Chapter 14
Electromagnetism II
Abstract Chapters 13 and 14 are devoted to electromagnetism concerned with
motion of charged particles in electric and magnetic fields, Lorentz force, cyclotron
and betatron, magnetic induction, magnetic energy and torque, magnetic dipole
moment, Faraday’s law, Hall effect, RLC circuits, resonance frequency, Maxwell’s
equations, electromagnetic waves, Poynting vector, phase velocity and group velocity, dispersion relations, waveguides and cut-off frequency.
14.1 Basic Concepts and Formulae
Self-Inductance (L)
L =
N ϕ
i
=
Total flux linkage
Current linked
(14.1)
ξ = −L
di
dt
(14.2)
For a long solenoid or toroid
L =
μ 0 N 2 A
l
(14.3)
where N is the number of turns, A is the area of cross-section of each turn and l is
the length of the coil.
The energy stored in an inductor is
W = 1 /2Li
2
(14.4)
L–R Circuit
Differential equation. L
di
dt
+ i R = ξ (for charging process)
(14.5)
631
Electromagnetism II
Abstract Chapters 13 and 14 are devoted to electromagnetism concerned with
motion of charged particles in electric and magnetic fields, Lorentz force, cyclotron
and betatron, magnetic induction, magnetic energy and torque, magnetic dipole
moment, Faraday’s law, Hall effect, RLC circuits, resonance frequency, Maxwell’s
equations, electromagnetic waves, Poynting vector, phase velocity and group velocity, dispersion relations, waveguides and cut-off frequency.
14.1 Basic Concepts and Formulae
Self-Inductance (L)
L =
N ϕ
i
=
Total flux linkage
Current linked
(14.1)
ξ = −L
di
dt
(14.2)
For a long solenoid or toroid
L =
μ 0 N 2 A
l
(14.3)
where N is the number of turns, A is the area of cross-section of each turn and l is
the length of the coil.
The energy stored in an inductor is
W = 1 /2Li
2
(14.4)
L–R Circuit
Differential equation. L
di
dt
+ i R = ξ (for charging process)
(14.5)
631