Electric and magnetic fields,

microwave therapy

Dubravka Krilov

Sanja Dolanski BabićNovember, 2010

Electric field

E – electric field strength = electric force per unit charge

the region around the charged body

Presentation of electric field

vector field – field lines

in each point of the region,

the magnitude and direction

of force acting at unit positive

charge (test charge)

is called strength of electric

field

the electric force changes

the energy of the body

scalar field –

equipotential surfaces

in each point of the

space the potential

energy of the test charge

is called electric

potential

qFE /

qW /

Electric field of the point charge

inhomogeneous field Strength of electric field

Principle of superposition

0rr

QrE

24

1)(

i i i

ii r

r

QrErE i0i

2

)()(

Potential energy in the electric field

- potential energy of unit charge at point A is electric potential:

A

A

Apot Wr

QQrE 21

4

1)(

A

Apot

Ar

Q

q

rEr 1

4

1)(

Q1

Q2

charge Q2 is in the electric field of charge Q1, at distance rA from Q1. The potential energy is:

)()( 2 AApot rQrE

- points of equal potential build

the equipotential surface

Charge in homogeneous field

d

UE

qEF

electric field of capacitor

electric field always act by electric force to charge and

always change amount of speed

UQW

WEkin

http://magnetizam.ifs.hr/

Charge in homogeneous field

Cell membrane as capacitor

d

UE

mVm

V

nm

mVE /10

106

1060

6

60 7

9

3

Intracellular

Extracellular

Electric dipole model for electrical

activity of the heart

i

i

i lqp

lqp

(p ~ 10-30 C m)

- electric dipole is a pair of

opposite charges q at distance ℓ;

it has a dipole moment

- for more dipoles the net dipole

moment is vector sum of

individual contributions -

situation in the heart

potential of a dipole

r

d

l

r+ = r

r- = r + d

d = l cos a

)coslr(

q

r

q

)q()q(

a

44

r >> l24

1),(

r

rpr 0

a

34

1

r

rpE 0

r l cos a << r2

Note: for point charge ~ 1/r; E ~ 1/r2

- q

+q

electric field of a dipole

Electric dipole in the external

electric field

d

EpM

EqlM

FdM

asin

torque of couple of forces rotates

the dipole in external electric field

Electromagnets

Bar magnets

the region around moving charge or electric current

Magnetic field

r

IB

r 20

l

INB

r

40

Magnetic induction

Magnetic induction - B

magnetic field is the vector field - the field lines are closed curves

force between two wires which carry electric currents:

magnetic induction is force on unit current element (I2 ℓ =1 Am):

21

2I

d

IF

d

IB

2

Point charge in electric and

magnetic field

EqBqF

v Lorentz force

Earth B ~ 50 T= 0.5 G

Model of dynamo

Biomagnetism

Some organisms use the Earth's

geomagnetic field for the

orientation and navigation.

Magnetotactic bacteria produce tiny

magnetite particles (Fe3O4 ), the

clearest in nature.

SourceMagnetic induction

( T )

Human brain ~ 10 -13

Urban noise ~ 10 -7

Earth’s field 0.5· 10 -4

Bar magnet 0.001-1

Electromagnet < 16

Electromagnetic induction

tUU sin0

tNU

tII sin0

If the flux of magnetic field

through the coil is time

dependent, the voltage will be

generated in the coil.

Faraday law:

Demonstration of electromagnetic induction

The magnitude of the

current depends on speed

of magnet motion in or

out of the coil, and the

number of loops in the

coil.

If we insert the magnet into

the coil it will cause the

change of magnetic field and

current flow due

electromagnetic induction.

Electromagnetic field

energy density of electric and magnetic field

electromagnetic wave is transversal – direction ofpropagation is perpendicular

to the planes of oscillation of

both fields

wave velocity depends on substance's properties

the source of field is oscillating charge

oscillating fields are mutually perpendicular

22

2

1

2

1 BE

V

E pot

tsinBB

tsinEE

0

0

00

11

cv

microwave frequencies 1- 3

GHz emitted by dipole aerialtypes of aerials

Microwave therapy

technique of heating

biological tissue by

electromagnetic radiation

high frequency oscillations

generated in magnetron

equipment

absorption coefficient, a

the best absorption of microwaves

occurs in muscle tissue

standing waves increase the heating at

tissue boundaries

x

t eIIa

0 Beer’s law:

Intensity of transmitted radiation

Intensity of entranced radiationMicrowave therapy