Effect of Dielectric on Capacitance | Physics

Dielectrics are usually placed between the two plates of parallel plate capacitors. They can fully occupy the region between the plates or can partially occupy. Copy the link given below and paste it in new browser window to get more information on Effect of Dielectric on Capacitance www.askiitians.com/iit-jee-electrostatics/effect-of-dielectric-on-capacitance/

1. Effect of dielectrics on Effect of dielectrics on
CapacitanceCapacitance

2. Dielectric
•A dielectric is a nonconducting material
inserted between the plates of a
capacitor.
•A dielectric increases the ability of a
capacitor to store energy.
•If the dielectric completely fills the space
between the plates, the capacitance
increases by a factor k, called the
dielectric constant.
d
Aεk
C
o
××
=

3. Dielectric
•When a dielectric is
inserted between the
plates of a charged
capacitor that is not
connected to a battery
(a source of additional
charge), but the
voltage is reduced by
a factor k.
new
old
V
V
k=

4. Dielectrics

5. Effect of the Dielectric Constant
o
dielectric
E
E
k
=
o
dielectric
E
E d d
k
· = ·
r
r rr
l l
o
dielectric
V
V
k
=
Potential difference with a dielectric
is less than the potential difference
across free space
o
o
Q Q
C k k C
V V
= = ´ = ´
Results in a higher capacitance.
Allows more charge to be stored before breakdown
voltage.

6. Effect of a Metallic Slab Between the Plates
A parallel-plate capacitor has a plate separation d
and plate area A. An uncharged metallic slab of
thickness a is inserted midway between the plates.

7. Charge on one plate must induce a charge of equal magnitude but
opposite sign on the near side of the metallic slab.
Net charge on the slab is zero, electric field inside the slab is zero.
Capacitor = two capacitor in series, each having a plate separation
of (d-a)/2 as shown.

8. ( ) ( )
( )
1 2
1 1 1 1 1 1
;
2 2
1 2 1 2 1 1
; ;
2
2
1
;
o oT T
o o oT T T
o
T
T o
A AC C C C
d a d a
A A AC C C
d a d a d a
Ad a
C
C A d a
e e
e e e
e
e
= + = +
´ ´
- -
= = =
´ ´ ´ ´
- - -
´-
= =
´ -

9. Effect of a Metallic Slab between the plates
What are the differences in the result as compared to the previous
example if we insert the metallic slab as shown?

10. Two Dielectric Slabs
•Consider a parallel-plate
capacitor that has the space
between the plates filled
with two dielectric slabs,
one with constant k
1
and
one with constant k
2
.
•The thickness of each slab
is the same as the plate
separation d and each slab
fills half the volume between
the plates.
•The two different dielectric
slabs represent two
capacitors in parallel with a
plate area A/2.

11. Two Dielectric Slabs
1 2
21
1 2
1 2
2 2
2
( )
2
T
oo
T
o o
T
o
T
C C C
k Ak A
C
d d
k A k A
C
d
A k k
C
d
ee
e e
e
= +
´ ´´ ´
= +
´ ´
´ ´ + ´ ´
=
´
´ ´ +
=
´

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