Michael Faraday started off his work in chemistry where he succeeded in liquefying some gasses and discovered benzene. Faraday discovered two laws of electrolysis, one said that electricity strength is proportional to the chemical change, and the second said that the amount of deposited substances as a result of electricity is proportional to the substances' chemical weights. The most significant of Faraday's discoveries is the relation between electric field and magnetic field.
Faraday designed an experiment called the Faraday's disk. In this experiment, the disk solely connects to a voltmeter while being placed between the two poles of a U-shaped magnet. When a person rotated the disk the voltmeter's pointer moved to indicate an electric current generated in the disk.
To know what is Faraday's law remember that Faraday designed an experiment called Faraday disk where an induced electric current was created.
Faraday's law of induction states that the electromotive force (EMF) or induced voltage is equal to the change in magnetic flux over time where the magnetic flux is the amount of magnetic field passing through a surface. This means that EMF and the change in flux are proportional so they decrease and increase by the same amount or rate. The Faraday's law formula:
{eq}EMF=-\frac {\Delta \Phi }{\Delta t} {/eq} where {eq}\Delta \Phi {/eq} is the change in the magnetic flux of a magnetic field.
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Faraday's Law: Example 1
There are many examples of the application of Faraday's law such as motors and wherever there are coils and magnets. Alternated electricity generation is the most well-known Faraday's law example. The electricity supply for residential and commercial buildings is created by the use of Faraday's law where wired coils cut through the magnetic field lines. There are many ways to make the coils rotate, but surrounded by a strong magnetic field the huge coils rotate, and induced electric current is created in a similar way to Faraday's disk. On a smaller scale, a car's alternator is another example of Faraday's law where the alternator is made of coiled wires that rotate while surrounded by a magnet that creates an induced current to recharge the car's battery.
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Faraday's Law Formula
The mathematical equation of Faraday's law can be given by the Faraday's law formula:
{eq}EMF=-\frac {\Delta \Phi }{\Delta t} {/eq}
where EMF refers to the electromotive force or the induced voltage magnitude. The presence of {eq}\Delta {/eq} refers to the change in magnetic field flux {eq}\Phi {/eq} over time {eq}\Delta t {/eq}. The negative sign refers to the direction of the induced current according to Lenz's law.
Assuming that the solenoid has an n number of loops per unit of length (loops per meter), a cross-section area of A ({eq}m^2 {/eq}), and the current that is induced is I (A). The solenoid cuts through the lines of a magnetic field of B (measured in weber or Wb) then the magnetic flux {eq}\Phi=B*A=N*\mu _{0} *A*\frac{\mathrm{d} I}{\mathrm{d} t} {/eq} and Faraday's law formula can be written as:
{eq}EMF=-N*\mu _{0} *A*\frac{\mathrm{d} I}{\mathrm{d} t} {/eq} where {eq}\mu _{0} {/eq} is a magnetic constant called vacuum permeability and is equal to {eq}4*\Pi *10^{-7} {/eq} weber per ampere meter or Wb/A m and EMF is measured in volts (V).
Using Faraday's Law of Induction Equation: Example 2
Using Faraday's law of induction helps to calculate the magnitude of the induced emf or electromotive force (voltage).
Example:
A solenoid has 200 turns per meter and a cross-section area of 2.0 {eq}cm^2 {/eq}. The current in its windings is increasing at a rate of 50 A/s. Find the magnitude of the induced emf.
Solution:
Apply Faraday's law of induction equation:
{eq}EMF=-N*\mu _{0} *A*\frac{\mathrm{d} I}{\mathrm{d} t} {/eq} and substitute but do not forget to convert to SI units when needed!
{eq}A=2.0 cm^2=2.0*10^{-4} m^2 {/eq}.
Substituting values then gives:
{eq}EMF=-200*4*\Pi *10^{-7}*2.0*10^{-4}*50=-25*10^{-3} {/eq} V or EMF= -25 mV
Faraday's Law and Lenz's Law
The Russian physicist Heinrich Lenz noted that the induced current creates its own magnetic field and called it induced B or {eq}B \prime {/eq}. Faraday's law stated that an induced current is created in a coil or solenoid when pushed through a U-shaped magnet as a result of the change in the magnetic field flux over time. Lenz's law states that the induced magnetic field {eq}B \prime {/eq} created by the induced current according to Faraday's law will be always in the opposite direction of the magnetic field B. What follows is that the induced electric current direction is decided on the premise that its induced magnetic field must always oppose the magnet's field. The minus sign in Faraday's law formula emphasizes Lenz's law.
Lenz's law explains that when the magnet moves toward the coil or solenoid, the strength of the magnetic field flux increases in the coil. Thus, according to Faraday's law, it induces an electric current in the coil's wires but the induced current in the coil creates another magnetic field in the opposite direction of the magnet's movement direction to oppose the increase in magnetic flux.
To recall Lenz's law, always keep in mind that if the magnet moves toward the coil, the induced current must be in a direction so that its induced magnetic field pushes it away. Also, if the magnet moves away from the coil, the induced current must be in a direction so that its induced magnetic field pulls the magnet.
Simply put, Lenz's law invites a new concept of "induction opposes any change in magnetic flux."
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