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= The Motor Effect =

The motor effect is what occurs when a current carrying conductor/ wire is in the presence of a magnetic field, and experiences a force. It is a critical physics concept, essential in many modern day technological advances.

Quantitative Analysis
Motor effect occurs due to the circular magnetic fields generated around current carrying conductors, with their strength varying with the size of the current flowing through the wire and inversely to the distance from the wire. The force on a charged particle moving in a magnetic field is proportional to the strength of the magnetic field. Therefore, a stronger magnetic field will exert a greater force on a current-carrying conductor. In increasing the voltage across a circuit, thus increasing the current as per V = IR, each charged particle will experience a force due to the external magnetic field. Therefore, if there is more current, more charged particles will have a force exerted on them, leading to a larger overall force on the conductor.

The longer the section of conductor is exposed to the magnetic field, the more moving electrons simultaneously experience a force due to the external field. Therefore, the length of the conductor varies the force on the current-carrying conductor.

The force on a charged particle moving through a conductor is at a maximum when the conductor is perpendicular to the magnetic field lines and at zero when the conductor is parallel with them. Thus, the force experienced by a current-carrying conductor varies with the angle between the direction of the magnetic field and the direction of the length of the conductor.

This can all be represented mathematically by the formula:

F = B I L sinθ

where F represents force, B represents magnetic field strength, L represents the length of current carrying wire in the magnetic field, and θ represents the angle between the field lines and the current.

Qualitative Analysis
When looking at the motor effect, it is not only the magnitude of the force that is important, but also determining the direction of the force. The method most commonly used to achieve this is known as the Left Hand Rule. This is because your left hand can be used to represent different components that are integral in the motor effect. As seen in the diagram to the right, the thumb represents the direction of the current, the index finger represents the field lines and the thumb shows the resultant direction of the force.

This allows for the direction of the force produced due to the motor effect to be determined very easily, as long as the direction of the field lines and current are known. This is an essential component in the application of the motor effect, as it is critical the direction of the force being produce is known, as this is how the motor effect is put to use in inventions such as the DC motor.

History
The Motor Effect was discovered by English Physicist Michael Faraday, who's research and experiments contributed greatly to the understanding of the motor effect and electromagnetism. This, however, came off the back of Faraday expanding of the work of other scientists. Danish scientist Hans Christian Oersted discovered that the flow of an electric current through a wire produced a magnetic field. This represented the first discovery to link electricity and magnetism, paving the way for future scientist in this field of Physics. French physicist André-Marie Ampère furthered this research, showing that the magnetic force was a circular one, creating what seemed like a cylinder of magnetism around the wire. Faraday was the first to interpret what these discoveries could lead to, and by setting out to understand Oersted and Ampère's research more clearly, Faraday devised and experiment which lead to the creation of the first electric motor in 1821.

In this creation, Faraday hung a wire down into a beaker, with a secured bar magnet underneath. The beaker was then partially filled with mercury (a heavy metal which is liquid at normal room temperatures and is a good conductor). The apparatus was then connected to a battery by Faraday, sending an electrical current through the wire and creating a magnetic field around it, which subsequently reacted with the field around the magnet and caused the wire to rotate clockwise. Thus, Faraday demonstrated the motor effect worked in his creations of the earliest motor.

Importance of the Motor Effect
The discovery of the motor effect revolutionised the way scientist looked at the way electricity and magnetism were looked at in terms of their relationship with each other. The discovery and its varying applications allowed for Michael Faraday to delve deeper in to the field of electromagnetism. The motor effect is an absolutely fundamental principal in the discipline of physics, allowing for innovation and invention across the field, as well as in other branches of science. It was one of the earliest major breakthroughs in the field of electromagnetism, allowing for much more research and innovation. One major and primary example being the Direct Current motor.

The Invention of the DC Motor
The principle of the motor effect, as the name would suggest, is integral in the functioning of a DC (Direct Current) motor. Simple DC motors utilise the motor effect by placing a coil or loop of current carrying wire between two fixed magnets, which create a magnetic field. Due to the motor effect, a force will act on each side of the coil perpendicular to the magnetic field (as depicted by the formula F=BILsinθ), and the direction of this force can be determined using the left hand rule also shown above.

In a DC motor, a force of equal magnitude but opposite in direction will be experienced on either side of the coil within the motor. As these forces are equal and opposite, they cancel each other out, having a net force on the motor as zero. The force on each side of the coil will produce a torque about the axis. The torque is at a maximum when the plane of coil is parallel to the field, and is zero when the coil is perpendicular to the field lines.

Components of the DC Motor
Pair of Permanent Magnets: Two permanent magnets on opposite sides of the motor which have the opposite poles facing each other. These magnets supply the magnetic field which interact with the current in the armature to produce the motor effect.

Armature: Consists of a cylinder of laminated iron mounted on an axle, often there are longitudinal grooves into which the coils are wound. This is where the rotor coils are carried, and the external magnetic field is greatly concentrated by the iron core. The lamination also reduce eddy currents, which prevents overheating the armature.

Rotor Coils: Turns of insulated wire wound onto the armature, with the ends connected to bars on the commutator. The current passes through the coils, and they provide torque as this current interacts with the magnetic field. As they are mounted onto the rotor, torque from the coils is transferred to the rotor and then to the axles.

Split Ring Commutator: A broad ring of metal mounted on the axle at one end of the armature, and cut into an even number of separate bars (two in a simple motor). Each opposite pair of bars is connected to one coil. It provides points of contact between the rotor coils and the external electric circuit. It serves to reverse the direction of current flow in each coil every half-revolution of the motor, ensuring torque on each coil is always in the same direction.

Brushes: compressed carbon blocks, connected to the external circuit, mounted on opposite sides of the commutator and spring-loaded to make close contact with the commutator bars. They act as the fixed position electrical contacts between the external circuit and the rotor coils.

Axle: Cylindrical steel bar which passes through the centre of the armature and the commutator. It provides the centre of rotation for the moving parts of the motor.

Loudspeakers
A very common modern day technology which utilise the motor effect is the loudspeaker. Loudspeakers are used to transform electrical energy into sound energy. They consist of one circular magnet being accompanied by the opposite pole around the outside. A voice coil is attached to the speaker cone, and is allowed to vary the volume of the sound by changing the current in it. The voice coil is caused to vibrate or move in and out of the magnet by the motor effect. This is then attached to a paper speaker cone that creates sound waves in the air as it vibrates. Therefore, a larger current increased the force on the coil, which increases the sound that is produced.

The Galvanometer
A galvanometer is a device used to measure the magnitude and direction of small direct currents. When current is flowing through the coil, it experiences a force due to the motor effect. As the force is increased due to the iron core, the needle is rotated until the magnetic force is counter-balanced by the spring. As the curved magnets emit a radial magnetic field and the torque will be constant, the scale of the galvanometer will be constant. Due to these remaining constant, as per the equation

T = nBIACosθ

Where T = torque, n = number of coils (integer), B = Strength of the magnetic field (T), I = Current (A), A = area of the coil (metres squared), θ = Angle in which Force is acting on (N)

Because all components are kept constant except for the current, it is safe to say that:

T is proportional to I

By providing a means to measure small direct currents, the galvanometer is a critical piece of apparatus used throughout scientific and physics disciplines. It is an integral piece of equipment in the science world, and is made possible only through the motor effect.