Question

In an experiment ,two coils C1 and C2 are placed close to each other.find out the expression for the induced emf in the coil C1 due to a change in the currrent through the coil C2?

Answer 1

Derivation:
let ФВ be the magnetic flux linked with the secondary coil when a current I flows through the primary coil.
Then,
ФВ α I
or
ФВ=MI
where M is the constant for the pair of coils and it is called as coefficient of mutual induction e
if I=1, then M=ФВ
The mutual inductance of two coil is numerically equal to the magnetic flux linked with one coil (secondary) when unit current flows through the neighboring(primary coil)
the emf induced in secondary coil is
ε=-dФВ/dt
=-d(MI)/dt
ε=-MdI/dt
If dI/dt =1, then M=ε(numerically)
The mutual inductance of two coil is equal to the emf induced in one coil(secondary) when there is unit rate of change of current in other coil.(primary).

Answer 2

Hey !!

Let a magnetic flux be (Φ₁) linked with the coil C₁ due to current (I₂) in coil C₂

We have :

=>                           Φ₁ ∝ I₂

                              Φ₁ = Ml₂

∴                       dΦ₁/dt = M dl₂/dt

=>                    e = -M dl₂/dt

GOOD LUCK !!