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 = µ

_{0}n² πr² l … (7)

8. Growth of current through an LR circuit

i = i

_{0}(1 - e

^{-tR/L}) … (8)

= i

_{0}(1 - e

^{-t/ τ }) … (9)

where

i = current in the circuit at time t

i

_{0}= 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 = i

_{0}(1 - e

^{-tR/L}) … (10)

= i

_{0}(1 - e

^{-t/ τ }) … (11)

i = current in the circuit at time t

i

_{0}= 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 = B²/2µ

_{0}

14. Mutual induction

Ф = Mi … (14)

Where

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

Є = -Mdi/dt …. (15)

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