The current potential in the cylindrical coordinate system

j

j

Q

r e

P R e

Q

j

ln Q ln Q e

ln Q ln Q j

Im ln(Q)

Q P b

y

z x jy

j

1

P

r

R

b

x

R

j

b) Im ln

b

1

e

b

Inside the cylinder.

sin(k )

U

r

k

(1)

(1)

General case.

gk

cos(k ) hk

k 1

Case of the line current source

U r, ck rk sin(k )

(potential on the x-axis = 0):

k 1

Outside the cylinder.

sin(k )

Um

r

k

(2)

(2)

General case.

gk

cos(k ) hk

k 1

Case of the line current source:

Um r, dk r k sin(k )

k 1

Current potential on the

i

1

k

sin k

surface of the cylinder.

Uc

t

2

k

k 1

Relative magnetic

r

permeability

0

ck Rk dk R k

i

tk

2 k

kck R

k 1

0kdk R

k 1

0i

R

k 1

R

2 bk

k 0

k

k

i

k

System for series

ck

R

dk R

t

2 k

coefficients

i

k

k

k

r ck R

dk

R

t

2 k