210

DOC.

6

PONDEROMOTIVE FORCES

Let

us

examine,

in

the second

place,

the

case

when

the

disk

is

made of

a

hard

magnetic

metal,

e.g.,

steel,

and constitutes

a

permanent

magnet,

with circular lines

of

force

distributed around

its center.

In

this

case,

the

magnetic

field

produced

by

the

passage

of the

current

through

the

disk

superposes

on

the

magnetic

field

resulting

from

this

magnetization

of the

disk.

If

we

let

Hm

denote the

strength

of the latter

field,

and

Bm

its

induction,

then

reasons

of

symmetry

permit

us

to conclude from Maxwell's

equations

that

Hm

=

0,

but

obviously

Bm

is

not

equal

to

zero.

On the other

hand,

the additional

magnetization we

have

considered

cannot

give

rise

to

a

corresponding

additional

ponderomotive

force,

for the latter

would

be the

only

ponderomotive

force

that

would

appear,

and the

system

would violate

the

law

of

equality

of

action

and reaction.

Thus,

the additional

ponderomotive

force

vanishes

together

with

Hm,

even

if

Bm

is

different

from

zero.

It

follows

that

it

is

formula

(1),

and

not

formula

(2),

that

satisfies

the

principle

of

equality

of

action

and reaction.