Download electric potential and capacitance

ELECTRIC POTENTIAL AND CAPACITANCE
1 MARK QUESTIONS
Q1: The electric potential is constant in a given region . what can you say about
electric field there?
Ans:
E=-dV/dr
As V is constant, E is zero.
Q2:A charge of 2C moves between two points maintain at a potential difference of
1 Volt. What is the energy acquired by charge?
Ans:
Energy(W)=QxV=2 x 1 joule.
Q3:How much work is done in moving a 500 microcoulomb charge between
two points on an equipotential surface?
Ans: Zero.
Q4:Write the physical quantity that has its unit Coulomb/Volt? Is it vector or
scalar quantity?
Ans:Capacitance. It is a scalar quantiy.
Q 5:Write down the relation between dielectric constant and electricsusceptibility?
Ans: K=1+x.
Q.6 For the following graph, which of the two: the charge on the capacitor or the
potential used to charge it is kept constant?
E
C
Ans.6 The given graph represents E α 1/C . This is satisfied by E= Q2/2C. Hence
charge is kept constant.
Q.7 Draw an equipotential surface in a uniform electric field.
Ans.7
E
Q.8 What should be the work done if a point charge is taken from a point A to the
point B in the given diagram with charge +q at the centre?
A
+q
Ans.8 W=Charge x Pot. Diff
B
W= Chargex0
W=0
2 MARKS QUESTION
1. Find the equivalence capacitance between X and Y.
2. A parallel plate capacitor is charged by a battery to a potential V. It
is disconnected and a dielectric slab is inserted completely to fill
the space between the plates. How will
Q.3 Derive the Relation between electric field and potential
Let dV = potential difference between A and B.
= work done in taking unit +ve charge from A → B or from B → A against
the field
= E. dr
Negative gradient of potential is electric field.
Q.4 Derive the expression for the Electric Potential Energy
The electric potential energy of a system of charges is defined as the work done in
assembling the system of charges assuming them initially at infinity from one
another.
(i) For a system of two charges: If two charges q1 and q2 are at a distance r12, then
electric potential energy is given by
(ii) For a system of three charges:
(iii) For a system of n -charges:
3MARKS QUESTION
Q.1. (a)Derive expression for capacity of parallel plate capacitor.
(b) Derive expression for capacity of parallel plate capacitor with dielectric as
medium between the plates
Q.2 Derive the expression for electric potential due to dipole at an axial point.
Q 4. Draw an equipotential surface for a system, consisting of two
charges Q, Q separated by a
distance ‘ r’ in air.
5 MARKS QUESTION
Q.1 Derive expression for energy stored in a capacitor and hence obtain the
expression for energy density of a parallel plate capacitor.
Ans.1 Consider a parallel plate capacitor of capacity C. Let at any instant the charge
on thecapacitor be Q’. Then potential difference between the plates will be
V’.Suppose the charge on the plates increases by d Q’. The work done will be
Q:2:
Q3 A capacitor is charged from a battery. Assuming that the capacitor is
disconnected from the
charging battery, explain how;
a) the capacitance
b) potential difference across the plates and
c) the energy stored in the capacitor change, when a medium of dielectric constant
k is introduced between the plates.
Ans (a) Capacitance increasesaas C=KC0
(B)potential decreases as V=V0/k
(c) Energy decreases as U=1/2CV2
Q.4 Derive an expression for the Electric Potential due to a point charge
Ans.4 The electric potential due to a point charge at a any point is defined as the work
done in bringing per unit (infinitesimal and positive) test charge from infinity to given
point. Let q be the charge and P a point at a distance r from q at which the potential is to
be found.
Suppose test charge
is being brought from infinity to point P . When test charge
at a distance x,the electrostatic coulomb force on the test charge is
Where
is unit vector along
.
Work done by external force against electric force during small displacement dx is
is
Work done in bringing test charge
from infinity to point P is
The electric potential at point P (distant r from point charge q ) is
Clearly, the potential due to a point charge varies inversely with distance r from the
point charge (fig.)