18 From Gauss’ law, egeedl fir-ds one ~ a or Here, ris the perpendicular distance from the charged (i) (@) Electric field due to a thin infinite plane sheet of charge with uniform surface charge density 6 at any nearby point (Gaussian surface [for infinite plane sheet of charge] and £0 [for any charged conducting surface] (b) Electric field intensity due to two equally and ‘oppositely charged parallel plane sheet of charge at any point E=£ [between the two plates] 80 and E=0 Joutside the plates} Chapterwise CBSE Solved Papers : PHYSICS: (iii) Electric field due to a thin charged spherical shell of radius R at a distance r from its centre. ‘To find the field ata distance r from the centre of the spherical shell () For point lying outside the shell (r>) fas Sine, Band dS avin eo the same direction, Ef as = = Since, (b) Field at a point inside the shell (r< R) Here, the charge inside the Gaussian surface shell As, q=0 > (o) Field at a point on the surface (r= R) On putting > 4 4g R? eo where, o is surface charge density, Previous Years Questions 1 Mark Questions Multiple Choice Questions 1. A charge Q is placed at the centre of a cube. The electric flux through one if its face is ‘BSE 2023 Q Q Q Q @) 2 oe oe @ 2 or OZ, 8 Ox, 2. A cylinder of radius r and length fis placed in an uniform electric field parallel to the axis of the cylinder. The total flux for the surface of the cylinder is given by ‘CBSE SOP 2021.27 (@) zero war (Ex? (@2En7 Which statement is true for Gauss’ law? ‘CBSE SP 2021-22 () All the charges whether inside or outside the ‘gaussian surface contribute to the electric flux. (b) Blectric flux depends upon the geometry of the ‘zaussian surface. (©) Gauss theorem can be applied to non-uniform electric field. (@) The clectric field over the gaussian surface remains continuous and uniform at every point.Electric Charges and Fields —— 4, The magnitude of electric field due to a point charge 2g at distance ris £. Then, the magnitude of electric field due to a uniformly charged thin sphere shell of radius R with total charge g at a distance Foo R) will be E oF wo (CBSE 2022 (Term-t} (2 (@4E 5. A square sheet of side a is lying parallel to XY-plane at z=a. The electric field in the region is B= cz*k. ‘The electric flux through the sheet is CBSE 2022 (Term-I) @ate Fare @jate @o 6. A charge q is placed at the point of intersection of body diagonals of a cube. The electric flux passing through any one of its face is (CBSE SP 2019-20 @t a) od " 2 Bec} 6 ot Aa 7. The electric flux through a closed Gaussian surface depends upon Det 2020 (@) net charge enclosed and permitivity ofthe medium (b) net charge enclosed, permitivity ofthe medium and the size ofthe Gaussian surface (©) net charge enclosed only (@) permittivity ofthe medium only Assertion-Reason Questions Directions (Q. Nos. 8-9) In the following questions, two statements are given- one labelied Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below (@) Ifboth Assertion and Reason are correct and Reason is the correct explanation of Assertion. (©) Ifboth Assertion and Reason are correct but Reason isnot the correct explanation of Assertion. (©) If Assertion is comect but Reason is incorrect (@) Ifboth Assertion and Reason are incorrect. 8. Assertion In a region, where uniform electric field cexists, the net charge within volume of any size is 2er0. Reason The electric flux within any closed surface in region of uniform electric field is zero. 9. Assertion With the help of Gauss’s theorem, we can find electric field at any point. 19% Reason Gauss’s theorem cannot be applied for any type of charge distribution. Very Short Answer Questions 10. How does the electric flux due to a point charge enclosed by a spherical Gaussian surface get affected when its radius is increased? Dethi 2016 141, What is the electric flux through a cube of side 1 em which encloses an electric dipole? All Inia. 2015 12. What is the flux due to electric field E =3x10? INC“! through a square of side 10 em, when itis held normal toE? Al nics 20156 13. Two charges of magnitudes ~20 and + Q are located at points (a, 0) and (4,0), respectively. What is the electric flux due to these charges through a sphere of radius 3a with its centre atthe origin? All India 2013 14. A charge q is placed at the centre of ‘a cube of side J ‘What isthe electric flux passing through each face of the cube? All India 2010; Foreign 2010 15. Figure shows three point charges, +2g, —g and +3g. ‘Two charges +2g and -g are enclosed within a surface S. What is the electric flux due to this configuration through the surface 5°” Delhi 2010 sek 2 Marks Questions 16. Given a uniform electric field E=5 10° INC. Find the flux of this field through a square of side 10 cm whose plane is parallel to the ¥Z-plane. What ‘would be the flux through the same square if the plane makes an angle of 30° with the X-axis? Delhi 2014 17. Given a uniform electric field E=2x103 1 NC. Find the flux of this field through a square of side 20 em whose plane is parallel to the YZ-plane. What would be the flux through the same square if the plane makes an angle of 30° with the X-axis? Foreign 2014 18. Given a uniform electric field E = 4x10°iNC™. Find the flux of this field through a square of side 5 em whose plane is parallel to the ¥Z-plane. What would be the flux through the same square if the plane makes an angle of 30° with the X-axis? Delhi 2014¢_— 19. A sphere S; of radius », encloses a net charge 0. If there is another concentric sphere S, of radius 13(r, >») enclosing charge 20. Find the ratio of the electric flux through S, and S,. How will the electric flux through sphere 5, change if a medium of dielectric constant K is introduced in the space inside 5, in place of air? All India 2014 20. CH 20. A thin straight infinitely long conducting wire having linear charge density 2 is enclosed by a cylindrical surface of radius rand length , its axis coinciding with the length of the wire. Find the expression for the electric ux through the surface of the cylinder. All Indie 2011 241. Show that the electric field at the surface of a charged spherical conducting shell is given by E =f, where e is the surface charge density and fis a unit vector normal to the surface in the outward direction All nia 2010 22. Consider two hollow concentric spheres S, and S, enclosing charges 20 and 40 respectively as shown in the figure. (i) Find out the ratio of the electric flux ‘through them, (ii) How will the electric flux through the spheres S, change if a medium of dielectric constant , is introduced in the space inside S, in place of air? Deduce the necessary expression. 2010 3 Marks Questions 23, State Gauss’s law on electrostatics and derive an expression for the electric field due to a long straight ‘thin uniformly charged wire (linear charge density 2) at a point lying at a distance r from the wire. Delhi 2020 Chapterwise CBSE Solved Papers : PHYSICS 24. A hollow conducting sphere of inner radius 7, and outer radius ry has @ charge Q on its surface. A point charge ~q is also placed at the centre of the sphere. (i) What is the surface charge density on the (a) inner and (b) outer surface ofthe sphere? (ii) Use Gauss’s law of electrostatics to obtain the expression forthe electric field at a point lying outside the sphere. ‘All india 2020 25. (@) An infinitely long thin straight wire has a uniform linear charge density 2. Obtain the expression for the electric field £ at a point lying at a distance x ‘rom the wire by using Gauss” law. Gi) Show graphically the variation of this electric field E as a function of distance x from the wire. All india 2020 26. A point charge +0 is placed at the centre O of an uncharged hollow spherical conductor of inner radius @ and outer radius 6. Find the following (@ The magnitude and sign of the charge induced on the inner and outer surface of the conducting shell (i) The magnitude of electric field vector at a distance (@)r=$ and (b)r=2b, from the centre of the shell (CBSE SQP 2011 27. Two large charged plane sheets of charge densities @ and —2c C/m? are arranged vertically with a separation of d between them. Deduce expressions for the electric field at points (i) to the left of the first sheet (ii) to the right of the second sheet and (ii) between the two sheets. All india. 2019 28. A spherical conducting shell of inner radius 7, and outer radius 7, has a charge Q. (0 A charge q is placed at the centre of the shell. Find out the surface charge density on the inner and outer surfaces of the shell. (i) Is the electric field inside a cavity (with no charge) zero independent of the fact whether the shell is spherical or not? Explain. ll indio 2019Electric Charges and Fields. —— 29. Define electric flux and write its SI unit, The electric, field components in the figure shown are E, =x, E,=0E, = 100N, Caleulate the charge m within the cube, assuming a =01 m, ), where case 2018¢ 30. A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge Q/2 is placed at its centre C and an other charge +2 Q is placed outside the shell ata distance x from the centre as shown in the figure Find (@ the force on the charge at the centre of shell and at the point 4 (ii) the electric flux through the shell. All India 2015 31. Two infinitely large plane thin parallel sheets having surface charge densities 6 | and 6 (6; ><) are shown in the figure. Write the ‘magnitudes and directions of the net fields in the 1 regions marked If and IIL. Foreign 2014 | In case of two thin parallel plane sheets with different surface charge densities, flux will be multiplied by area of ‘each faces of Gaussian cylinder with electric field, 32. A hollow cylindrical box of y length 1 m and area of cross-section 25 cm? is ol x placed in a three-dimensional coordinate system as shown x kim&—im—w in the figure. The electric ; field in the region is given by E=50.xi, where £ is in NC and x is in metre, a Find (i) net flux through the eylinder. (ii) charge enclosed by the cylinder. 33. (i) State Gauss’ law. (i) A thin straight inifintely tong conducting wire of linear charge density . is enclosed by a cylindrical surface of radius r and length J. Its axis coinciding, with the length of the wire. Obtain the expression for the electric field indicating its direction at a point on the surface of the cylinder. Delhi 2012 Delhi 2013 34, State Gauss’ law in electrostatics. A cube with each side a is kept in an electric field given by E = Cxi as shown in the figure, where C is a positive dimensional ae] pa I | aha Zz, the net electric flux through the cube. Gi) the net charge inside the cube. Foreign 2012 35. Using Gauss’ law obtain the expression for the electric, field due to uniformly charged spherical shell of radius, Rat a point outside the shell. Draw a graph showing the variation of electric field with r, for r> R and rR. All india 2011 5 Marks Questions 36. (i) Use Gauss’ law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density 2. (Gi) An infinitely long positively charged straight wire has a linear charge density A. An electron is revolving in a circle with a constant speed v such that the wire passes through the centre, and is perpendicular to the plane, ofthe circle. Find the kinetic energy of the electron in terms of ‘magnitudes of its charge and linear charge density 2.on the wire. (Gii) Draw a graph of kinetic energy as a function of linear charge density 2. (cBsE 2023 37. (i) Define electric flux and write its $I Unit. (Gi) Use Gauss’ law to obtain the expression for the electric field due to a uniformly charged infinite plane sheetZp (ii) A cube of side Z is kept in space as shown in the figure. An electric field E= (Ax +B)i x exists is the region. Find the net charge enclosed by the cube. y aa 2 case 2023 38. (i) State Gauss’ law in electrostatics. Show that with help of suitable figure that outward flux due to a point charge Q, in vacuum within gaussian surface, is independent of its size and shape. (Gi) In the figure there are three infinite long thin sheets having surface charge density +20, -26 and + respectively. 4] 8 | c | 0 Give the magnitude and direction of electric field at a point to the left of sheet of charge density +2. and to the right of sheet of charge density +6. (CBSE SP 2020-21 39. (i) Using Gauss’ law derive expression for intensity of electric field at any point near the infinitely Jong straight uniformly charged wire. (Gi) The electric field components in the following figure ate E, =ax,E, =0,E, =0; in which @ =400N/C m Calculate (a) the electric flux through the cube, and (b) the charge within the 20-20 @ cube assume that a=01m. CBSE SaP 2019-2020, lence 7 x t z 40. (i) Define electric flux. Is it a scalar or a vector quantity? A point charge q is at a distance of d?2 directly above the centre of a square of side d as shown inthe figure. Use Gauss’ law to obtain the = expression forthe electric flux through the square. Fy aie} Chopterwise CBSE Solved Papers : PHYSICS (Gi) Ifthe point charge is now moved to a distance d from the centre of the square and the side of the square is doubled, explain how the electric flux will be affected, CBSE 2018 41, (i) Use Gauss’ law to derive the expression for the electric field (E) due to a straight uniformly charged infinite line of charge density 2 C/m. i) Draw a graph to show the variation of £ with perpendicular distance r from the line of charge. (ii) Find the work done in bringing a charge q from perpendicular distance 7, to 79(% >,). CBSE 2018 42. (j) Use Gauss’ theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density o. Gi) An infinitely large thin plane sheet has a uniform. surface charge density 4c. Obtain the expression for the amount of work done in bringing a point charge q ftom infinity to a point of distant rin front of the charged plane sheet. ‘All india 2017 43, (i) Anelectric dipole of dipole moment p consists of point charges +g and -q separated by a distance 2a apart, Deduce the expression for the electric field E due to the dipole at a distance x from the centre of the dipole on its axial line in terms of the dipole ‘moment p . Hence, show that in the limit x>>a,E—+2p/(4negx?) i) Given the electric field in the region E =2xi, find the net electric flux through the cube and the charge enclosed by it. ll India 2015; Delhi 2015 " 44, (i) Define electric flux. Write its SI unit, Gauss” 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. (ii) Use Gauss” law to prove that the electric field inside a uniformly charged spherical shell is zero. Delhi 2015, 45. (i) Deduce the expression for the torque acting on a dipole of dipole moment p in the presence of uniform electric field £. (Gi) Consider two hollow concentric spheres S, and 53 enclosing charges 20 and 40 respectively asElectric Charges and Fields shown in the figure (a) find out the ratio of the electric flux through them. (b) How will the electric flux through the sphere S, changes if a medium of dielectric L is introduced in the space inside S; in place of air? Deduce the necessary expression? ‘All india 2014 —_. | ©) Re 3 46. Using Gauss’ law, deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point (@ outside the shell (fi) inside the shell Plot a graph showing variation of electric field as a funetion of r> R and r< R. (rbeing the distance from the centre of the shell) All india 2013 47. (i Define electric flux. Write its ST unit, (Gi) Using Gauss’ law prove that the electric field at a point duc to a uniformly charged infinite plane sheet is independent of distance from it. How is the field directed if the sheet is (a) positively charged? (b) negatively charged? Case Based Question (4 Marks) {For Complete Chapter) Directions (Q.No. 48) This question is case study based question. Attempt any 4 sub parts. Each question carries 1 ‘mark 48. Faraday Cage A Faraday cage or Faraday shield is an enclosure made of a conducting material, The fields within a conductor cancel out with any external fields, so the electric field within the enclosure is zero. These Delhi 2012 23 Faraday cages act as big hollow conductors you can put things in to shield them from electrical fields. Any electrical shocks the cage receives, pass harmlessly around the outside of the cage. (CBSE SP 2020.21 () Which of the following material can be used to make a Faraday cage? o (Plastic () Glass (©) Copper (a) Wood (Gi) Example of a real-word Faraday cage is, o (@)car (b) Plastic box: (© lightning rod (@) metal rod (iii) What is the electrical force inside a Faraday cage when itis struck by lightning? o (@) The same asthe lightning (b) Half that ofthe lightning (©) Zero (4) A quarter of the lightning (iv) An isolated point charge + q is placed inside the Faraday cage. Its surface must have charge equal to o (2) Zer0 +4 -4 @+% (¥) A point charge of 2 4Cis placed at centre of Faraday cage in the shape of eube with surface of 9 cm edge. The number of electric field lines passing through the cube normally will be (dy (@) 1.91 10°Nm? Centering the surface (b) 1.91 105Nm?/Cleaving the surface (6) 2.25 10°Nm? /Cleaving the surface (@) 2.25% 10°Nm?/ Centering the surface