Gauss Law Questions and Answers

A particle of charge q is placed at the origin A circular plate of diameter d is placed at a distance 3d 2 below this plate symmetrically Calculate the electric flux passing through this plate

apart 0 A charge Q is placed at the center of a cube of side length a Find the electric flux through each fact the cube Solve the problem if the charge is kept at a corner of the cube 1 A particle of charge q is placed at the origin A circular plate of diameter d is placed at a distance 3d 2 below this plate symmetrically Calculate the J

Q3 22 July 2021 Shift 1 The total charge enclosed in an incrementalathongo volume of 2 x 10 m located at the origin is mathon D e siny i e cosy i 2zkC m mathan mathon mathongamathongo nC if electric flux density of its field is found as mathons

A sphere a cylinder and a very thin disk are made out of the same material of them carry the same amount of charge Q spread uniformly over their surfaces The radius of the cylinder is identical to its height The radii of sphere cylinder and disk are in the ratio 1 2 3 I II and III are points in space very close to the sphere curved surface of the cylinder away from the edges and centre of flat surface of the disk respectively Then magnitudes of electric fields at the points I II and III are approximately in the ratio 1 2 A 1 49 12 23 B 1 C 1 2 3 D 1 4 9 now of the

Charges Q and Q lie inside and outside respectively of closed Gaussian surface S Let E be the field at any poin on S and be the flux of E over S If Q changes both E and will change If Q2 changes E will change If Q 0 and Q 0 then E 0 but 0 If Q 0 and Q2 0 then E 0 but 0

40 Gaus s law is given by Eds q if net charge 45 A poi perper of a sq square enclosed by a Gaussian surface is zero then 1 E must be zero on the surface 2 Number of incoming and outgoing electric lines are equal 3 there is a net incoming of electric lines 4 none FS0039 9 0 q 3 4

The electric potential Vin a certain region of space depends only on the x coordinate as V ax Vo where ao and V are constants Consider a cuboid in space of dimensions L x x whose length L 2 2 stretches along the x axis from x 0 to x L Then choose the correct option s Af Afga ga 7 faya faha AV ar Atz gem Ai A f 1 L x 1 1 20 2 yg qay qz fauz Afg Buh x 0 x as gura a 2 a 3 fachcu fachcut chi J47 MA A The charge contained within the cuboid is a L5 X 5 qay Bigz Zuk ao Correct Answer B The charge contained within the cuboid 0a0 L5 2 is 34 32 D the cuboid is o ao L 2 C The electric flux through the surface of ao L5 2 q adz yur mm faya u 5 The charge density at x 2 ao 5 2 is 30 a L

a 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 placed on the x axis from x to x a 4 5a 4 placed at Two point charges 7 C and 3 C are a 3a 4 7 0 and 3 32 0 4 respectively Consider a cubical surface formed a a a by six surface x y z The electric flux through this cubical surface is y 1 2C E0 2 2C 80 3 X 10C 80 4 12C 80 40 14

Q 1 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 Zora

64 A point charge q is placed at the centre of a non concentric cavity of a neutral metallic sphere a Kq 1 2 3 O do R A Find the electric field at point A K 4 EO Kq 2 R 4 None of these figure

Consider a solid hollow sphere of an inner radius a and an outer radius b which has a net uniform charge of q 4 50 fC What is the magnitude of the electric field at radial distances r a b r a and r b

with charge density varies with distance r from the center and 1 28 Let there be a spherically symmetric charge distribution given as 5 r p r Po 4 R C and p r 0 for r R The electric field at a distance r R from the origin is given as Por 5 r 480 3 R for r R 4por 5 r 480 4 R B D 4 por 5 r 380 3 R Por 5 r 380 4 R

ALLEN A charge q is placed at a vertex of the given 39 geometry of angle 60 Then the flux coming out from this geometry will be 6 2 16 0 3 820 4 12 Three conducting concentric spherical shells of 40 1 6E0 60 1 6 0 auf und fuf fri 2 16 0 3 8 0 4 1260

Problem 3 5 Points A point charge Q1 4 C is placed at the origin and held there a If a lkg mass with charge Q2 2 C starts with velocity 1 5 m s toward the charge at the point x 15cm find its position when it stops 3 Points

5 In the circuit shown in the figure no current flows through the 8 resistor then the potential difference between points A and B V V is A 1 14 V 0 8 V 292 ALT 20 V M 18 Q 822 i 0 6 V 8 V 2 12 V A 12 V B R c

The electric field in a certain region is acting radially outward and is given by E Ar A charge contained in a sphere of radius a centred at the origin of the field will be given by AIPMT 2015 1 Aa 2 2 4 e Aa 3 A a 6 ES AVS 15 450 E0

40 A parallel plate capacitor with plate area A and plate separation d is charged by a current of 5 mA The displacement current through a 2A plane surface of area and drawn symmetrically 1 5 mA 10 3 mA parallel to the plates between the plates is 2 2 5 mA 4 5 mA

d V 1 57 A ring of radius R having a linear charge density moves itch R so that the centre towards a solid imaginary sphere of radius 2 of ring passes through the centre of sphere The axis of the ring is perpendicular to the line joining the centres of the ring and the sphere The maximum flux through the sphere in this process is A C R 0 R 4 0 R Figure 1 417 B AR 2E0 R 3 0 R 2

5 Charge is distributed non uniformly in a volume of solid insulating sphere of radius a such that volume charge density p varies with distance from the centre r as p r Cr r a and C is constant Magnitude of electric field strength outside the sphere at a distance from centre will be 1 2 3 Ca 5 r Ca 56 Ca 4 r

A square surface of side L meters in the plane o the paper is placed in a uniform electric field E volts m acting along the same plane at an angle 0 with the horizontal side of the square as shown in figure The electric flux linked to the surface in units of volt m is 1 Zero 2 EL2 3 EL2cose A ELA E E

A polythene piece rubbed with wool is foun d to have negative charge of 3 6 10 7 C ca Iculate the number of electrons are transferr ed from wool to polythene if an electron ha s a mass 9 1x10 31 kg find mass transferr ed to polythene NB TUTOR PLEASE DO IT IN A PIECE OF PA DER

8 Two charges of magnitude 2Q and Q are located at points a 0 and 4a 0 respectively What is the electric flux due to these charges through a sphere of radius i 3a and ii 5a with its centre at the origin iii How will the electric flux through the sphere of radius 3a change if a medium of dielectric constant k is introduced in the space inside this

Two spherical conductors A and A of radii r and r r r are placed concentrically in air A is given a charge Q while A is earthed Then the equivalent capacitance of the system is 4RE012 12 11 4 E0 r 4T Eo 12 4 Ep 1

Two point charges 91 and 92 are placed along x axis at some separation one of the electric field line emanating from charge q1 is along the curve as indicated in diagram If then find the value of 6x 1 3

Two charges 9 q are placed at A and B respectively A line of force emerges from q at angle a with line AB At what angle will it terminate at q A circular ring 1 A Ja 9 92 B with uniform positive charge density per unit length is fixed in the Y Z plar moo is pmiected from the poi

40 For a spherical capacitor shown at which points the electric field will be zero r is the distance of point from centre O 1 At point r tr R 3 Both 1 2 R O 2 At point r R 4 Neither 1 nor 2

Some magnetic flux is changed from a coil of resistance 10 22 As a result an induced current is developed in it which varies with time as shown in figure The magnitude of change in flux through the coil in weber is LEA 2 B 4 C 6 D 8 0 1 t s

Electric field in the following figure is directed along X direction and given by Ex 5Ax 2B where Er is in N C and x is in metre A and B are constants with dimensions Taking A 10 N C m and B 5 N C KZ AY 10cm Calculate a the electric flux through the cube b net charge enclosed within the cube

When a point charge placed at corner of a cube then total flux through cube is p What is the flux from each face of cube when the same charge placed at centre of cube Question Type Single Correct Type 1 80 2 6 3 40 3

27 A sphere Si of radius r encloses a total charge Q If there is another concentric sphere S of radius r2 r1 and there be no additional charges between Sand S what is the ratio of electric flux through S and S a 1 b 1 c 2 d infinity

Q2 If the net electric flux through a closed surface is zero then we can infer a No net charge is enclosed by the surface b uniform electric field exists within the surface c electric potential varies from point to point inside the surface d charge is present inside the surface

Consider a square surface of side 2a a circular area of radius a is removed from the square symmetrically A charge q is placed at distance a on the axis of circle The flux through remaining pa N Find N 6e0JNN is 9

Problem 2 15pts A sphere of radius R is uniformly charged The sphere contains two spherical holes of radius R centered on the y axis at y d and y d see figure below If the flux of the electric field through a closed surface that includes all the sphere is o find a 4pts The charge density p in terms of the quantities above and fundamental constants Assume that p 0 b 6pts The electric field at z aR magnitude and direction c 5pts The value of the potential with respect to infinity at the point z R 0

Consider an imaginary cylinder with radius r and length that has an infinite line of positive charge running along its axis The charge per unit length on the line is 21 Eo A The electric flux through the cylinder due to this infinite line of charge is B The electric flux through the cylinder if its radius is increased to 2r is 21 Eo C The electric flux through the cylinder if its length is increased to 31 and radius is increased to 3r is Al Eo D The electric flux through the cylinder if its length is increased to 31 and radius 321 is increased to 3r is

A point charge 8 85 10 12 C is placed at one corner of a cube The electric flux passing through the cube is 1 N m C 1 1N m c 1 6 8 N m C 1 Nm 6 1

1C 7UC 4 C 10 C 2 c 5 c and are situated at the eight comers of a cube of side 20 cm A spherical surface of radius 80 cm encloses this cube The centre of the sphere coincides with the centre of the cube Then the total outgoing flux from the spherical surface in units of Vm is A 367x10 Fightchar B 684 7x10 D none of these

A cylinder of length L and radius b has it axis coincident with the x axis The electri field in this through the left end of cylinder is A 0 B 200 b C 100 b D 200 zb 2 region is E2001 The flu

An electric field travelling in a con connected to a battery has a speed of the of 1 ZERO as electric field inside a conductor 2 Drift speed 3 Speed of electromagnetic Waves 4 None of the above

Consider a conducting shell as shown in figure Two point charges are inside the shell and two are outside the shell Then induced charge on the outer surface of conducting shell is 94 9 9 93

Find the net electric flux through the spherical closed surface shown in the figure below The two charges on the right are inside the spherical surface Take q 1 94 nC q 1 06 nC and q3 2 91 nC O 9 of of

Figure sh length moves towards right at uniform speed of v At t 0 the right end of the rod first touches left face of the cube The correct plot of graph between electric flux through cube versus time is O O a 80 7 a Eo 0 a V 2a 3v 2a V 3a 5a 2v 2v a o a 5a V K h a

Figure shows a closed surface which intersects a conducting sphere If a positive charge is placed at the point P the net flux of the electric field through the closed surface P closed surface conducting sphere 1 will remain zero 2 will become positive 3 will become negative 4 will become undefined

23 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 of total flux Reason R According to Gauss theorem total electric flux through a closed surface enclosing a charge is equal to 1 e times the magnitude of the charge enclosed

An infinite line charge carrying a uniform line charge of density is placed along the body diagonal AG of a cube of side a as shown Then H B The flux of the electric field of this charge through one of the sides of the cube is a 2 380 3 a The flux of the electric field of this charge through one of the sides of the cube is 280 The flux of the electric field of this charge through one of the sides the cube is a 4 380 The flux of the electric field through the face ABFE is same as that through BCGF

I A 4 t s 0 1 Magnetic flux changes in a coil of resistance 10 Q As a result an induced current is developed in it which varies with time as shown in figure The magnitude of change in flux through the coil in weber is 4 8 02

Why are we assuming the sphere as a shell Volume sho uld be 4 3pir 2 but why 4pir 2 Make the solution clear with theory 7 An insulating solid sphere of radius R is charged in a non uniform manner such that volume charge A density p r where A is positive constant and r is the distance from the center Electric field at any inside point at r r is 1 4 A 1 4 EO 1 3 A 1 A 2 4E0 4 A

1 A t s 0 1 Magnetic flux changes in a coil of resistance 10 Q As a result an induced current is developed in it which varies with time as shown in figure The magnitude of change in flux through the coil in weber is 0 4 0 8 02

12 Consider the loop ABCDEFA as shown in the figure a origin 2a If electric field in the region is given by E E 4x Find the magnitude of flux through ABCDEF in terms of E and a 19 A 17 3 C Ega D None of

EM AModuleLeater Phi Gauss law 5 A thick shell with inner radius R and outer radius 3R has uniform density p c m It has a spherical cavity of radius R as shown in the figure The electric field at the centre O of the cavity is 19 J 2 p

55 A point charge Q is placed at the center of a cube of side a in vacuum permitivity to The flux of the electric field through the shaded face is given by A B C 0 4 0 Q 660