  # Electromagnetic Induction In this picture an ammeter is connected in the circuit of a conducting loop.  When the bar magnet is moved closer to, or farther from, the loop, an electromotive force (emf) is induced in the loop.  The ammeter indicates currents in different directions depending on the relative motion of magnet and loop.  Notice that, when the magnet stops moving, the current returns to zero as indicated by the ammeter. Take a look as some Electromagnetic Induction Experiments and find out how to launch a ring or crush a pop can with a circuit.

 Q:     A current loop is placed in a uniform magnetic field.  What orientation of the loop makes the magnetic flux maximum?  What orientations make the magnetic flux minimum? A:    The concept of the flux is defined as the "amount of lines of field" traversing a surface.   Therefore, the maximum "amount of lines of field" passes through a surface when the surface is perpendicular to the lines of field, and the "amount of lines of field" passing through a surface is minimum (equal to zero) when the surface is parallel to the lines of field.  A convenient mathematical representation of this conceptual definition of flux is given by expressing flux as the dot (scalar) product between field and surface (both considered as vectors): B = B . dA.  The magnitude of this scalar product is B = BA cos .  When = 0 (meaning that the area is perpendicular to the field), cos = 1 and the flux has its maximum value.   When = 90° (meaning that the area is parallel to the field), cos = 0 and the flux has its minimum (zero) value.   Remember that an area can be considered a vector with magnitude equal the magnitude of the area and the direction in the normal of the area. Q:     Will dropping a magnet down a long tube of conducting material cause a current in the tube? A:    According to Faraday-Lenz law of electromagnetic induction, a current is generated in a closed conducting path (in this case the wall of the tube) if the cross-sectional area defined by the tube is traversed by a variable magnetic flux.  The magnet creates a dipole-like magnetic field that will pass through the cross-sectional area of the cylinder, thus defining a magnetic flux.  This flux varies in time only when the magnet approaches entrance and enters into the tube, and also when it approaches the exit and exits from the tube.  Only during these transient periods of time a current will be induced in the tube.  During the time when the magnet travels through the interior of the tube (as assuming that the tube is very long and the magnet is very far from both of the tubes ends) the magnetic flux remains constant and therefore no current will be induced in the tube. Q:     What is the purpose of putting an inductor in a circuit? A:    Presence of an inductor in an electric circuit has the effect of slowing down the increase of the current when the circuit is being closed, and slowing down its decrease when the circuit is being opened.  The behavior of such a circuit is characterized by the "time constant" ( = L/R ) of the circuit.  The larger the inductance, the larger the time constant. Inductances in circuits maybe purposely inserted or parasitic.  The purposely inserted inductors are most often used in oscillating circuits used e.g. in radio emission or radio transmission applications.

## References

### Facts

The SI unit for magnetic flux ( B) is the weber, 1 Wb = 1 T . m2
The SI unit for inductance is the henry, 1 henry = 1 H = 1  T . m2 / A

Lenz's Law:  An induced current has a direction such that the magnetic field of the current opposes the change in the magnetic field that produces the current.

### Equations

 Magnetic flux ( B) through an area in a magnetic field (B) B = B . dA Magnitude of Magnetic flux ( B) where is the angle between B and A. B = BA cos Faraday's law of induction for a loop Faraday's law of induction for a closely packed coil of N turns Relation of emf ( ) to E Faraday's law (most general form) The inductance (L) of an inductor Inductance per unit length near the middle of a long solenoid of crass-sectional area A and n turns per unit length Self-induction Rise of current in an RL circuit Decay of current in an RL circuit Magnetic energy UB = L i2 Magnetic energy density Mutual induction # List of Topics

 Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization  ครั้งที่

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