Chapter 23- Magnetic fields

• When a wire carries a current a magnetic field is created around the wire; the field is created by the electrons moving within the wire
• The right hand rule gives the direction of a magnetic field or direction of current. The thumb points in the direction of conventional current (+ ~~~~> -) and the fingers point in the direction of the magnetic field
• An x represents the current is going into the paper, a circle represents the current is coming out of the paper
• Flemings left hand rule: thumb is force, first finger is the magnetic field and the second finger is the current
• For F=BIL sinθ, θ is the angle between the magnetic field and the current direction
• Magnetic flux density is the strength of a magnetic field
• Magnetic flux density is a vector
• Magnetic flux density can be determined using two magnets and a top-pan balance. There is a uniform field between the magnets and when a wire length L is held perpendicular to the magnetic field, a down force is experienced by the magnets producing a mass on the scale. The current I of the wire is recorded using an ammeter then B is calculated using the equation
• A charged particle moving in a magnetic field will experience a force which can be predicted using Flemings left hand rule. The force can be calculated using F=Bev
• A charged particle moving in a circular path will have the same equations as circular motion with centripetal force equal to the magnetic force
• faster moving particles travel in bigger circles
• More massive particles move in bigger circles
• Stronger magnetic fields make the particles move in smaller circles
• Particles with greater charges will move in smaller circles
• A velocity selector used magnetic and electric fields to select charged particles of a specific velocity
• A velocity selector uses two parallel horizontal plates connected to a power supply to produce a uniform magnetic field and a uniform magnetic field is applied perpendicular to the electric field. the charged particles enter and the electric and magnetic fields deflect them in opposite directions and only particles with a specific speed will have equal and opposite deflections and so will be unaffected
• When a magnet is moved within a coil, an emf is induced across the ends of the coil
• Magnetic flux is the component of the magnetic flux density that is perpendicular to a given area and that cross-sectional area

  $\phi=$$BA\cos\theta$
• The unit for magnetic flux is the Weber Wb
• Magnetic flux linkage is the product of number of turns in a coil and the magnetic flux. This also has the unit of Weber but is sometimes weber-turn to distingush it


  magnetic flux linkage = N$\phi$
• E.m.f is induced in a circuit whenever there is a change in the magnetic flux linking the circuit
• Faradays law states that the magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux


  $\epsilon=$$-\frac{\Delta\left(N\phi\right)}{\Delta t}$
• Lenz's law states that the direction of the induced e.m.f or current is always such as to oppose the change producing it. This provides the negative sign the the equation for faradays law
• A transformer consists of a laminated iron core, a primary input coil and a secondary output coil
• In a transformer, an alternating current is supplied to the primary coil which produces a varying magnetic flux in the soft iron core. The secondary coil is wound around the same core and is therefore linked by the changing flux. According to faradays law a varying emf if produced across the ends of the second coil.


  $\frac{n_s}{n_p}=$$\frac{V_s}{V_p}$
• A step-up transformer has more turns on the secondary coil than on the primary coil therefore the voltage is greater across the secondary coil
• A step-down transformer has less turns on the secondary coil than on the primary coil therefore the voltage is smaller across the secondary coil
• The iron core of a transformer ensures that all the magnetic flux created by the primary coil links the secondary coil and none of it is lost
• For a totally efficient transformer the output power of the secondary coil is equal to the input power of its primary coil


  $\frac{I_p}{I_s}=$$\frac{V_s}{V_p}$
• In a step-up transformer the voltage is stepped up but the current is stepped down
• In a step-down transformer, the voltage is stepped down but the current is stepped up
• Transformers can be made efficient by;

  • using low resistance windings to reduce power losses due to the heating effect of the current
  • Making a laminated iron core with layers of iron separated by an insulator to reduce eddy currents induced in the core itself also minimising the heating effect
  • Using soft iron to make the core as it is very easy to magnetise and demagnetise