Gauss's Law for Magnetic Fields Flashcards Preview

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Flashcards in Gauss's Law for Magnetic Fields Deck (23)
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1
Q

How do you determine the direction of a magnetic field due to a current in a wire?

A
  • using the right hand rule
  • thumb point in the direction of conventional current
  • fingers curl in the direction of the magnetic field
2
Q

Describe the Magnetic Field in a Solenoid

A
  • magnetic field lines are always in a loop
  • a solenoid appears to have a north pole at one end and a south pole at the other
  • but actually the loops are continuous throughout
3
Q

Solenoids and Divergence

A
  • the divergence of the field of a solenoid is zero everywhere
  • in any small volume dV, any field line going in is also going out as the lines are in loops so divergence is zero
4
Q

Magnetic Dipole

A
  • very similar field pattern to an electric dipole
  • but the field lines are in loops whereas electric field lines stop and start on charges
  • at the centre the magnetic field lines are in the opposite direction to the electric field lines
5
Q

Gauss’s Law for Magnetic Fields - Differential Form

Equation

A

∇ . |B = 0

6
Q

Gauss’s Law for Magnetic Fields - Integral Form

Description

A
  • the total magnetic flux passing through any closed surface is zero, i.e for every field line entering the volume enclosed by the surface there is also a field line leaving it
  • there are no point in space from which a magnetic field line diverges from or converges to
  • magnetic monopoles do not exist
7
Q

Gauss’s Law for Magnetic Fields

Derivation

A

∇ . |B = ΔV->0 lim 1/ΔV ∮|B.n^dA = ϕB
-net flux, ϕB, is telling you whether inside the closed surface you have a net source or a net sink of magnetic field lines and whether the net flow is in or out
-since there are no monopoles the net flux across any closed surface is always zero so divergence must also be zero:
∮|B.n^dA = 0

8
Q

What is a vector field with zero divergence called?

A
  • solenoidal fields
  • all magnetic fields are solenoidal
  • any vector field can be written as the sum of an irrotational field and a solenoidal field
9
Q

Biot-Savart Law

Magnetic Field of a Moving Point Charge

A

|B(|r) = μ0/4π * q|v x |r /r²

10
Q

Biot-Savart Law

Magnetic Field of a Steady Current

A

|B(|r) = I*μ0/4π * ∫ {d|I’ x |r / r²}

|I' = an element of length along the wire
|r = the vector from the source to the point P
11
Q

Biot-Savart Law

Magnetic Field of an Infinite Wire

A

B = I*μ0/2πa

a = perpendicular distance from the wire

12
Q

Lorentz Force

Magnetic Field

A

|Fmag = Q(|v x |B)

The force Fmag, on a charge Q moving with speed v through a magnetic field B

13
Q

Lorentz Force

Magnetic and Electric Field

A

|F = Q{|E + (|v x |B)}

The force |F, on a charge Q moving with speed v through an electric field E and a magnetic field B

14
Q

Gauss’s Law for Magnetic Field’s - Integral Form

Equation

A

∮|B.n^dA = 0

15
Q

Difference Between Electric and Magnetic Fields

A
  • direction of magnetic field is perpendicular to the magnetic force, direction of electric field is parallel or antiparallel to force
  • for determining magnetic field, speed and direction of the test charge must be considered
  • for magnetic field, the component of the magnetic force in the direction of displacement is always zero
  • electrostatic fields are produced by electric charges whereas magnetostatic fields are produced by electric currents
16
Q

Similarities Between Electric and Magnetic Fields

A
  • field is proportional to fields

- the field is defined by the force on a test charge

17
Q

Sketching Magnetic Fields

A
  • magnetic fields don’t originate and terminate on charges, they form closed loops
  • field lines appear to originate on the north pole of a magnet and terminate on the south pole of a magnet, the field lines actually pass all the way through the magnet in closed loops
  • the net magnetic field is the vector sum of all magnetic fields at that point
  • magnetic field lines never cross
18
Q

Magnetic Field of a Solenoid

Equation

A

|B = μoNI/L ^x

19
Q

Magnetic Field of a Torus

Equation

A

|B = μoNI/2πr ^φ

20
Q

Magnetic Flux

uniform B perpendicular to S

A

ΦB = | |B | * surface area

21
Q

Magnetic Flux

uniform B at an angle to S

A

ΦB = |B . |n * surface area

22
Q
Magnetic Flux
(non-uniform B at variable angle to S)
A

ΦB = ∫ |B.n^dA

23
Q

Gauss’s Law for Magnetic Fields - Differential Form

Description

A
  • the divergence of a magnetic field is zero everywhere
  • since there are no point sources or sinks of magnetic field, the amount of incoming field must equal the amount of outgoing field everywhere