Table of contents  
What are Eddy Currents?  
Some Practical Applications 
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During braking, the brakes expose the metal wheels to a magnetic field which generates eddy currents in the wheels. The magnetic interaction between the applied field and the eddy currents acts to slow the wheels down. The faster the wheels spin, the stronger is the effect, meaning that as the train slows the braking force is reduces, producing a smooth stopping motion.
The shiny metal disc in the electric power meter rotates due to eddy currents. The magnetic field induces the electric currents in the disc. You can also observe the shiny disc at your house.
Electric power meters
In a rapidly changing magnetic fields, due to a large emf produced, large eddy currents are set up. Eddy currents produce temperature. Thus a large temperature is created. So a coil is wound over a constituent metal which is placed in a field of the highly oscillating magnetic field produced by high frequency. Industrial induction furnace
The temperature produced is enough to melt the metal. This is used to extract metals from ores. Induction furnace can be used to prepare alloys, by melting the metals at a very high temperature.
To know the speed of any vehicle, these currents are used. A speedometer consists of a magnet which keeps rotating according to the speed of our vehicle. Eddy currents are been produced in the drum. As the drum turns in the direction of the rotating magnet, the pointer attached to the drum indicates the speed of the vehicle
SpeedometerQues: Eddy currents are produced in a metallic conductor when
(a) The magnetic flux linked with it changes
(b) It is placed in the changing magnetic field
(c) Placed in the magnetic field
(d) Both A and B
Ans: D
Solution: They are produced when the magnetic flux passing through the metal object continuously changes. This may happen due to many reasons.
1. The object is placed in the region with changing magnetic field.
2. The object continuously moves in and out of the magnetic field region.
Power dissipation of eddy currents
Under certain assumptions (uniform material, uniform magnetic field, no skin effect, etc.) the power lost due to eddy currents per unit mass for a thin sheet or wire can be calculated from the following equation:
where
P is the power lost per unit mass (W/kg),
B_{p} is the peak magnetic field (T),
d is the thickness of the sheet or diameter of the wire (m),
f is the frequency (Hz),
k is a constant equal to 1 for a thin sheet and 2 for a thin wire,
ρ is the resistivity of the material (Ω m), and
D is the density of the material (kg/m^{3}).
This equation is valid only under the socalled quasistatic conditions, where the frequency of magnetisation doe snot result in the skin effect; that is, the electromagnetic wave fully penetrates the material.
The derivation of a useful equation for modelling the effect of eddy currents in a material starts with the differential, magnetostatic form of Ampère’s Law, providing an expression for the magnetizing field H surrounding a current density J:
Taking the curl on both sides of this equation and then using a common vector calculus identity for the curl of the curl results in
From Gauss’s law for magnetism, ∇ ·H = 0, so
Using Ohm’s law, J = σE, which relates current density J to electric field E in terms of a material’s conductivityσ,and assuming isotropic homogeneous conductivity, the equation can be written as
Using the differential form of Faraday’s law, ∇ × E = −∂B/∂t, this gives
By definition, B = μ_{0}(H+M), where M is the magnetization of the material and μ_{0} is the vacuum permeability. The diffusion equation therefore is
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157 videos452 docs213 tests
