Gauss Law Questions and Answers

If we displace the enclosed charges within a X Gaussian surface without crossing the boundary then both E and remain same If we displace the enclosed charges without crossing the boundary then changes but remains the same If the charge crosses the boundary then both and would change Both 2 and 3

Consider two concentric spherical surface S with radius R and S with radius 2R both centered at the origin There is a charge 2q at the origin and there are no other charges Compare the flux through S with the flux 1 2 through S 1 202 14 2 1 2 1

A charge q is placed just above the centre of a horizontal circle of radius r and a hemisphere of this radius is erected about the charge Compute the electric flux through the closed surface that consists of the hemisphere and the planar circle Do not use Gauss law ge

Electric Charges and Fields b base E R total 0 curved TR E c base TR E 0 0 0 total 0 180 denc 0 qenc 0 curved R E Like Coulomb s Laws Gauss Law can also be used to find Electric field strength So they are complimentary to each other Gauss Law can be used to find field in symmetric situations very easily E A 4 R R V

18 A spherical conducting shell of inner radius r and outer radius R has a charge Q on its surface A charge q is placed at the centre of the shell What is the surface charge density on the i inner surface and ii outer surface of the shell Also write expression for the electric field at a point x R from the centre of the shell

28 A ball having a charge 100e is placed at the centre of a hollow spherical shell which has a net charge of 20e What is the charge on the shell s outer surface a 80e b 20e c 100e d 120e 37 F

1 Which of the following statements is incorrect for Gauss s law a Gaussian surfaces are arbitrary surfaces on which the electric field magnitude can be written as a constant b Gauss s law is the average of the total loads inside the Gaussian surface drawn c Gauss s law calculates the electric field magnitude but not the electric field direction D For Gauss s law to be valid space must be electrically permeable to The integral expression of Gauss s law is the expression of a special case of the fundamental divergence theorem Answer option b Please explain why the answer is b

Figure shows a cylindrical Gaussian surface for an infinitely long thin straight wire of unifor linear charge density Answer the following i For which surface is the electric flux zero ii Over which surface is E zero iii Over which surface is constant iv Over which surface does E change

A positive charge Q is uniformly distributed along a circular ring of radius R A small test charge q is placed at the center of the ring then R q Z Q i If q 0 and is displaced away from the center in the plane of the ring it will be pushed back towards the centre ii If q 0 and is displaced away from the centre in a plane of the ring it will never return to the centre and will continue moving till it hits the ring iii If q 0 it will perform SHM for small displacement along the axis iv q at the centre of the ring is in an unstable equilibrium within the plane of the ring for q 0 Mark the correct option A i and iv are correct B ii and iii are correct C all are correct

Example 1 11 The electric field components in Fig 1 27 are E x E E 0 in which a 800 N C m 2 Calculate a the flux through the cube and b the charge within the cube Assume that a 0 1 m y n a a R X

38 If charge is distributed uniformly in xy plane with charge density to in first quardrant and o in remaining three quadrants then work done by electric field in moving a point charge q from 0 0 d to 0 0 2d is a oqd b d q 4F c oqd d aq

As seen in the figure a point Q charge is placed in the center of an uncharged conductor with inner radius ri and outer radius r2 Using Gauss s law a r r b ri r r2 c Calculate the electric field in regions r2 r Q

Find electric field everywhere on a plane containing the borders of two parallel half planes extending in opposite directions Distance between the half planes is d and they have uniform surface charge density o each Angle between the plane and the half planes is 0 Ito outside O at all paints between half plave 11 of side gido I carries uniform charge on all of it

94 point ges points as shown in figure S is the spherical Gaussian surface of radius R Which of the following is true according to Gauss s law 9 92 R 93 S 94 280 1 E E E A E E A 91 92 93 2 E E E dA 91 92 93 E0 3 4 E E E E A 91 92 93 Eo

D Same case for cube or cuboid e are 6 faces An infinitely large plate of width b is placed in horizontal x y plane A point charge q is placed b 2 symmetrically at a distance of perpendicular to plane of this plate as shown Find electric flux passing through this plate 1 90 E0 3 Zero 22 b b 2 b 2 2 4 9 2 0 90 E0

Charge is distributed uniformly in some space The net flux passing through the surface of an imaginary cube of side a in the space is The net flux passing through the surface of an imaginary sphere of radius a in the space will be 3 1 47 2 3 2 3 4 6 47 3

The electric field near the centre of a uniformly charged nonconducting disc is E If the nonconducting disc is now replaced by a conducting disc with the charge same as before the new electric field at the same point is 1 2 3 4 2E E E 2 None of these

A hollow cylinder has a charge q coulomb within it If o is the electric flux in units of voltmetre associated with the curved surface B the flux linked with the plane surface A in units of voltmetre will be charge is symmetrically placed within it AIPMT Prelims 2007 1 3 C 9 9 ola B 2 4 q 2 0 elm A 3

A cylinder of radius R and height h is placed in uniform electric field as shown in Fig a if the axis of the cylinder made inclined with vertical as shown in Fig b Calculate the flux of electric field entering the cylinder 15 H 0 193

nr 3 A sphere of radius R has charge density given by P Po 1 3R where po is a constant r is distance from centre of sphere For a spherical gaussian surface of radius R centered at the centre of sphere the flux is zero Find n

47 An infinite uniformly charged sheet with surface charge density o cuts through a spherical Gaussian surface of radius R at a distance x from its center as shown in the figure The electric flux through the Gaussian surface is A R Q X solgreint solscenei baigns iden pionove boonlq ons p bre 11 1 02 000 aat of loups os ploilmugitmos orl to TR B G 2n R x o T R x o R x o

Electrostatics 2 16 A non uniform electric field in x direction is increasing uniformly from 2N C at x 1m to 8 N Ca x 7m The center of cube is at x 2m If the charge enclosed inside a small cube of side lengt 10cm is 8 85 10 5n C The value of n will be X

7 Two identical metallic spheres A and Bo exactly equal masses are given equal positive an negative charges respectively Then 1 mass of A Mass of B 2 mass of A Mass of B Mass of B 3 mass of A 4 mass of A Mass of B

3 S S2 S3 are three concentric spherical shells as shown in figure S and S have charge 4Q and 8G respectively whereas S3 is uncharged Find the ratio of the flux passing through S to that through S3 S3 S S O 1 1 3 3 2 1 4Q 8Q 2 1 2 4 1 6 Bad Office Askoch Tower Buse Road New Delhi 110005 Ph 011 47623456

30 Consider a solid uniformly charged sphere of radius R with a hole of radius R at the centre as shown in the figure If the total charge of the sphere is q what is E in the regions I II and III at a distance r from the centre Brother s Academy LALPUR Campus Circular Road Lalpur Ranchi 834001 Ph 7488408051 8235071441 Brother s Academy DORANDA Campus Opp Eylex Cinemas Hinoo Ranchi 834002 Ph 6201469038 8092071442 40 Physics Electrostatics

An insulating ring of charge 2 b radius b is concentric with a charged conducting solid sphere of charge Q and radius a b a as shown in the figure Then DI I A Potential of the sphere is Q 2 4 a 2 a B If sphere is grounded then charge on the sphere will be 87 C Electric field inside the sphere is non zero D The sphere is equipotential body

Due to the presence of a charge at the centre of a sphere of radius 10 cm the electric flux passing through the surface of the sphere is 6 x 103 N m C 1 ii i What is the magnitude of charge inside the sphere If a concentric spherical Gaussian surface with a radius double that of the sphere is taken what will be the amount of electric flux now passing through this sur face i 5 31 x 10 8 C ii remains the same as before

open hemisphere is centred at origin Point A d B are on the y axis at equal distances from the centre of sphere When a point charge q is kept at B flux from the hemi sphere is If the point charge is shifted at A then flux from the hemi sphere will be A 1 2 3 9 0 80 9 20 B q cio

A point charge Q is located on the axis of a disc of radius R at a distance a from the plane of the disc If one fourth 1 4th of the flux from the charge passes through the disc then find the relation between a R R a

An electrical circuit is shown in the given figure The resistance of each voltmeter is infinite and each ammeter is 100 2 The charge on the capacitor of 100 uF in steady state is 4 mC Choose correct statements s regarding above circuit A Reading of voltmeter V is 16 V B Reading of Ammeter A is OA and A is 1 25 A C Reading of voltmeter V is 40 V D EMF of the ideal cell is 66 V V 20092 ideal cell 10002 ww www 9000

In a spherical capacitor we have two concentric spherical shells the inner one carrying a charge Q and outer one carrying a charge of Q If the inner shell is displaced from the center without touching the outer shell the capacitance of the capacitor will increase the capacitance of the capacitor will remain same the energy of capacitor will decrease the potential difference between inner and outershell will increase

Consider a system of two uniform thin non conducting shells of charge with respective charges Q and 2Q and radii R and 3R A poir charge 4Q is placed at a distance 5R from the common centre of the shells Net force experience by the outer shell is 1 2 3 20 5 ER 20 25 R 2Q 97 R

A 3 5 cm radius hemisphere contains a total charge of 6 6 x 10 7The flux through the rounded portion of the surface is 4 46 x 10 Nm C The flux through the flat base is Select one O a 0 O b 3 0 10 Nm C O c 2 0 x10 N 1 m C O d 2 0 x10 N m C O e 4 46x10 Nm C

A ball is placed in a non uniform E in free space where there is no charge present Comment on the net flux through the surface of the ball Will the flux at some points on the ball s surface be inwards Justify 09

4 Q 4 M 1 Iultiple Correct Answer Type A large insulating thick sheet of thickness 2d carries a uniform charge per unit volume p A particle o mass m carrying a charge q having a sign opposite to that of the sheet is released from the surface of th sheet The sheet does not offer any mechanical resistance to the motion of the particle Find the oscillation frequency v of the particle inside the sheet A v 1 2 qp m o B v 1 2 2qp m o C v 1 4 qp m o D v 1 2 qp m o

Electric field in is a region given by 3xi 4yj 5zk where x y and z are in meter In the figure below a cube of side 2 m has its orientation as shown If the flux of electric field through the cube s surface in S I unit is then value of 24 2 m is equal to 0 0 0

Consider the force F on a charge q due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it Which one of the following statements is true for F if q is placed at distance r from the centre of the shell A B C F F F 1 Qq 4 E r r 1 Qq 4 R R for all r 1 qQ 4 R R forr R F 0 for R

Four dipoles each consisting of a 10 C charge and a 10 C charge are located in the xy plane with their centers 1 0 mm from the origin as shown A sphere passes through the dipoles as shown in the figure What is the electric flux through the sphere due to these dipoles y a 9 0 x 106 Nm C b 4 5 x 106 Nm C c 0 00 N m C d 11 x 105 N m C e None of the above 10 points 1 0mm oto 1 0mm oto 1 0mm Spher 1 0mm

Calculate the charge contained in a sphere of radius 0 2 m centred at the origin 24 State gauss s theorem Use it to find electric field due infinite line of charge What is the effect on electric field when charge density gets double and distance between point and line of charge is half 25 An electric dipole AB consists of charges 15 nC and separated by a distance of 2 X 10 m as shown

4 Consider a hollow sphere of radius R its quarter part is cut and kept such that geometrical centre lies at origin as shown in figure x y axis lies in plane of paper and z axis is to the plane of the paper Sphere is kept in a manner such that plane portions of sphere lies in x z and y z plane Uniform electric field Eoi 2Eoj 2Eok N c lies in the complete space Electric flux coming out of the curved surface of sphere is a R E bR E0 2TR Eo C d Zero

18 A long cylindrical volume contains a uniformly distributed charge of density p Find the flux due to the electric field through the curved surface of the small cylinder whose axis is OP and whose radius is a Here O lies on the axis AB of the main cylinder containing the charge density p and its axis OP is perpendicular to AB and lies completely within the main cylinder A O X B 1 TED EA

45 A hemispherical surface of radius R is kept in a uniform electric field E as shown in figure The flux through the curved surface is E 1 E2 R 2 E R 3 E4 R

4 Choose the correct option a No of field Lines Leaving the sphere No of 2 field lines entering the sphere b Electric field is constant on sphere c Total flux through sphere is positive d flux due to q charge is negative 29 2

2 A point charge q is placed over a horizontal square of side L at a normal distance of 4 centre Electric flux through the square is 1 3 q 9 680 q 2 q 680 q from its

A spherical conductor has a radius of R and charge Q A spherical shell of thickness R and uniform charge Q is kept so as to be concentric to the conductor and touching the conductor The electric field at a distance of 1 5 R from the center of the sphere is A 83Q 504 ER 750 B 504 R 830 2 252 R C D 530 252 R 9

A spherical charge distribution of radius R is given by p po 1 r R where r is the radial distance and p is the volume charge density The electric field E is maximum at r equals O R 3 O 2 0R O 0 745R O 2R 3 O Zero

A non conducting solid sphere has radius R and uniform charge density A spherical cavity of radius R4 is hollowed out of the sphere The distance between center of sphere and center of cavity is R2 If the charge of the sphere is Q after the creation of the cavity and the magnitude of electric field at the center of the cavity is E K the approximate value of K Q 4 R M determine E E Sogg RSD Dagar bodo son 08 0 Soo R gago he fess sword wer 600J He todos Sud Cocos Ko R KA

A disk of radius a 4 having a uniforml is placed in the x y plane with its centre at a 2 0 0 rod of length a carrying a uniformly distributed charge 80 placed on the x axis from x a 4 to x 5a 4 Two po charges 7C and 3C are placed at a 4 a 4 0 3a 4 3a 4 0 respectively Consider a cubical surfa formed by six surfaces x a 2 y ta 2 z ta 2 T electric flux through this cubical surface is IIT JEE 200 34 a c 2 Eo 10C b d 2C E0 12C

Consider a uniform electric field E 3 x 10 N C a What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane b What is the flux through the same square if the normal Ans a 30 b 15 to its plane makes a 60 angle with the x axis

Example 1 7 Two identical spheres having positive charges are placed 3m apart repel each other with a force 8x 10 N Now charges are connected by a metallic wire they begin to repel each other with a force of 9 10 3 N Find initial charges on the spheres