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ELECTRIC POTENTIAL & CAPACITORS
1. Find the work done in placing a charge of 8nC on a condenser of capacity 100μF.
2. Find the electric field b/w 2 metal plates 5mm apart, connected by a 12V battery.
3. Give two examples for polar and non-polar dielectrics
4. Sketch a graph to show how the charge Q acquired by a capacitor of capacitance C varies with increase in potential
difference between its plates. What does the area under the graph indicates?
5. A regular hexagon of side 10cm has a charge of 5μC at each of its vertices. Calculate the potential at the centre of the
hexagon.
6. An electron is placed inside a capacitor (5μF). It is found to be stationary i.e. its weight is balanced by the electrostatic
force. Find the potential difference across the plates of the capacitor if the plate separation is d.
7. What is the work done in moving a charge 100nC from point A to point B 5cms apart, where both points A and B lie on
the same equipotential surface? Explain your answer.
8. Define electric potential. What is the line integral of electric field over a closed loop?
9. The fig shows the variation of electrostatic potential V with distance ‘x’ for a given charge distribution. From the points
marked A, B, and C identify the point at which the electric field is i) Zero ii) maximum. Explain your answer in each
case.
V
A
B
x
10. A parallel plate capacitor with air between the plates has a capacitance of 8 p F. What will be the capacitance if the
distance between the plates is reduced by half and the area of the plates is doubled?
11. Two point charges 4q and q are fixed a distance 2m apart. Find the point on the line joining them at which the net
electric field intensity in zero. What is the potential at this point? If a charge of magnitude –3q is placed at this point, in
which direction will it move? What will be its potential energy at this point?
12. When 2 capacitors C1 and C2 are connected in series, then the net capacitance is 1.2 farad, when they are connected in
parallel the net capacitance is 5 farad. Find the values of C1 and C2.
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13.
14. A uniform electric field (E) exists b/w the 2 charged plates as shown in the figure. What would be the work done in
moving a charge q along the path ABCDA. Hence define conservative fields and give 2 properties.
15. Charges of 4μC each are placed at the four corners of a square of side 1m. Find the electric field and potential at the
center. What would these quantities be if one of the given charges were negative?
16. Three charges –Q1, +Q2, -Q3 are placed as shown in the figure. Find in vector form the force acting on Q2 charge.
17. Find the ratio of the potential differences that must be applied across the i) parallel ii) series combination of two
identical capacitors so that the energy stored in the two cases becomes the same.
18. A thin metal sheet is placed in the middle of a capacitor. What will be the effect on the capacitance?
19. A hollow sphere of radius R is given a charge Q. Sketch a graph to show the variation of Electric field intensity with
distance from center. On another graph plot the potential against distance.
20. The values of electric field intensity and electric potential at a point due to a point charge are 32N/C and 16 J/C
respectively. Calculate the magnitude of charge and distance of the charge from the point of observation
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21. Find the equivalent capacitance b/w points A and B. Capacitance of each capacitor is of 1μF.
22. A metal wire is bent into a circle of radius 10cm. It is given a charge of 200µC, which spreads on it uniformly. Calculate
the electric potential at its centre.
23. Calculate the voltage needed to balance an oil drop carrying 10electrons, when located between plates of a capacitor,
which are 5mm apart.
24. Two pith balls, each of mass 5x10 -4 kg are suspended by silk threads, each of length 0.2m from the same point and are
given the same charge. They separate till the angle between the threads is 60°. Calculate the charge on each pith ball.
25. Twenty seven spherical drops of radius 3mm and carrying 10 -12 C of charge are combined to form a single drop. Find
the capacitance and the potential of the bigger drop.
26. An isolated capacitor (sphere) has a capacitance 50pF. (i) Calculate its radius. (ii) How much charge should be placed on
it to raise its potential to 10 4 V?
27. A capacitor of 1μF is connected in series with the parallel combination of three capacitors of 2μF, 3μF and 6μF.The
energy stored 6μF capacitor is 27J. Calculate the total energy stored in the system.
28.
The radius of the metallic sphere is 10m and the dielectric strength of the gas is 108V/m. For safety reasons, the field
should never exceed 20% of this value. What is the maximum charge that can be given to the sphere?
29. A charge of 5C is placed at the origin and –10C is placed at the point x = 30. Find a point on the x axis at which
a.
Electric field is zero
b. Potential is zero
30. 3 charges of 5C each are kept on the corners of a square of side 1m. Find the electric field and potential at the fourth
corner.
31. A parallel plate capacitor is made of 2 plates having area A separated by a distance d. A dielectric slab of thickness d/4
and having dielectric constant 100 is introduced in b/w the plates. Derive the capacitance of this capacitor
32. Two capacitors when joined in series give a net capacitance of 2F and when these capacitors are joined in parallel, the
net is 9F. Find the values of the two individual capacitors
33. The potential at point A is 10 volts and at point B is 20 volts. What is the direction of electric field b/w A and B? Find the
amount of work done in moving a charge of 2C from point A to point B.
(b) What is the amount of work done in moving a 100nC charge b/w two points 5cm apart on an equipotential surface
34. A parallel plate capacitor of capacitance 100 μF is charged to 200 V. After disconnecting it form the battery, using an
insulated handle, the distance between the plates is doubled. Find the new
i) Potential difference between the plates
ELECTRIC POTENTIAL – CAPACITORS-XII
and
ii) Energy stored in the capacitor.
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35. What is an equipotential surface? A uniform electric field of 300 N/C is directed along PQ. A, B and C are three points in
the field having x and y coordinates as shown in the figure. Calculate potential difference b/w A & B , A & C and B & C.
36. A capacitor of 60C is connected to 200V supply and another capacitor of 30C is connected to 100V . Find the charge and
energy stored on each capacitor. Now these 2 capacitors are disconnected from the supply and are joined to each other
such that positive plate of 1st is connected to positive plate of 2nd and similarly negative plates of both are also joined
together. Find the loss in energy for the system. Why does this loss occur?
37. The flux of the electrostatic field, through the closed spherical surface S ’, is found to be four times that through the
closed spherical surface S. Find the magnitude of the charge.
38. An electrician requires a capacitance of 2µF which is to be operated across 1KV. A large number of 1µF capacitors are
available to him each of which can take up to a maximum voltage of 400V. Suggest a possible combination to use minimum
number of capacitors? How many capacitors do we need in the arrangement?
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