Uniform: same B no matter where is the path

Ampere’s Law: A Toroid

Symmetry: B || path
Is magnetic field constant across
the toroid?

Magnetic Flux

• The magnetic field passing through a loop is also affected by the tipping of the loop.
• The axis of the loop is a line through the center of the loop that is perpendicular to the plane of the loop.
• The effective area of the loop is reduced when the loop is tipped.
• The effective area is defined as

Aeff = ab cos  = A cos 

Magnetic Flux

Magnetic Flux

• The magnetic flux depends on the strength of the field and the effective area of the loop:
• The SI unit of magnetic flux is the weber.
• 1 weber = 1 Wb = 1 T ⋅ m2

Question 1

• Which loop has the larger

magnetic flux through it?

• Loop A
• Loop B
• The fluxes are the same.
• Not enough information to tell

Question 1

• Which loop has the larger

magnetic flux through it?

• Loop A
• Loop B
• The fluxes are the same.
• Not enough information to tell

Φm = L2B

Question 2

• The metal loop is being pulled through a uniform magnetic field. Is the magnetic flux through the loop changing?
• Yes
• No

Question 2

• The metal loop is being pulled through a uniform magnetic field. Is the magnetic flux through the loop changing?
• Yes
• No

1. Magnetic field

1. Magnetic field

each point in the M-field has a special direction. when the q moves along this direction( or opposite the direction), no force acts on it.
The direction of M-field at this point
Gauss’law in Magnetic field
Take a moving charge( and q) as a test charge.
The characters of the force on the moving charge by the magnetic field:
Definition
--the magnitude of M-field
tesla(T)
or
 M-force depends on q,v and angle  between and M-field direction.
along the direction of
 The direction of the M-force acting on q always perpendicular to and M-field direction.

3. Magnetic flux and Gauss’ Law in magnetics

unit：weber(Wb)T·m2
For any closed surface S ,
---- Gauss’ Law in magnetics
----M-field is non-source field
M-flux：The number of -lines through a given surface.

Thank you for your attention