Topic D Flashcards
What is the magnetic field equation at point P a distance r for a current element?
dB= μ_0IdL x r^/4πr^2
Where rˆ is a unit vector along r.
μ_0is the permeability of free space; value of 4πx10^-7 Hm^-1
(Henrys/metre). The unit of B is the tesla (T). dB is normal to
the plane containing the vectors IdL and r
How can you calculate the resultant magnetic field?
By use of a suitable integration the Biot-Savart law can be used to calculate the B-field
resulting from a circuit L which can be decomposed /split into an infinite number of connected
current elements.
What is Ampère’s Circuital Law?
∮B ⋅ dL =μ_0ΣI
‘the line integral of B around a closed loop L is equal to the algebraic sum of the currents
which flow through the area bounded by L multiplied by μ_0.’
System must have high symmetry
What is the e differential form of Ampère’s circuital law?
∇xB =μ_0 J
What is the curl?
∇x - The ability of a vector field to cause rotation
The curl is found by using the discriminant
What is the magnetic force acting on a current element or moving particle?
dF=IdLxB
the direction of the magnetic force is normal to the plane containing both B and IdL
For a charged particle moving with velocity v in a magnetic field
F=qvxB
The resultant force is normal to both the field B and the velocity v of the charge.
What is the torque acting on a coil?
T = IAxB = m x B [For rectangle but can be extended to any shape coil]
where A is the vector corresponding to the area of the circuit and the resultant torque T is given by a vector that point along the axis of rotation
where m is the magnetic dipole moment of the circuit
What is the potential energy of a magnetic dipole placed in a uniform magnetic field?
U = =m • B
What is the magnetitic field of a circular coil at large distances?
Both the torque and the magnetic field produced is analogous to electric field
B= μ_0INa^2/2x^3
where a is the radius of the coil, N is the number of turns and x is the distance from the circular coil
B falls as 1/x^3 analogous to electric field
What are the fundamental properties of a magnetic field/conclusion?
Magnetic monopoles do not exist. There is no equivalent of the single isolated charge of electrostatics.
Magnetic fields can also be produced by certain (magnetic) materials
How are magnetic fields produced in certain materials?
Magnetic field
results from the motion of the electrons around the nuclei of the material.
What behaviour is consistent in magnetic monopoles?
Resultant B-field and the effect of applying a B-field to the material are also consistent
with the non-existence of magnetic monopoles
What is the consequence of non-existence of magnetic monopoles?
There is no magnetic
equivalent of single charges there are no sources or sinks of the B-field.
As you cannot separate the north and south pole
Hence the lines of B
are continuous and have no start or end.
What is the consequence of not having magnetic monopoles in relation to Gauss’ Law?
You cannot have an isolated charge only magnetic dipoles, which is like having two equal but opposite monopoles so the summation of Gauss’s Law for B-fields will be 0.
What is Gauss’s law for the magnetic field?
∮B•dS=0
∇•B=0 (shows that no point in space can we destroy or creat magnetic field lines)
Above is the integral and differential forms of another of Maxwell’s
equations. Their form arises because of the non-existence of magnetic monopoles.
The equations are not really useful but they summarise in a condensed form an important property of magnetic fields
What is Gauss’s law for the magnetic field used to describe?
Allows us to check if a vector can describe a magnetic field because a vector can only describe a magnetic field if the divergence equals to 0
Any real magenic field must obey
