Formula revision Electromagnetic induction - July-Dec Revision

1. Faraday’s law of electromagnetic induction
Є = -dФ/dt … (1)

Where

Є = emf produced
Ф = ∫B.dS = the flux of the magnetic field through the area.

2. i = Є/R = -(1/R) dФ/dt …(2)

where i = current in the circuit
R = resistance of the circuit

3. Є = vBl

Where
Є = emf produced
v = velocity of the conductor
B = magnetic field in which the conductor is moving
l = length of the conductor

4. Induced electric field

∫E.dl = -dФ/dt .. (4)

where

E = induced electric filed due to magnetic field B

5. Self induction
Magnetic field through the area bounded by a current-carrying loop is proportional to the current flowing through it.

Ф = Li … (5)

Where

Ф = ∫B.dS = the flux of the magnetic field through the area.
L = is a constant called the self-inductance of the loop.
i = current through the loop.

6. Self induced EMF

Є = -dФ/dt = -Ldi/dt ….(6)

7. Self inductance of a long solenoid

L = µ₀n² πr² l … (7)

8. Growth of current through an LR circuit

i = i₀(1 - e^-tR/L) … (8)
= i₀(1 - e^{-t/ τ} ) … (9)

where

i = current in the circuit at time t

i₀ = Є/R
Є = applied emf
R = resistance of the circuit
L = inductance of the circuit
τ = L/R = time constant of the LR circuit


10. Decay of current in a LR circuit

i = i₀(1 - e^-tR/L) … (10)
= i₀(1 - e^{-t/ τ} ) … (11)

i = current in the circuit at time t

i₀ = current in the circuit at time t = 0
R = resistance of the circuit
L = inductance of the circuit
τ = L/R = time constant of the LR circuit

12. Energy stored in an inductor

U = ½ Li² … (12)

13. Energy density

u = U/V = B²/2µ₀


14. Mutual induction


Ф = Mi … (14)

Where
M = constant called mutual inductance of the given pair of circuits

Є = -Mdi/dt …. (15)