CBSE Class 12 Physics 2014 Delhi Set 1 Paper

Question : 24 of 30

Marks: +1, -0

Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.
(b) The electric field inside a parallel plate capacitor is

{\E}

. Find the amount of work done in moving a charge

q

over a closed rectangular loop abcda.

OR
(a) Derive the expression for the capacitance of a parallel plate capacitor having plate area

{A}

and plate separation

d

.
(b) Two charged spherical conductors of radii

R_1

and

R_2

when connected by a conducting wire acquire charge

q_1

and

q_2

respectively. Find the ratio of their surface charge densities in terms of their radii.

Solution:

(b)

W\;=\;\text " Force "\; × \;\text " Displacement "\;

F\;=q E

As displacement

=0

, so work done is also zero.

(a)

\;E\;=\;{σ}/{ε_0}=\;{Q}/{A ε_0}

∴ \;V=E d=\;{Q d}/{A ε_0}

\;\text " Capacitance, "\;\;C=\;{Q}/{V}=\;{ε_0 A}/{d}

(b) When the two charged spherical conductors are connected by a conducting wire they acquire the same potential.
i.e.,

\;{K q_1}/{R_1}\;=\;{K q_2}/{R_2}

⇒ \;\; \;{q_1}/{q_2}=\;{R_1}/{R_2}

Hence, ratio of surface charge densities,

\;\;{σ_1}/{σ_2}=\;{q_1 \/ 4 π R_1^2}/{q_2 \/ 4 π R_2^2}

\;\;{σ_1}/{σ_2}=\;{q_1 R_2^2}/{q_2 R_1^2}

\;\;{σ_1}/{σ_2}=\;{R_1}/{R_2} × \;{R_2^2}/{R_1^2}=\;{R_2}/{R_1}

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