Magnetic fields

• Magnetic fields strength, B:

  $B=$$μ0I/2πr$
• Magnetic flux :

  $Φ=$$B X A$

  unit of Φ= weber(wb)
• Magnetic flux linkage:

  $=$$N x Φ$
• EMF induced:

  • emf induced = -(Δ magnetic flux linkage)/(Δ time)
  • on a graph: emf induced = - gradient
• Relationships:

  $Φ∝B$

  Graph Φ will be similar in shape to B. (Values can be different)

  $B∝I$

  Graph B will be similar in shape to I. (Values can be different)

  $Φ∝I$

  Graph Φ will be similar in shape to I.

  $NΦ∝Φ$

  Graph NΦ will be similar in shape to Φ.
• Magnetic force on a moving charge in the magnetic field:

  $F=$$BQvsinθ$
• Magnetic force:

  $F=$$IBLsinθ$
• When charge travels in circle:

  centripetal force = magnetic force

  $mr^2/r=$$BQvsinθ$

  $r=$$mv/Bq$
• charge in both electric and magnetic fields:

  Electric force = Magnetic force

  $Eq=$$BQvsinθ$

  $v=$$E/B$

  NOTE:

  • If speed increases, magnetic force increases. electron moves downwards.
  • If speed decreases, electric force greater than magnetic force, electron moves upwards.
  • Even if q changes, it won't affect the velocity, hence it will go in straight line,
• Current balance:

  Δ weight in balance reading = magnetic force on wire

  Current into:

  If current is into paper and magnetic poles are north south, there is a downward magnetic force on the wire. But there will be an upward reaction force on the balance, so balance reading decreases.

  Current out:

  If current is out of paper and magnetic poles are north south, there is an upward force on the wire. Hence, there will be a downward reaction force on the balance. So balance reading will increase.
• Hall effect:

  At equilibrium(Vh)

  upward force = downward force

  $Eq=$$Bqv$

  Vh = BI/net