Does The Dielectric Constant decides the strength of electric field? If so then why?
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Dielectric constant
K
K
is actually the same thing as relative permittivity, and it increases the overall permittivity
ϵ
ϵ
. So in general, whenever you see the permittivity of free space
ϵ
0
ϵ0
in an equation, if you're dealing with a dielectric, you can multiply it by the dielectric constant and see how the equation changes.
For example, since
C=
ϵ
0
A
D
C=ϵ0AD
, multiplying
ϵ
0
ϵ0
by
K
K
increases capacitance by
K
K
. Since
∮E⋅dA=
Q
ϵ
0
∮E⋅dA=Qϵ0
by Gauss's Law, multiplying
ϵ
0
ϵ0
by
K
K
decreases electric field magnitude by
K
K
.
There is no contradiction because there is no increase in electric flux. The dielectric decreases the electric field magnitude, which decreases the electric flux and decreases the voltage across a capacitor as well.
C=
Q
V
C=QV
and the capacitance increases because the voltage decreases while the charge remains the same.
K
K
is actually the same thing as relative permittivity, and it increases the overall permittivity
ϵ
ϵ
. So in general, whenever you see the permittivity of free space
ϵ
0
ϵ0
in an equation, if you're dealing with a dielectric, you can multiply it by the dielectric constant and see how the equation changes.
For example, since
C=
ϵ
0
A
D
C=ϵ0AD
, multiplying
ϵ
0
ϵ0
by
K
K
increases capacitance by
K
K
. Since
∮E⋅dA=
Q
ϵ
0
∮E⋅dA=Qϵ0
by Gauss's Law, multiplying
ϵ
0
ϵ0
by
K
K
decreases electric field magnitude by
K
K
.
There is no contradiction because there is no increase in electric flux. The dielectric decreases the electric field magnitude, which decreases the electric flux and decreases the voltage across a capacitor as well.
C=
Q
V
C=QV
and the capacitance increases because the voltage decreases while the charge remains the same.
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