KENDRIYA VIDYALAYA BARKUHI

ASSINGNMENT – 1

(BASED ON UNIT – I: ELECTROSTATICS)

Section – A

Marks – 1

  1. What is the amount of work done in moving a point charge Q around a circular

arc of radius r at the centre of which another point charge q is located ?

  1. A charge q is moved from a point A above a dipole of dipole moment p to a point B below the dipole in equatorial plane without acceleration. Find the work done in the process.
  1. Define Electric Flux. Write its SI unit?
  2. A point charge Q is placed at point O as shown in the figure. The potential difference VA– VBpositive. Is the charge Q negative or positive?
  3. Figure shows a point charge +Q, located at a distance R/2 from the centre of a spherical metal shell. Draw the electric field lines for the given system?
  4. Depict the electric field lines due to two positive charges kept a certain distance apart.
  5. The figure shows the field lines of a positive point charge. What will be the sign of the potential energy difference of a small negative charge between the points Q and P ? Justify your answer.
  1. Why do the electrostatic field lines not form closed loops ?
  2. . A point charge +Q is placed in the vicinity of a conducting surface. Trace the field lines between the charge and the conducting surface.
  3. . Define dielectric constant of a medium. What is its S.I. unit ?
  4. The field lines of a negative point charge are as shown in the figure. Does the kinetic energy of a small negative charge increase or decrease in going from B to A ?
  1. Represent graphically the variation of electric field with distance, for a uniformly charged plane sheet. (1)
  2. Draw a graph to show a variation of resistance of a metal wire as a function of its diameter keeping its length and material constant. (1)
  3. What is the electric flux through a cube of side 1 cm which encloses an electric dipole ? 1

Section – B

Marks – 2

  1. What is electrostatic shielding ? How is this property used in actual

practice ? Is the potential in the cavity of a charged conductor zero ?

  1. Derive an expression for the work done in rotating a dipole from the angle Ɵ0 to Ɵ1in a uniform electric field E.
  2. The small metallic spheres, A and B of identical size have charges 6 µC and -2 µC respectively. They are brought in contact with each other and then separated and kept at distance of 10 cm between their centres, estimate the coulomb force acting between them in air.

Section – C

Marks – 3

  1. Find the electric field intensity due to a uniformly charged spherical shell at a point

(i)outside the shell and

(ii) Inside the shell.

Plot the graph of electric field with distance from the centre of the shell?

  1. Derive an expression for the electric field intensity at a point on the equatorial

P line of an electric dipole of dipole moment

and length 2a. What is the

direction of this field ?

  1. (a) A parallel plate capacitor (C1) having charge Q is connected, to an

identical uncharged capacitor C2 in series. What would be the charge

accummulated on the capacitor C2?

(b) Three identical capacitors each of capacitance 3mF are connected, in tern,

in series and in parallel combination to the common source of V volt. Find

out the ratio of the energies stored in two configurations.

  1. A thin metallic spherical shell of radius R carries a charge Q on its surface. A

point charge Q/2 is placed at the centre C and another charge 12Q is placed

outside the shell at A at a distance x

from the centre as shown in the figure.

(i) Find the electric flux through the shell.

(ii) State the law used.

(iii) Find the force on the charges at the centre C of the shell and at the

point A.

  1. . Calculate the equivalent capacitance between points A and B in the circuit

below. If a battery of 10 V is connected across A and B, calculate the charge

drawn from the battery by the circuit.

6. . Define an equipotential surface. Draw equipotentialsurfaces :

(i) in the case of a single point charge and

(ii) in a constant electric field in Z-direction.

Why the equipotential surfaces about a single charge are not

equidistant ?

(iii) Can electric field exist tangential to an equipotential surface ? Give

reason.

7. Derive an expression for the electric field intensity at a point on the equatorial

P line of an electric dipole of dipole moment and length 2a. What is the

direction of this field ?

8. Define an equipotential surface. Draw equipotentialsurfaces :

(i)in the case of a single point charge and

(ii)in a constant electric field inZ-direction.

Why the equipotential surfaces about a single charge are not equidistant ?

(iii)Can electric field exist tangential to an equipotentialsurface ? Give reason.

9. A charge is distributed uniformly over a ring of radius ‘a’. Obtain an expression for the electric intensity E at a point on the axis of the ring. Hence show that for points at large distances from the ring, it behaves like a point charge.

10. Two parallel plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates while Y contains a dielectric

medium ofr= 4.

(i)Calculate capacitance of each capacitor if equivalent capacitance of the combination is 4F.

(ii)Calculate the potential difference between the plates of X and Y.

(iii)Estimate the ratio of electrostatic energy stored in X and Y.

11. Given a uniformly charged plane/ sheet of surface charge density σ = 2X1017 C/m2 .

(i)Find the electric field intensity at a point A, 5mm away from the sheet on the left side.

(ii) Given a straight line with three points X, Y & Z placed 50 cm away from the charged sheet on the right side. At which of these points, the field due to the sheet remain the same as that of point A and why?

12. A network of four 10 F capacitors is connected to a 500 V supply as shown in the figure. Determine the (a) equivalent capacitance of the network and (b) charge on each capacitor.

13. A 16  resistance wire is bent to form a square. A source of emf 9 V is connected across one of its sides as shown. Calculate the current drawn from the source. Find the potential difference between the ends C and D. If now the wire is stretched uniformly to double the length and once again the same cell is connected in the same way, across one side of the square formed, what will now be the potential difference across one of its diagonals ?

14. A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected : (a) The electric field between the plates of the capacitor (b) The energy stored in the capacitor Justify your answer by writing the necessary expressions.

15. Calculate the potential difference and the energy stored in the capacitor C2 in the circuit shown in the figure. Given potential at A is 90 V, C1 = 20 F, C2 = 30 F and C3 = 15 F.

16. Two capacitors of capacitance 10 F and 20 F are connected in series with a 6 V battery. After the capacitors are fully charged, a slab of dielectric constant (K) is inserted between the plates of the two capacitors. How will the following be affected after the slab is introduced : (a) the electric field energy stored in the capacitors (b) the charges on the two capacitors (c) the potential difference between the plates of the capacitors Justify your answer.

17 Define the electric resistivity of a conductor. Plot a graph showing the variation of resistivity with temperature in the case of a (a) conductor, (b) semiconductor. Briefly explain, how the difference in the behaviour of the two can be explained in terms of number density of charge carriers and relaxation time.

18. Three circuits, each consisting of a switch ‘S’ and two capacitors, are initially charged, as shown in the figure. After the switch has been closed, in which circuit will the charge on the left-hand capacitor (i) increase, (ii) decrease and (iii) remain same ? Give reasons.

Q51. Find the equivalent capacitance of the network shown in the figure, when each capacitor is of 1 . 19. When the ends X and Y are connected to a 6 V battery, find out (i) the charge and (ii) the energy stored in the network.

20. If N drops of same size each having the same charge, coalesce to form a bigger drop. How will the following vary with respect to single small drop?

(i) Total charge on bigger drop (ii) Potential on the bigger drop (iii) Capacitance

21. Two capacitors of unknown capacitances C1 and C2 are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C1 and C2 . Also calculate the charge on each capacitor in parallel combination.

22. Use Gauss’s Law to derive the expression for the electric field due to a uniformly charged thin spherical shell of radius R at a point r :

  1. Inside the shell and
  2. Outside the shell

23 (a)
Define torque acting on a dipole of dipole moment p placed in a uniform electric
field E. Express it in the vector form and point out the direction along which it
acts.
(b) What happens if the field isnon-uniform?
(c) What would happen if the external field / and
E is increasing (i) parallel to / p
(ii)anti-parallelto p ?

24. In the following arrangement of capacitors, the energy stored in the 6F capacitor is E. Find the value of the following :

(i)Energy stored in 12F capacitor.

(ii)Energy stored in 3F capacitor.

(iii)Total energy drawn from the battery.

Section – D

Marks – 5

Q1 (a) Derive ac expression for the electric field E due to a dipole of length ‘2a’ at point distant r from the center of the dipole on the axial line.

(b)Draw a graph of E versus r for r>a.

(c)If this dipole were kept in uniform external electric field E0 diagrammatically represent the position of the dipole in stable and unstable equilibrium and write the expressions for the torque acting on the dipole in both the cases.

Q2. Use Gauss’s theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density σ.

(b) An infinitely large thin plane sheet has a uniform surface charge density +σ. Obtain the expression for the amount of work done in brining a point charge q from infinity to a point, distant r, in front of the charged plane sheet.

Q3 (a) Distinguish, with the help of a suitable diagram, the difference in the behaviour of a conductor and a dielectric placed in an external electric field. How does polarised dielectric modify the original external field ?

(b) A capacitor of capacitance C is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following

change ?

(i) charge stored by the capacitor.

(ii) field strength between the plates.

(iii) energy stored by the capacitor.

Justify your answer in each case.

Q4(a) Explain why, for any charge configuration, the equipotential surface

through a point is normal to the electric field at that point.

Draw a sketch of equipotential surfaces due to a single charge (2q),

depicting the electric field lines due to the charge.

(b) Obtain an expression for the work done to dissociate the system of three

charges placed at the vertices of an equilateral triangle of side a as shown

below.

Q5. (a) Deduce the expression for the torque acting on a dipole of dipole

Moment P placed in a uniform electricfield E. Depict the direction

of the torque. Express it in the vector form.

(b) Show that the potential energy of a dipole making angle u with the

u( )=- p E . Hence find out the u52 direction of the field is given by.

amount of work done in rotating it from the position of unstable

equilibrium to the stable equilibrium.

Q6. (i) Use Gauss s law to find the electric field due to a uniformly charged

infinite plane sheet. What is the direction of field for positive and

negative charge densities ?

(ii) Find the ratio of the potential differences that must be applied across the

parallel and series combination of two capacitors C1

and C2 with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases

becomes the same.

Q7 (i) If two similar large plates, each of area A having surface charge densities

1s and 2s are separated by a distance d in air, find the expressions for

(a) field at points between the two plates and on outer side of the plates.

Specify the direction of the field in each case.

(b) the potential difference between the plates.

(c) the capacitance of the capacitor so formed.

(ii) Two metallic spheres of radii R and 2R are charged so that both of these

have same surface charge density s. If they are connected to each other

with a conducting wire, in which direction will the charge flow and why ?

Q8. . (a) Two isolated metal spheres A and B have radii R and 2R respectively, and same charge q. Find which of the two spheres have greater :

(i)Capacitance and

(ii) (ii) energy density just outside the surface of the spheres. (2

(iii) (b) (i) Show that the equipotential surfaces are closed together in the regions of strong field and far apart in the regions of weak field. Draw equipotential surfaces for an electric dipole. (1+1) (ii) Concentric equipotential surfaces due to a charged body placed at the centre are shown. Identify the polarity of the charge and draw the electric field lines due to it. (1)

Q9. (a) Compare the individual dipole moment and the specimen dipole moment for H2O molecule and O2 molecule when placed in (i) Absence of external electric field (ii) Presence of external electric field. Justify your answer.

(b) Given two parallel conducting plates of area A and charge densities + σ & -σ. A dielectric slab of constant K and a conducting slab of thickness d each are inserted in between them as shown. (i) Find the potential difference between the plates. (ii) Plot E versus x graph, taking x=0 at positive plate and x=5d at negative plate. (2)

Q10. (a) Show, using Gauss’s law, that for a parallel plate capacitor consisting of two large plane parallel conductors having surface charge densities +  and –  , separated by a small distance in vacuum, the electric field (i) in the outer regions of both the plates is zero, (ii) is / o in the inner region between the charged plates. Hence obtain the expression for the capacitance of a parallel plate capacitor. (b) Explain what is the effect of inserting a dielectric slab of dielectric constant k in the intervening space inside the plates on (i) the electric field, (ii) the capacitance of the capacitor

Q31. (a) Define the term ‘electric flux’. Write its S.I. unit. (b) Given the components of an electric field as Ex = x, Ey = 0 and Ez = 0, where  is a dimensional constant. Calculate the flux through each face of the cube of side ‘a’, as shown in the figure, and the effective charge inside the cube.

Q11 (a) Define equipotential surface. Why is the electric field at any point on the equipotential surface directed normal to the surface ? (b) Draw the equipotential surfaces for an electric dipole. Why does the separation between successive equipotential surfaces get wider as the distance from the charges increases ? (c) For this dipole, draw a plot showing the variation of potential V versus x, where x (x > 2a), is the distance from the point charge – q along the line joining the two charges.

Q12. (a) Deduce the expression for the potential energy of a system of two charges q1 and q2 located at  1 r and 2 r respectively in an external electric field.

(b) Three point charges, + Q, + 2Q and – 3Q are placed at the vertices of an equilateral triangle ABC of side l. If these charges are displaced to the mid-points A1 , B1 and C1 respectively, find the amount of the work done in shifting the charges to the new locations

Q13. Define electric flux. Write its S.I. unit. State and explain Gauss’s law. Find out the outward flux due to a point charge + q placed at the centre of a cube of side ‘a’. Why is it found to be independent of the size and shape of the surface enclosing it ? Explain.

Q14. Define electric flux. Write its S.I. unit. State and explain Gauss’s law. Find out the outward flux due to a point charge + q placed at the centre of a cube of side ‘a’. Why is it found to be independent of the size and shape of the surface enclosing it ? Explain.

Q15. (a) Define electric flux. Write its S.I. unit. ‘‘Gauss’s law in electrostatics is true for any closed surface, no matter what its shape or size is.’’ Justify this statement with the help of a suitable example.

(b) Use Gauss’s law to prove that the electric field inside a uniformly charged spherical shell is zero.

Q16 (a) Derive the expression for the energy stored in a parallel plate capacitor. Hence obtain the expression for the energy density of the electric field.

(b) A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than that stored initially in the single capacitor.

Q17. (a) Derive the expression for the potential energy of an electric dipole of dipole moment  p placed in a uniform electric field E . Find out the orientation of the dipole when it is in (i) stable equilibrium, (ii) unstable equilibrium. (b) Figure shows a configuration of the charge array of two dipoles.

Obtain the expression for the dependence of potential on r for r > a for a point P on the axis of this array of charges.

Q18. (a) Define electric flux. Write its S.I. unit. (b) Using Gauss’s law, obtain the electric flux due to a point charge ‘q’ enclosed in a cube of side ‘a’. (c) Show that the electric field due to a uniformly charged infinite plane sheet at any point distant x from it, is independent of x.

Q19. (a) State Gauss’s law in electrostatics. Show, with the help of a suitable example along with the figure, that the outward flux due to a point charge ‘q’, in vacuum within a closed surface, is independent of its size or shape and is given by q / o .

(b) Two parallel uniformly charged infinite plane sheets, ‘1’ and ‘2’, have charge densities +  and – 2  respectively. Give the magnitude and direction of the net electric field at a point (i) in between the two sheets and (ii) outside near the sheet ‘1’.

Q20. (a) Define electrostatic potential at a point. Write its S.I. unit. Three point charges q1, q2 and q3 are kept respectively at points A, B and C as shown in the figure. Derive the expression for the electrostatic potential energy of the system.