12_physics_electrostatics_test_03_.pdf

8/17/2019 12_physics_electrostatics_test_03_.pdf

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01: ,

.

02: . & .

.

03: +

( ) ( )K q K q

r r

− +

+

04: o A

d

∈

8 × 8 10 12

128 10o AC

d

−

∴ = ×

/2 6

12

''

' 8 10 2 6'

o

o

AC C K

d

AC C K

d

−

⇒ = ×

= × = × × ×

05:

∴ 1 + 2

1 11

1 2 1 22

/ 2

2

/ 2

2 2 2 2

o o

o o o o

K A K AC

d d

K A K A K A K AC C

d d d d

∈ ∈= =

∈ ∈ ∈ ∈= = ⇒ = +

C’ = 96 × 10-12

pF

1 2( )2

o AC K K d

∈

= +

A B

D C

o

+10 cσ

P

A B

r r

p

a a

-q + qv


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Ans 06: Suppose a capacitor is connected to a battery and it supplies small amount of change dq

at constant potential V, then small amount of work done by the battery is given by

dw = Vdq

⇒ dw = q/cdq (Since q = CV)Total work done where capacitor is fully changed to q.2 2 2

0

1 /

2 2

q q

o

q C V dw W q c dq W qdq W

C C C = = ⇒ = ⇒ = =∫ ∫ ∫

This work done is stored in the capacitor in the form of electrostatic potential energy.

⇒

Ans 07: Gauss’s Theorem states that electric flux through a closed surface enclosing a charge q

in vacuum is 1/ o∈ times the magnitude of the charge enclosed

Is

σ /2.

1, 2, & 3

According to Gauss’s theorem / ...........(1)o

o

S q

σ φ = ∈ =

∈

We know . E dsφ = ∫ For the given surface

1 2 3

. . .S S S

E ds E ds E dsqφ = + +∫ ∫ ∫

1 3

. cos cosS S

E ds o Eds oφ • •⇒ = + +∫ ∫

2

290 .o

S forS E ds oθ

= ∴ = ∫

∵

1 2

.2 .........(2)

S S

S S

o o

E ds E ds

E ds ds

E S

φ

φ

φ

= +

= +

=

∫ ∫

∫ ∫

Combined eq. (1) & (2)

E.2S =o

S σ

∈

W = ½ CV2

W = U =1

2

CV2

/ oqφ = ∈

E =2

o

σ

∈


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Ans 08: (a) Dielectric constant is defined as the ratio of capacitance of a capacitor when the

dielectric is filled in between the plates to the capacitance of a capacitor when these

is vaccuum in between the plates

In K =Capacitance of a capcitor when dielectric is in between the plates

Capacitance of a capcitor with vaccuum in between the plates.

Cm

Co

Capacitance of a parallel plate capacitor with dielectric depends on the following

factors omKA

C d

∈=

(1) Area of the plates

(2) Distance between the plates

(3) Dielectric constant of the dielectric between the plates

(b) Let the capacitance of each capacitor be C

Cp = C + C = 2C

CS =2

C C C

C C

×=

+

Let Vp and VS be the values of potential difference

This2 2 21 1

22 2

Up CpVp C Vp CVp= = × × =

22 21 1

2 2 2 4

C CVsUs CsVs Vs= = × × =

But UP = US (given)

22

2

2

4

1/ 4

CVsCVs

VpVs

=

= ⇒

Vp : Vs = 1 : 2

12_physics_electrostatics_test_03_.pdf

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