Posts Tagged ‘ELECTROSTATICS’

ELECTROSTATICS TEST PAPER FOR CLASS XII

1. What orientation of an electric dipole in a uniform electric field corresponds to its stable equilibrium?

2. What is the area of the plates of a parallel plate capacitor of capacitance 2F and with separation between plates 0.5 cm?

3. What is the work done in carrying a point charge 10 nC between two points separated by a distance 5 cm on an equipotential surface?

4. A parallel plate capacitor is made by stacking ‘n’ equally spaced plates connected alternatively. If the capacitance between any two plates is ‘C’, determine the resultant capacitance of the combination

5. Calculate the coulomb force between two a particles separated by a distance of 3.2 x 10^-15 m

6. Draw graph showing variation of electric field with distance for a uniformly charged metallic sphere.

7. An electron and proton are free to move in an electric field. Which one will have greater acceleration? Why?

8. Sketch two equipotential surfaces for (a) a point charge. (b) between two plane sheets of charge.

9. Show that the work done in rotating an electric dipole of dipole moment p in a uniform electric field E by an angle θ from the equilibrium postition W = PE(1-cos θ)

10. The given graph shows the variation of charge ‘q’ verses potential difference for two capacitors C1 and C2 .The capacitors have same plate separation, but the plate area of C2 is double that of C1.Identify the line in the graph corresponding to C1 & C2 and why?

11. Derive an expression for the torque acting on an electric dipole placed in a uniform electric field.

12. Derive an expression for the capacitance of a parallel plate capacitor.

13. You are given three capacitors of value 2μF, 3μF, 6μF. How will you connect them to a resultant capacity of 4μF?

14. Two equally charged identical metal spheres A and B repel each other with a force of 2·0 x 10^-5 N. Another identical uncharged sphere C is touched to A and then placed at the mid point between A and B. What is the net force on C?

15. A dielectric slab of thickness t introduced between the plates of a parallel plate capacitor separated by a distance d. (t < d). Derive an expression for the capacitance of the capacitor

16. Describe the principle construction and working of a Van de graff Generator with the help of a neat labeled diagram.

17. Use Gauss theorem to derive an expression for the electric field at a point due to

a. an infinite plane sheet of charge of uniform charge density σ

b. a thin infinitely long straight line  of charge of uniform charge density λ

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Electrostatics Notes – Module II (Electric field, Dipole, Gauss Theorem)

Click the Link below to download Electrostatics Notes – Module II (Electric field, Dipole, Gauss Theorem and Applications)

Click Electric Charges and Field-2 to Download

Electrostatics Module 1 (Notes)

Please find below the link to the lecture notes for the first module of Electrostatics.

Electric Charges and Field-1

The download contains important points to remember, which will be an excellent aid for revision and recollection

Capacitance Study Materials and numerical problems for practice

Important concepts and formulas from CAPACITANCE
Conceptual Problems (Solved) from CAPACITANCE
Unsolved Numerical Problems for Practice from CAPACITANCE
Solved Numerical Problems from CAPACITANCE

Practice Numericals from Electrostatics

1. Four point charges +5 mC, +2 mC, +10mC and +2 mC are kept at the corners of a square of side 10 cm. A charge q=+1mC is placed at its centre. Find the net force on q.
2. Calculate the distance between two prorons such that the electrostatic force between them is equal to the weight of either.
3. Two point charges are 0.1 m apart and their combined charge is 9 mC. If they repel each other with a force 18N, then calculate the magnitude of each charge.
4. Calculate the coulomb forcebetween two alpha particles separated by a distance of 3.2 x 10^-15 m
5. A proton moves through a uniform electric field of 5.01 x 10 3 N/C. Calculate (a) the accelerationwith which the proton is moving and (b) the time taken by the proton to cover a distance of 4.8 cm.
6. How many electrons would have to be removed from or added to a penny to leave it charged with 1.0 x 10^-6 C?                    [Ans:  6.25 x 10 ¹²]
7. An electrically neutral coin of mass m = 3.0 g contains equal amount of positive and negative charge. Assuming the coin is made up of pure copper, what is the magnitude of the total positive (or negative) charge on the coin. Molar mass of copper = 63.5 g mol^-1 [Ans: 1.32 x 10⁵ mC
8. What is the Coulomb’s force between two small charged spheres having charges of 2.0 x 10^-7 C and 3.0 x 10^-7C placed 30 cm in air?           [Ans:  6.0 x 10^-3N]
9. Find the electrostatic force between two protons placed in free space separated by a distance 20 cm [Ans: 5.76 x 10^-27N]
10. The electrostatic force between 200mC and 500 mC placed in free space is 5 gf. Find the distance between the two charges. [Ans: 135.5 m]
11. A pith ball A of mass 9 x 10^-5 kg carries a charge of 5mC. What must be the magnitude and sign of the charge on another pith ball B held 2 cm directly above the pith ball A so that the pith ball remains stationary? [Ans:  - 7.84 x 10^-12 C]
12. Two similar charges repel each other with a force of 44.1 N when placed two cm apart in air. Calculate the strength of the charges. [Ans: ± 1.4 mC]
13. The force between two charged objects is to be kept unchanged even though the charge on one of the objects is halved keeping the other the same. If d is the original separation between charges, then what is the new separation? [Ans: d/Ö2]
14. The electrostatic force of repulsion between two positively charged ions carrying equal charges = 3.7 x 10^-9N when they are separated by a distance of 5 Å. How many electrons are missing from each ion? [Ans: 2]
15. Two fixed point charges +4q and +2q units are separated by a distance x. Where should the third point charge be placed for it to be in equilibrium? [Ans:  at a distance of 0.59 x from +4q]
16. How far apart should two electrons be if the force of repulsion between them is equal to the weight of electron?  [Ans:  5.1 m]
17. Two identical charges repel each other with force of 0·1 N when placed O· 5 m apart in ail (a) Find the value of charges (b) Determine the magnitude of the charges if they were placed in a liquid whose permittivity is tell times that of the vacuum. [Ans. (a) 1·67 mC (b) 0·53 mC]
18. Two small spheres each of mass 10 mg are suspended from a point by threads 0·5 m long. They are equally charged and repel each other to a distance of 0·28 m. What ia the charge on each? g = 10 ms^-2. [Ans. 1·59 x 10^-8C]
19. The normal hydrogen atom consists of proton and an orbital electron. Assume the orbit to be circular with radius 5·3 X 10^-11 m. Find the force between the proton and electron by using Coulomb’s law. [Ans. 8·2 x 10^-8N]
20. Two point charges q1 and q2 are 3 m apart and their combined charge is 20 mC. If one repel the other with a force of 0·075 N, what are the two charges? [Ans. 15 mC and 5mC ]
21. Two equally charged identical spheres P and Q repel each other with a force of 2 x IO^-5 ­N. Another identical uncharged sphere R is touched to P, then placed at the midpoint between P and Q. Find net force on R. [Ans. 2 x 10^-5 N ]
22. Two sphere of charges + 10 C and + 40 C are placed 12 cm apart. Find the position of the point between them where force on + 1 C is zero. [Ans. 0·04 m from + 10 C]
23. There are two equal charges each of 1.0 C. What should be the separation between them so that the force between them is equal to the weight of a 20 kg child? [Ans. 6·78 km]
24. Two equal charges are separated by 1 m. Calculate the magnitude of the charges so that the force between them is equal to the weight of a 20 kg child. [Ans. 1·476 x 10^-4C]
25. Two equal charges each of 1·0 C are separated by a distance of 1 cm. Calculate the mass of a body so that the force between these charges equals the weight of the body. [Ans. 9·18 X 10¹² kg]
26. Two insulating spheres are rubbed against each other and are placed 1 mm apart. If they attract each other with a force of 2.0 N, how many electrons were transferred from one sphere to the other during rubbing? [Ans. 9 x 10¹⁰]
27. Two small pith balls are 1 cm apart in air and carry charges of 2 x 10^-9 C and – 6 x 10^-9 C respectively. Calculate the force of attraction. If the balls are touched and then separated by a distance of 1 cm, what will be the force between them? [Ans. 108 X 10^-5 N ; 36 X 10^-5 N repulsive]
28. Calculate the value of two equal charges if they repel one another with a force of I kgf when separated by a distance of 1 cm in air. Now, if the charges are situated in an insulating liquid having relative permittivity 8 times that of air, then what would be the magnitude of the charges if they exert the same force on each other? [Ans. 0·33 mC ; 0·87 mC]
29. Five electrons have been removed from each atom to form ions. Find the electrostatic force between two such ions when separated by a distance of 4Å in air. [Ans, 3·6 x 10^-8 N]
30. Four charges + 4 mC, + 5 mC, + 4 mC and + 5 mC are placed at the corners A, B, C and D of a square of side 10 cm. Calculate the force on a charge of + I mC placed at the centre of the square. [Ans. 0 N]
31. Two identical metallic spheres P and Q. have charge on each as 6 x 10^-7 C. They are placed half meter away from each other. Another identical sphere R having no initial charge is first touched with sphere P and then with Q. Sphere R is then with drawn. Find the new force between P and Q. [Ans.4·86 x 10^-3 N]
32. Calculate the magnitude and direction of force on unit positive charge at the centre of a square of each side 2 m, when three charges of +8 mC each are placed at the three corners of the square. [Ans. 3·6 x 10⁴N towards the corner without charge]
33. Four equal charges each of + 2mC are placed at the corners of a square of side 50 cm. Find the force on anyone of the charges. [Ans. 275·6 x 10^-3 N repulsive along the diagonal of square]
34. Two identical balls each carrying a charge Q are suspended from a common point by two strings of equal length l. Calculate the mass of each ball if the angle between “the strings is 2q in equilibrium.
35. Two equally charged identical metal spheres A and B repel each other with a force of 2·0 x 10-5 N. Another identical uncharged sphere C is touched to A and then placed at the mid point between A and B. What is the net force on C? [Ans. 2.0 x 10^-5 N along BC]

Long ANswer Type Questions from Electrostatics

1. Obtain an expression for the electric field intensity due to a uniformly charged ring of radius r at a point on the axis of the ring.
2. Express Coulomb’s law in vector for.
3. Derive an expression for the electric field due to an electric dipole at a point on (a) the axial line (b) the equatorial line.
4. Derive an expression for the torque acting on an electric dipole placed in a uniform electric field.
5. Show that the work done in rotating an electric dipole of dipole moment p in a uniform electric field E by an angle ? from the equilibrium postition W = PE(1-cos ?)
6. Derive Coulomb’s law from Gauss’ law.
7. Use Gauss theorem to derive an expression for the electric field at a point due to an infinite plane sheet of charge of uniform charge density ?
8. Use Gauss theorem to derive an expression for the electric field at a point due to a thin infinitely long straight line  of charge of uniform charge density ?
9. Derive an expression for the electric field at a point due to uniformly charged spherical shell using Gauss’ law.
10. Derive an expression for the capacitance of a parallel plate capacitor.
11. Find the equivalent capacitance of three capacitors of capacitances C1, C2 and C3 connected in (1) series (2) parallel
12. Derive an expression for the electric potential due to a point charge q at a distance r from it.
13. Giving a labeled diagram explain the principle and working of a Van de Graaff generator.
14. A dielectric slab of thickness t introduced between the plates of a parallel plate capacitor separated by a distance d. (t < d). DEerive an expression for the capacitance of the capacitor.