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Electric potential : It is the amount of work done to move a unit +ve charge from infinity to a point in the electric
field against electric force without acceleration.
V = W/Q. ( It is a scalar quantity )
SI unit : Volt or J/C
Dimensional formula : [ M L T A ]
Electric potential due to a point charge : Consider a +ve charge Q is
placed at the point O. Let P be the point where we have to find the potential
due to the charge Q. Let a unit +ve charge q is placed at a point A at a
distance x from the point O.
Let dW be the small amount of work done to move the charge q from point A through a
small displacement dx
At what distance from a point charge the value of electric field and potential have same value?
Ans. At a distance r =1m
6 charges each of value 6μC are placed at the each corner of a regular hexagon of side 9cm respectively. Find
out the potential at the centre of the hexagon?
Q1.
Q2.
Ans.
Q3. Eight charges each of value q are placed at the vertices of a cube find out the net potential at the centre of
the cube?
1
Two charges 3 μC and -2 μC are located 15 cm apart at what distance on the line joining the two charges the
electric potential zero? If potential at infinity is takenas zero.
Q4.
Ans.
Four charges Q, Q, -Q and -Q are placed at the corner A, B, C and D of a square of side, a respectively (i)
find out the electric potential at the centre. (ii) If E and F are the midpoint of the side, BC and CD. What will
be the work done in carrying a charge e from O to E and F.
Q5.
Ans.
2
# At a point on the axis
# At a point on the equator
4
Q6. Two charges q and -q are located at points (0,0,-a) and (0,0,a) respectively. (a) what is the electrostatic
potential at the points. (0,0,z) and (x,y,0). (b) Obtain the dependency of potential on the distance are of the
point from the origin where r >> a. (c) How much work is done in moving a small test charge from point (5,0,0)
to (-7,0,0)
Ans. As the system act as a dipole and the point (0,0,z) lies at a point on the axis of dipole
Point (x,y,0) lies at the equator of dipole
As the point (5,0,0) and (-7,0,0) lies at the equator of the dipole so
Show that the electric field is equal to the -ve of potential gradient
Consider electric field due to charge Q located at the origin O. Let A
and B be the two adjacent points separated by a distance dr.
# The negative sign indicate that in
the increasing direction of electric
field potential will decrease
If the potential in the region of space around the point ( -1m, 2m, 3m ) is given by V = ( 10x + 5y - 3z ). Find out the
component of electric field at this point.
Q7.
Q8. A uniform electric field of 300 N/C is it directed along -ve X-axis A, B and C are
the 3 points in the field having xy coordinates as shown in the fig. Find out the
value of ΔV ΔV and ΔV
As point A and B are at same potential.
V = V
ΔV
Q9. The variation of electrostatic potential with the distance X for a given
charge distribution is as shown in figure. From the points marked A,B and
C identify the point at which electric field is zero and maximum
Q10. The variation of V as a function of x is as shown in Fig. Plot the graph showing
the variation of E with x
5
Ans.
Ans.
Ans.
Ans.
Q14. 27 spherical drops are combined to each other to form a bigger drop is each smaller drop is charged to
a potential potential of 100 V. Find out the potential of bigger drop
Ans.
Q15. The given figure shows the field lines of an isolated positive and negative
charge
(a) give the sign of potential difference between point P and Q and between
point B and A
(b) give the sign of potential energy difference of a small negative charge
between points, Q and P & A and B
(c) give the sign of work by the field in moving a small positive charge from
Q to P
(d) give the sign of work done by the external agency in moving a small
negative charge from point B to A
(e) does kinetic energy of a small negative charge, increase or decrease in
going from B to A
Ans.
7
(c) In moving a small +ve from Q to P work has to be done by external agency against the electric force.
So work done by the field is-ve
(d) A small negative charge from B to A. Work has to be done by external agency, so it is positive.
(e) Due to force of repulsion on negative charge, velocity decreases and kinetic energy decrease in
moving from B to A.
Equipotential surface :
Surfaces potential at any point of which will remains same known as
equipotential surface
Properties of equipotential surfaces:
- Work to move a charge over an equivalent surface is zero
- Electric field is always perpendicular and equipotential surface at every point.
Reason:
Two equipotential surfaces will never intersect each other.
Closer the equipotential surfaces stronger is the field and vice - versa.
Q16.
What would be the work done if a point charge q is taken from point A to B on the surface of a
sphere
Ans.
10
Equipotential surfaces for two identical +ve charge :
Equipotential surface for uniform electric field :
Q19. Draw 3 equipotential surfaces for uniform electric field, increasing in +z direction.
Q20. Charges q and -q are placed at points A and B respectively which are 2L distance apart. C is the
midpoint between A and B. Find out the work done in moving a charge Q from C to D along the
semicircle CRD.
Electrostatic Potential energy : It is the amount of energy required to assemble the charges at a
location from infinity.
Potential energy for a system of two charges (in the absence of external field) :
Consider a point charge q is at rest at point P in space
# Potential energy for a system of 3 charges ( in the absence of external field):
Q21. Four charges are arranged at the corner of a square of side d as shown in figure. (i)
Find out the amount of work required to put together this arrangement. (ii) A charge
q is brought to the centre of the square. The four charges being held fixed at its
corner. How much extra work is needed to do this.
Ans.
11
13.
Potential energy of a system of two charges in the presence of external field :
Q26.
(a) Determine the electrostatic potential energy of a system consisting of two charges, 7 μC and -2 μC in
the absence of action placed at ( -9cm , 0,0) and ( 9cm ,0,0) respectively.
(b) How much work is required to separate them infinitely away from each other.
(c) Suppose the same system is now placed in an external field E = A / r where A =.
What would be the electrostatic energy of the configuration.
14.
Behaviour of a conductor in electric field:
1. Net electric field inside the conductor is zero.
When the conductor is placed in electric field E. Its free electron begins to
move in opposite direction as that of negative charges are reduced on the left
end of the conductor and positive charges will induce on the right end. The
process will continue till E becomes equal and opposite to the external field,
so that net field become zero
Just outside the surface of a charged conductor electric field is perpendicular to the surface of
conductor.
If electric field is tangential to the surface of conductor, their exist a surface current around the
surface of conductor, which is not possible in electrostatic
Reason:
3. Net charge inside the surface of a conductor is zero.
As inside the surface of a conductor E. = 0
4. Potential on the surface and within the surface of a conductor is constant and will be equal to
the potential on the surface of conductor
Electric field at a point on the surface of a charge conductor is proportional to surface charge
density.
6. Net electric field in the cavity of a hollow charged conductor is zero
Electrostatic shielding: The phenomenon of making a region free from any electric field
# Electric inside the cavity of a hollow conductor vanishes. Such a field free region is called
Faraday cage.
Applications of electrostatic shielding : 1. In a thunderstorm with lightning it is safe inside a car than
under a tree. The metallic body of car provides electrostatic shielding.
- Sensitive electronic components are protected from external electric disturbances by placing metal
shields around them.
Capacity of a parallel plate capacitor:
Consider two plates P and Q having surface charge densities
and
respectively. Let A and d be the cross sectional area and
separation between the plates respectively
Factors on which capacity of a parallel plate capacitor depends :
Cross sectional area of each plate.
Separation between the plates.
Permitivity of the medium between the plates.
Q29. A parallel plate capacitor has plate area of 25 cm² and separation of 2 mm between its plate. The
capacitor is connected to 12 V battery. (i) Find out the charge on the each plate of capacitor. (ii) If
the plate separation is decreased by 1 mm , what extra charge is given by the battery to the positive
plate.
16.
Force between the plates of a parallel plate capacitor:
17.
Combination of capacitors :
(i)
Series combination:
Consider 3 capacitors having capacities
are connected in series with a battery of V volt
(ii) Parallel combination
Consider 3 capacitors having capacities
are connected in parallel with each other with
a battery of V volt
Q30. Find out the equivalent capacitance of the combination of
capacitors between point A and B as shown in figure. Also
calculate the total charge in the circuit when a battery of 100 V is
connected between the points A and B.
Q31.
Find out the capacitance between point A and B as shown in figure
Q34. Find out the equivalent capacitance of the network as shown in figure.
If both plates of a parallel plate capacitor are connected
to the same potential the capacitor will be short circuit
19.
20.
Q35. In the circuit shown in the figure, if the point C is grounded and
potential at point A is 1200 V. Find out the charge on each capacitor
and potential at point B
Q37. Find out the potential difference between point A and B in the circuit.
Under what condition V - V. = 0
