How to calculate the direction of induced emf : Lenz's law

• The direction of induced current and emf is given by lenz's law.
  
• Due to change in magnetic flux through a closed loop an induced  current is established in the loop.
  
• Lenz's law states that
    'The induced current due to the induced emf always flow in such a direction as to oppose the change causing it'
  
• Now we can combine faraday's law  to find the direction of emf.
  
• Thus we can say that "The emf induced in a coil is equal to the negative rate of the change of the magnetic flux linked with it "
  
  
  
  
  
  

Explaination of lenz's law

• To explain this law again consider faradays experiment 1 in which north pole of the magnet  moves towards a closed coil.
  
• This movement of north pole of magnetic induces current in the coil in such a direction so that end of the coil ,facing and approaching north pole becomes a magnetic north pole.
  
• The repulsion between two poles opposes the motion of the magnet towards the coil.
  
• Thus work has to be done to push the magnet against  the coil.
  
• It is this mechanical work which causes the current to flow in the coil against its resistance R and supply
  the energy for the heat loss.
  
• The mechanical workdone is converted to electrical energy which produces the heat energy.
  
• If the direction of the induced current were such as not to oppsose the motion ,then we would be obtaining electrical energy continuously without doing any work ,which is impossible.
  
• So ,every things seems to be all right if we accept lenz's law otherwise the principle of conservation of the
  energy would be violated.
  
• Direction of the induced current can be found using Fleming right hand rule.
  " If we stretch thumb ,index  and middle finger  perpendicular to one another then index fingers points in direction of the magnetic field ,middle finger in direction of induced current and thum points in direction of the motion of the conductor"
  

Electromagnetic Induction (Motional EMF)

Internal Resistance of Battery (or cell)

-The resistance offered by medium in between plates of battery (electrolytes and electrodes of the cell) to the flow of current within the battery is called internal resistance of the battery.
Internal resistance of a battery usually d branch containing batteryenoted by r and in electric circuit its representation is shown below in the figure














-Internal resistance of a battery depends on factors like seperation between plates, plate area, nature of material of plate etc. For an ideal cell r=0 , but real batteries or sourcesof emf always has same finite internal resistance.
-If P and Q are two terminals of the battery shown below in the figure






then potential difference between terminals P and Q is
VP=(VP-Vx) - (VQ - Vx) = E-Ir
let VP-VQ=V
V=E-IR
now for I=0 and V=EMF
and this potential difference V is called the terminal difference of the cell or battery and defined as the emf of the battery when no current drawn from it.
-For real battery equation(4) which gives V=E-Ir whereI is the current in the branch containing battery.
-From figure(4) potential difference across the external resistance R of the circuit would be equal to terminal potential difference of the cell. Thus
V=IR also V=E-Ir
or, IR=E-Ir
which gives
I=E/(R+r) =Net EMF/Net resistance
-From equation(4) we can calculate that when current is drawn from the battery terminal potential difference is less than the EMF of the battery.

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