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Electric field intensity - closed path denoted by ABCD
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permitivity
About Permeability And Permitivity
The strength of electric field orelectrostatic force strength or
intensity of field (all synonymous
terms) is measured & expressed in terms of force experienced
by unit positive charge placed insphere of influence of another
source charge, which has produced the electric field.
We often express the strength ofelectric field as electric lines
of forces. When we say electric linesof forces i t is nothing but a
vectorial way of saying; which specifies the direction of electric
field. Thedirection is actually the direction of line denoting the
electric electrostatic force. So we can sayelectric field intensity
is basically a force on unit positive charge hence direction of
these force arethe direction lines denoting electric lines of
force.
Let us consider a closed path denoted by ABCD.
This closed path (Hollow or solid,immaterial at this stage of
discussion)is placed in uniform electric field ofstrength E.
Electric field intensity = E
Now the force on unit positive chargeis = E
This force will act on each & everypoint of surface ABCD.
The totalnumber ofelectric lines of forces willbe total force
acting inside the closedpath ABCD.
This can be understood by a visualexample. Let us suppose that
rain isfalling and we placed a similar closedpath under the rain.
We cannot count
the total number of lines along whichrain drop are falling but
we definitelycan count or estimate totalamount/volume of rainfall
inside theclosed path (Which is nothing but rain flux).
Similarly we cannot count physically the total number of
electric lines of force so alternatively wecalculate the total
force on the whole surface ABCD. Since for each point on ABCD there
would bea line of force so this can be mathematically obtained by
taking the surface integral of electric fieldover the surface
ABCD.
The physical quantity thus obtained is electric flux and in case
of magnetism it is magnetic flux.
The above integral has to be carried over surface ABCD so we can
write:
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7/29/2019 About Permeability and Permitivity
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Equation 1
Equation 2
Equation 6
Equation 7
Now the above equation one is not fully correct as we not
incorporated or taken intoconsideration the fact that the (free
space or vacuum or anything else) be themedium has different
ability or power to let through or establish an electric field.
The above fact can be best understood as suppose the closed
surface ABCD iskept in medium other than vacuum, the total number
of electric lines of forces (orthe intensity of field in new
medium) through the surface ABCD gets modified.Say D and flux is 1
.
It is very clear from below figure that the field intensity (or
number of lines of forces) upon enteringthe closed surface ABCD is
different from what it was before entering.
So for medium inside ABCD we can write equation 2.
Now from equation 1 and 2:
/ 1 = E/D [Equation 3]
The ratio represented by equation 3 is called reciprocal of
permittivitythat is:
1/ 1 = D/E = 1/0
Hence we can finally write in case of electrostatics:
D = E 0 [Equation 4]
Hence we can finally write in case of magnetism:
B = H 0 [Equation 5]
So we can observe from equation 4 and 5that the strength of
electric filed or magnetic field isaltered by a factor0 or0.
Hence for any point on closed surface ABCD, the strength of
electric & magnetic field which wassupposed to be E orB
respectively has become E 0 orH 0 because of limitation to the
establishment of electric field or magnetic field in any medium.
Now the rectified equation 1 validfor any medium other than vacuum
is:
Now using 4 in above equation we can write:
Now equation 7is the final equation for total electric flux
through the surfaceABCD in any medium. If we want to calculate the
density of that flux than it willbe:
Because ofequation 8:
1. D in electricity and B in magnetism are called flux
density.
