Inductance

Question 1

what’s back emf and its equation

Answer 1

when the current changes in a solenoid (aka inductor) the magnetic field changes. this induces a current in itself that opposes the change.

ε = -L dI/dt
L: inductance
I: Current
- because it opposes the current producing it

Question 2

energy density of a magnetic field equation

Answer 2

u = B²/2µ₀
u: magnetic field energy density
B: field strength

Question 3

inductance equation

Answer 3

L = µ₀n²lA = µ₀N²A/l
l: length
n: turn density
A: area of cross-section
L: inductance

Question 4

what is mutual inductance

Answer 4

if two wire loops are close to each other:
I₁ current flows in 1 (increasing). this creates an increasing B-field, B₁.
this B-field passes through loop 2 causing an increasing flux, Φ₂.
this induces an emf, ε₂ and this current I₂ in the opposite direction to I₁

Question 5

mutual inductance equation

Answer 5

Φ₂ = M*I₁
Φ₂ : flux through the second loop
I₁: current in the first loop

(this also works vice-versa)

Question 6

unusual method to find the inductance

Answer 6

equate the magnetic field energy to the energy stored in an inductor.

∫B²/2µ₀ dV = ½LI²