DOC.

6

PONDEROMOTIVE FORCES

209

Doc.

6

On the Ponderomotive

Forces

Acting on

Ferromagnetic

Conductors

Carrying

a

Current in

a

Magnetic

Field

by

A. Einstein

[Archives

des sciences

physiques

et

naturelles 30

(1910):

323-324]

A

current-carrying

conductor

in

a magnetic

field

H

is subjected

to

a

ponderomotive

force,

the formula

for

which

is

F

=

[iH],

(1)

where

i is

the

vector

of the

current

density,

and

the

expression

in

the brackets

is

the

vector

product.

This

formula

is

applicable,

in

particular,

in

the

case

where the

body

conducting

the

current is

not

magnetizable,

i.e.,

where the

magnetic

induction

B

is

equal

to

the

intensity

of the

magnetic

field

H. If the conductor of the

current

is

magnetizable

and

its

magnetic

state

is consequently

characterized

by

two vectors

H

and B

that

are

different

from

each

other,

then

one

has to ask

oneself

which

of these

two vectors

gives

rise to

the

ponderomotive

force

sought.

Till

now

this

role

has

been attributed

to

B,

and

it has

been

accepted

that

F

=

[iB].

(2)

But

we

will show in

a simple special case

that,

even

in

the

case

of

a

magnetic

conductor,

formula

(1)

is

the

correct

one.

Let

D be

a

metal

disk

through

which

a

current flows from

its

center to

its

periphery.

This

current

is

provided

by

a battery P;

the other

lines in

the

diagram

complete

the

circuit.

By

virtue of

the

principle

of

equality

of

action and reaction,

regardless

of

the

material

of

which

the

disk

is

made,

the resultant of

all

the

electrodynamic

forces

acting

on

the

different

parts

of the

system

is

zero.

This must

be

especially so

if

the disk D

is

made of

a nonmagnetic

substance

(B

=

H).

D