1Preliminaries

IB Electromagnetism

1.2 Forces and Fields

In modern physics, we believe that all forces are mediated by fields (not to

be confused with “fields” in algebra, or agriculture). A field is a dynamical

quantity (i.e. a function) that assigns a value to every point in space and time.

In electromagnetism, we have two fields:

– the electric field E(x, t);

– the magnetic field B(x, t).

Each of these fields is a vector, i.e. it assigns a vector to every point in space

and time, instead of a single number.

The fields interact with particles in two ways. On the one hand, fields cause

particles to move. On the other hand, particles create fields. The first aspect is

governed by the Lorentz force law:

Law (Lorentz force law).

F = q(E + v × B)

while the second aspect is governed by Maxwell’s equations.

Law (Maxwell’s Equations).

∇ ·E =

ρ

ε

0

∇ ·B = 0

∇ ×E +

∂B

∂t

= 0

∇ × B − µ

0

ε

0

∂E

∂t

= µ

0

J,

where we have two constants of nature:

– ε

0

= 8.85 × 10

−12

m

−3

kg

−1

s

2

C

2

is the electric constant;

– µ

0

= 4π ×10

−6

m kg C

−2

is the magnetic constant.

Some prefer to call these constants the “permittivity of free space” and “per-

meability of free space” instead. But why bother with these complicated and

easily-confused names when we can just call them “electric constant” and “mag-

netic constant”?

We’ve just completed the description of all of (classical, non-relativistic) elec-

tromagnetism. The remaining of the course would be to study the consequences

of and solutions to these equations.