Magnetic Fields

Force on a current carrying wire

A Magnetic Field is a region where a force is exerted on magnetic materials. 

Magnetic Fields can be represented by field lines/flux lines and go from the North to South Pole. The closer together the lines are, the stronger the field is.

When current flows through a wire, a magnetic field is induced around the wire. The RIGHT HAND RULE can be used to work out the direction of the magnetic field. 

If a current-carrying wire is placed into an extrenal magnetic field, the field around the wire and the existing field are added together which results on a force on the wire.The direction of the force can be known through using FLEMING'S LEFT HAND RULE. If the current is parallel to the field lines, the size of the resultant force is zero.  

Convential current is measured from Positive to Negative.

The size of a force on a wire is given by the equation F=BIL

When the wire is at an angle with the magnetic field, the force is given by F=BILsintheta

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Charged Particles in a Magnetic Field

A current-carrying wire experiences a force in a magnetic field because current is the flow of negatively charged electrons.

Using the equations, current = charge/time and Velocity = distance/time with F=BIL, we can derive the equation F=BQv. 

The force on a moving charge is ALWAYS perpendicular to its direction of travel. (Which relates to circular motion). The force due to a magnetic field experienced by a particle, is independant of its mass. The radius of the circular path that is followed by a charged particle in  amagnetic field can by found by the equation, r=MV/BQ

Therefore, as the radius increases, the mass or velocity increases. If the radius decreases, the strength of the magnetic field or the charge on the particle increases. 

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The Cyclotron

Circular deflection is used in particle accelerators such as cyclotrons.

They can be used to produce;

  • Radioactive tracers
  • Radiation for radiotherapy 

How does a cyclotron work?

A cyclotron consists of two hollow electrodes attached to an alteranting PD supply placed ina vacuum chamber with a magnetic field at right angles to them.

  • Charged electrons are fired into one of the electrodes and the magnetic field makes them follow and circular path and leave the elctrode.
  • The PD between the elctrodes accleerates the particle across the gap and into the next electrode.
  • The particle ones again follows a circular path, but due to the HIGHER SPEED, the radius increases.
  • The PD is reversed so the particle is accelerated in the other direction. The process repeats until the particle leaves the cyclotron.
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Electromagnetic Induction

Magnetic Flux is a measure of how many magnetic field lines are passing through an area of Am^2. It is measured in Webers.

The more field lines that pass through an area, the greater the concentration and the stronger the magnetic field. A magnet is therefore strongest at its poles. 

If there is motion between a conducting rod and a magnetic field, the elctrons in the rod will experience a force. This will cause them to gather at one end of the rod which induces an e.m.f.

This electromagnet induction can be caused by, moving a coil towards or away from the poles of a magnet. The magnetic flux is changing which produces the e.m.f. Consequently, a current will flow. 

The size of the e.m.f produced depends on;

  • Magnetic flux through coil
  • Number of turns in the coil

Magnetic Flux Linkage ϴ is the product of the number of turns and the magnetic flux.

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Electromagnetic Induction 2

If the magnetic flux isn't perpendicular to the area, you need to use trig. 

Magnetic Flux = BAcostheta

Faradays's Law: The induced emf in a circut is equal to the rate of change of flux linkage through the circuit. 

  • The more turns in the coil, the greater the emf.
  • The greater the area of the coil, the greater the emf.
  • The stronger the magnetic field, the greater the emf.
  • The faster the speed of movement, the greater the emf. 

The area under the graph of emf against time is the change in flux linkage.

Lenz' Law: The direction of the induced emf in a conductor is such that it opposes the change producing it. 

  • When a magnet is dropped through a coil of wire, the flux in the coil increases as it approaches and induces a positive emf.
  • When the magnet is in the middle of the coil, there is no change in flux and therefore no emf produced.
  • When the magnet leaves the coil, flux decreases and so a negative emf is produced. This emf is greater as the magnet accelerates as it falls.
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Alternators

An alternator is a generator of alternating current.

A generator converts kinetic energy into electrical energy. The electric current is induced by rotating a coil in a magnetic field.

The output voltage and current chnage direction every half rotation so an alternating currrent is produced. This happens because, as the coil turns, the amount of flux through the coil varies. The most emf is induced when the magnetic field lines are being cut by the coil. 

Image result for emf time graph for generator (http://community.boredofstudies.org/attachments/264/motors-generators/22739d1299409621-someone-explain-graph-induced-emf-vs-time-graph-please-untitled.jpg)

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Alternating currents

An alternating current or voltage is one that changes with time and can be displayed on an oscilloscope. 

An alternating current/voltage produces a vertical line on the oscilloscope (provided there is no time base). A direct current/voltage produces a dot (with no time base).

To find the rms voltage or current, simply divide the peak voltage/current by root2.

Use thr rms values to find Power. 

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Transformers

A transformer is used to change the size of the voltage for an alternating current.

  • A current flows through the primary coil, creating a magnetic field. 
  • These field lines cut through the turns of wire on the secondary coil.
  • An emf and a current is induced in the secondary coil.
  • The secondary coil also has an alternating current. 

For a step up voltage: 

The voltage in the secondary coil is greater than in the primary coil.

The current in the secondary current is smaller than the current in the primary coil.

There will be more turns of wire on the secondary coil, meaning more flux linkage. 

The efficiency of a transformer can be increased by: 

- Using low resistance windings to reduce power wasted due to heating effect of current.

Use a laminated core with layers of insulation  to reduce heating in the iron core and the production of eddy currents. 

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