Gauss Law Questions and Answers

If initially flux through hemisphere is zero Now 9 and 92 placed according to figure Due to which charge flux through hemisphere will change Question Type Single Correct Type 1 Only 91 9 92

31 Assertion A A point charge is lying at the centre of a cube of each side The electric flux emanating from each surface of the cube is 1 6 th of total flux Reason R According to Gauss theorem total electric flux through a closed surface enclosing a charge is equal to 1 o times the magnitude of the charge enclosed 11

5a A spherical conducting shell has a charge of 14 C on its outer surface and a charged particle in its hollow If the charge on the shell is 10 C what is the charge a on the inner surface of the shell and b of the particle 7 a T

A cube with side a is oriented such that the origin is at one of its corners and the axes as shown The cube is placed in an electric field given by 3y in N C The total flux through the cube is in Nm C Z A 3a B 3a C 3a D zero y

Which statements is true for electric field i An electric field leads to a force ii Electric field for point charge is iii iv ATTFO where q is test charge Direction of electric field and force same for negative test charge For electric field the test charge does not disturb other charges a Only i is correct b i iv are correct c ii iii are correct Ga Gia

Similar PYQs ques A thin metallic spherical shell of radius R carries a charge Q on its surface A point charge Q 2 is placed at its center C and another charge 2Q is placed at a distance x from the center Find force on the charge Q 2 and 20 PYQ 2015 C 2 2 Q Hint field inside shell is zero

Point charge causes an electric flux of 1 0 x10 Nm C pass through a spherical Gaussian surface of 10 0 cm radius centered on the charge a If the radius of the Gaussian surface were doubled how much flux would pass through the surface b What is the value of the point charge

Electric flux through a surface doesn t depend on the or area of a surfacebut it depends on the amount of O i shape of the surface O ii size of the surface O iii Both i and ii O i but not ii

A hollow metal sphere of radius R is uniformly charged The electric field due to the sphere at a distance r from the centre NEET 2019 1 Increases as r increases for r R and for r R 2 Zero as r increases for r R decreases as r increases for r R 3 Zero as r increases for r R increases as r increases for r R 4 Decreases as r increases for r R and for

A sphere encloses an electric dipole with charges 3 x 10 6 C What is the total electric flux across the sphere NEET 2019 Odisha 1 6 x 10 6 Nm C 2 3 x 10 6 Nm C 3 Zero 4 3 x 10 6 Nm C

Electric Flux Electric Dipole Dipole in a Uniform External Field 16 Electric field in a region is uniform and is given by ai bj ck Electric flux associated with a surface of area TR 1 is 1 anRe 3 2abR 2 3amR 4 acR

An infinite line charge is at the axis of a cylinder length 1 m and radius 7 cm If electric field at any point on the curved surface of cylinder is 250 NC 1 then net electric flux through the cylinder is 1 1 1 x 10 Nm C 1 2 9 74 x 10 Nm C 1 4 2 5 10 Nm C 1 3 5 5 x 106 Nm C 1

31 State and Explain Guass s law of Electric Flux Find the electric field due to infinitely long straight long charged wire Two charges of magnitudes 3Q and 2Q are located at points a 0 and 4a 0 respectively What is the electric flux due to these charges through a sphere of radius 5a with its centre at the origin

Consider a uniformly charged solid cylinder of large length and radius R Now consider a cylinderical surface of radius 2R and length 2R coaxial with cylinder and electric flux through cylindrical surface is do Now consider a spherical surface of radius 2R and one of the diameter 90 along axis of cylinder and electric flux through spherical surface is Find

positive pom placed at the through the surface is X units If the radius of the sphere is doubled the changes in electric flux will be a X 2 b 2X distribution Electric field is zero at point a A Q2 Figure shows the variation of electrostatic potential V with distance x for a given charge B C X b B c C d zero Q3 The value of charge q at the centre of line joining two equal and like charges Q so that these are in equilibrium is a Q b Q 4 c Q 4 Q6 In a region of constant potential a the electric field is uniform b the electric field is zero c there can be no charge inside the region d both b and c are correct d None of these Q4 If the force acting on a point charge kept on the axis of an electric dipole is F what will be the amount of force if the distance of the point charge is doubled from the dipole a 2 b F 8 c F 2 d F 4 d Q 2 Q5 A uniformly charged conducting sphere of 1 2 m diameter has surface charge density 8 1 C m The total electric flux leaving the surface a 4 1x106 Nm C b 1 3x104 Nm C c 4 1x106 Nm C d zero Q7 Energy stored in a capacitor and dissipated during a charging a capacitor bear a ratio a 1 1 b 1 2 c 2 1 d 1 3 C R R3 R Q8 A student connects 10 dry cells each of emf E and internal resistance r in series but by mistake the one cell gets wrongly connected Then net emf and net internal resistance of the combination will be a 8E 8r b 10E 10r c 8E 10r d 10E 8r Q9 Constantan wire is used for making standard resistance because it has a high melting point b low specific resistance c high specific resistance d negligible temperature coefficient of resistance Q10 Resistance of voltmeter is R Resistance of Ammeter is R and Resistance of galvanometer is R3 Which of the following is correct a R R R3 b R R R3 d R R R3 Q11 Potentiometer measures the potential difference more accurately than a voltmeter because a It has a wire of high resistance b It has a wire of low resistance C It does not draw current from external circuit d It draws heavy current from external circuit Q12 From the graph between current I and voltage V shown below identify the portion correspondin negative resistance J

A point charge q is kept at a point a 2a in the space Consider a triangular plane surface 2 3a whose co ordinates of vertices are a 2a 0 2 passing through the considered triangular surface is q A 12 B C q 2480 q 48 2a 0 and 5a 52 0 3a 2 2 The electric flux

density has the form ho 1C m 3 x z m 3 12 m3 10 P where z is z axis and the block extends from z 2m to z 2m Find the electric field at a location 1m

9 Two straight non conducting wires parallel to the z axis pass through points O and A as shown in the figure below The wires carry equal and uniform charge density 0 4 C m Determine the electric field at point P 0 45 A 8 0 m

A square sheet of side a is lying parallel to XY plane at z a The elect field in the region is E cz k The electric flux through the sheet is a a4c afc b 1 3 C a c

A positive point charge of Q coulomb is placed at the centre of a sphere of radius R The electric flux through the surface is X units If the radius of the sphere is doubled the change in electric flux will be a X 2 b 2x c X d Zero

ample Paper Physics Class XII Term 20 cm 20 cm 63

A point source is placed at 1 m perpendicular height of a square plate of side 2 m from its center A source is producing sound with power 18 J The amount of energy collected by plate per second Options 1 2 J 2 3 J 3 0 18 J

Let N be the number of electric field lines going out of an imaginary cube of side a that encloses an isolated point charge 2q and N be the corresponding number for an imaginary sphere of radius a that encloses an isolated point charge 3q Then N N is 1 b c d TC a T 2 3 9 4

A charged particle is placed on the axis of a cylinder as shown in the figure 4R 3 Options 1 2 130 1 10 20 Q Then find the electric flux through the curved surface of the cylinder 3 13 40 4 27 2 RI 3

D Electeurs always the path of a positively charged parce If the electric flux entering and leaving a closed surface are respectively of magnitude and 62 the the electric charge inside the surface will be 0 2 ST 4 4 D 4

3 E 22 A uniformly charged conducting sphere is having radius 1 m and surface charge density 20 Cm 2 The total flux leaving the Gaussian surface enclosing the sphere is 1 40 TE 1 3 20 1 2 80 1 4 60 TE

Max Marks 35 General Instructions 1 The question Paper contains three sections 2 Section A has 25 questions Attempt any 20 questions 3 Section B has 24 questions Attempt any 20 questions 4 Section C has 6 questions Attempt any 5 questions 5 All questions equal marks 6 There is no negative marking Page 2 of 28 SECTION A This section consists of 25 multiple choice questions with overall choice to attempt any 20 questions In case more than desirable numbers of questions are attempted ONLY first 20 will be considered for evaluation Q1 A positive point charge of Q coulomb is placed at the Centre of a sphere of radius R The electric flux through the surface is X units If the radius of the sphere is doubled the change in electric flux will be a X 2 b 2X c X

1 ELECTRIC CH Competency Bas 1 Electric flux through an area is defined as E A Gauss law is used to assess amount of enclosed change The concept of flux and Gauss law is very useful as in cases of non planar area calculation of flux is not easy Gauss law is also very important in calculating the electrostatic field Flux due to change is additive in nature Gauss Law does not depend on the shape i Gauss law is dependent on internal charge configuration a No it s not b Yes it depend on charge configuration c May be d Both a and b ii Is it necessary condition to have symmetric surface for Gauss law application a Yes b No c May be d Depends on situation iii Electric flux through a closed surface is due to a Total charge enclosed b Total charge present on the surface

Example 33 A long string with a charge of per unit length passes through an imaginary cube of edge a What is the maximum flux of the electric field through the cube

nq The figure shows a hollow hemisphere of radius R in which two charges 3q and 5q are placed symmetrically about the centre O on the planar surface The electric flux over the curved surface is Fill the value of n 0 3q 5q

A point charge Q is positioned at the center of the base of a square pyramid as shown Q The flux through one of the four identical upper faces of the pyramid is then F Px E is Assume that only 50 of the point charge belongs to that system 0

5 The electric field in a region of space varies as E 3v m xi 4v m yj 5v m zk Consider differential cube whose one vertex is x y z and the three sides are dx dy dz sides being paral to the three coordinate axes bid a The flux of electric field through the differential cube is zero b The flux of electric field through the cube 12 dx dy dz c The charge enclosed by the cube is zero d The charge enclosed by a spherical surface of radius r centered at origin is 16

The surface charge density of very large surface is equal to 3 0x10 C m From what distance should an electron of 200 eV energy be projected towards the plane so that its velocity becomes zero on reaching the plane Charge on an electron is 1 6x10 9 C leV 1 6x10 9 J o 9x10 2SI a 12 x 104 m b 9x10 m c 9x104m d 9x 10 m

and Fields And a second charge q2 is similarly placed at a distance 58 12 1 on the opposite side of circle 2 Choose the correct answer A 9 If the net flux through circle is zero then would be 3 Circle of radius 8 cm 4 Circle of radius 4 cm 1 2 14 2 1 a If the value of q and q are 100 C and 400 C respectively and they are separated by a distance of 30 cm The locus of all points in the plane where electric potential is zero would be 14 2 1 1 Straight line 2 Parabola whose axis is line joining the charges cm cm 2 3 If the values of q and q are q 2q respectively now a third charge q has to be placed on line AB so that it can be in stable equilibrium The distance of point where third charge is placed from charge q would be take a 12 cm 4 cm 13 20 9 B 2 9 2 R 91 92 14 3 2 2 1 44 q cannot be in stable equilibrium at any point Comprehension 1 A spherical shell of inner radius R and outer radius 2R has a uniform charge distribution and total charge Q Choose the correct answer 1 2 3 The charges inside the Gaussian sphere for given three regions are respectively 1 0 a R R a 2R ii 2R a 1 0 2 0 3 0 Q 2 0 1 0 a R ii R a 2R 2R a are respectively 1 0 3 0 4 0 4 0 Q Use Gauss s Law the electric fields at the surfa of the Gaussian surface when Q 28ma 25ma Q 32me a 1 3 E Q 30mega 4nEr 3 Q 2Q Comprehension Ill Q 4Q R BR R 3 2 3 Q Q 2me a Q 47 a The electric field in a region of space is E E The flux of electric field through a sphere of radu r centred at origin is Q 41 0 JEE Cha 1 2 E 4 Zero For a uniformly charged disc of radius R and surface charge density a centred at origin and

A disk of radius having a uniformly 4 distributed charge 6 C is placed in the X Y plane with its centre at a 2 0 0 A rod of length a carrying a uniformly distributed charge 8 C is 5a placed on the x axis from x 4 Two point charges 7 C and 3 C are placed at a a 3a 1 72 0 3 32 0 4 respectively Consider a cubical surface formed a a by six surface x y 2 and 2C 2C a z The 2 electric flux through this cubical surface is y a 24 3 X to x 10C A 12C

4 Electric charge is uniformly distributed along a long straight wire of radius 1 mm The charge per cm length of the wire is Q coulomb Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire as shown in fig The total flux passing through the cylindrical surface is 1 2 3 olu 0 100 Q 0 10 Q 1m 50cm

A uniform charged infinite straight line having linear charge density A is passed through centre of a sphere R is radius of the sphere The electric flux through the sphere is given by E 2 R AR 2 Go

charged nanging from silk thread such that it makes angle 0 with infinite large plane thin sheet of charge as shown The surface charge density of the sheet is proportional to USS 1 sine 3 tane 0 mg T 2 cos0 4 cote Fe

If there is only one type of charge in the universe then Electric field Area vector A 0 C E ds 40 on any surface fe Eds could not be defined f ds DE ds if charge is inside 0 if charge is outside 9 if charge is inside

2 er vand Shown in the figure is a spherical shell with 14 fargent after a feb alell inner radius a and outer radius b which is made of conducting material A point charge Q is placed at the centre of the shell and a total charge q is placed on the shell Charge q is distributed on the surfaces as 1 Q on the inner surface q on the outer surface 2 Q on the inner surface q Q on the outer surface 3 Q on the inner surface q Q on the outer surface 4 The charge q is spread uniformly between the inner and outer surfaces Qfq ak faata 1 2 31 Q 3 q Q 4 q make an a

A charge 8 85 C is placed at the centre of a cube The electric flux in Sl units through any one face will be 885 v Gia i fod ya baa Ter ad f ya kay SI HE EHIT OPTIONS MARK FOR REVIEW CLEAR SELECTION 106 6 1012 6 OC 10 13

9 What is the net charge on a conducting sphere of radius 10 cm Given that the electric field 15 cm from the center of the sphere is equal to 3 10 N C and is directed inward 1 7 5 x 10 5 C 3 7 5 x 10 5 C 2 7 5 x 10 9 C 4 7 5 x 10 9 C

In a region a uniform electric field is given by 21 6 8k N C The electric flux through a sphere of radius 1 m centered at the origin is O 8 N m C O Zero O 10 N m C O 16 N m C

The shape of equipotential surface due to long uniformly charged line is O Concentric spherical O Co axial cylindrical Planar equidistant Planar unequal distance

gatively balloons suspended from nonconducting strings being held by a studen What occurs as the student brings the balloons closer to each other without allowing them to touch A The magnitude of the electrostatic force between the balloons decreases and they attract each other B The magnitude of the electrostatic force between the balloons increases and they repel each other C The magnitude of the electrostatic force between the balloons decreases and they repel each other The magnitude of the electrostatic force

The electric flux for Gaussian surface A that enclose the charged particle in free space is given q 14 nC q2 78 85 nC q3 56 nC a 10 Nm C 1 c 6 32 x 10 Nm C 1 Gaussian surface A Gaussian surface B b 10 CN m d 6 32 10 CN m 2

This section consists of 25 multiple choice questions with overall choice to attempt any 20 questions In case more than desirable number of questions is attempted ONLY first 20 will be considered for evaluation Q1 A positive point charge of Q coulomb is placed at the centre of a sphere of radius R The Electric flux through the surface is X units If the radius of the sphere is doubled the changes in electric flux will be a X 2 b 2X c X d zero

4 380 The electric field due to an infinitely long straight line of charge with uniform charge density points straight away from the line and has magnitude E 1 2 where r is the distance from the wire Calculate the flux of this electric field through a right cylinder of height h and radius R co axial with the charged line Repeat the calculation for a cylinder of radius 2R

Question 14 A single phase 50Hz transformer has a turns on primary and 400 turns secondary winding If primary voltage 240V then what will be the max value flux density 0 0 013 0 6 0 8

The electric field components in the figure are Ex ox 2 E 0 E 0 where a 800N m If a 0 1 m is the side of cube then the charge within the cube is a 9 3 10 12C 6 x 10 12C a