Gauss Law Questions and Answers

4 The electric field in a certain region is acting radially outward and is given by E Ar The charge contained in a sphere of radius a centred at the origin of the field will be given by 1 A 80 a 2 4 3 4 4 TE 121 Aa Aa

Two conductors are of same shape and size One of copper and the other of aluminium less conducting are placed in an uniform electric field The charge induced in aluminium 1 will be less than that in copper 2 will be more than that in copper 3 will be equal to that in copper 4 cannot be compared with that of copper

93 A non conducting spherical ball of radius R contains a spherically symmetric charge with volume charge density p kr where r is the distance from the center of the ball and n is a constant What should be n such that the electric field inside the ball is directly proportional to square of distance from the centre

52 A point charge q is placed over a horizontal square 4 of side L at a normal distance of centre Electric flux through the square is 1 3 9 680 9 0 9 2 4 q 680 from its

A charge of 12 pC is placed at a distance of 10 cm directly above the centre of a square of side 20 cm What is the magnitude of electric flux through the square 1 0 225 m C N 2 2 70 10 m N m 3 1 35 obni

and points radially inward what is A uniformly charged conducting sphere of 2 4 m diameter has surface charge density of 80 0 C m a Find the charge on th sphere b What is the total electric flux leaving the surface of th sphere An infinite line charge produces a field of 9 x 104 N C at a distanc

4 20 A point charge causes an electric flux of through a spherical Gaussian surface of 10 0 cm radius centred 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 on unknown charge If

Example Ex x 63 The electric field components in Fig 1 88 are E E 0 in which a 800 N Cm Calcu late i the flux de through the cube and ii the charge within the cube Assume that a 0 1 m y NCERT Z AY a a a a X

N The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150 N C directed inward towards the center of the Earth This gives the total net surface charge carried by the Earth to be approximately Given 8 85 x 10 12 C N m RE 6 37 x 10 m 1 670 KC 3 680 KC 2 670 KC 4 680 KC S N

FIGURE 4 19 A point charge of 2 0 C is at the centre of a cubic Gaussian surface 9 0 cm on edge What is the net electric flux through the surface x Clectric flux of 1 0 10 Nm C to pass dius centred or

A rectangular surface of sides 10 cm and 15 cm is placed inside a uniform electric field of 25 V m such that the surface makes an angle of 30 with the direction of electric field Find the flux of the electric field through the rectangular surface 1 0 1675 N m C 2 0 1875 Nm C 2 Zom 4 0 1075 Nm C

8 Electric charge is uniformly distributed over a long straight wire of radius 1 mm The charge per cm length of the wire is Q coulombs A cylindrical surface of radius 50 cm and length 1m encloses the wire symmetrically as shown in fig The total flux passing through the cylindrical surface is 1 2 Fo 100Q Fo 3 10Q 50cm 4 100Q

5 The electric field near a conducting surface having a uniform surface charge density o is given by O and is parallel to the surface a 80 20 b and is parallel to the surface 0 O o c and is normal to the surface d 80 20 Eo and is normal to the surface

Two point charges q and q are fixed in space at separation a The flux through infinite plane perpendicular to line joining the charges and at a distance a 3 from q will be A C q 3 0 q B D q 2 0 2q fo 2 3 g 2a

A point charge of 2 0 C is at the centre of a cubic Gaussian surface of edge 9 0 cm What is the net electric flux through the surface An electric flux of 6 x 10 3 Nm C passes normally through a spherical Gaussian surface of radius 10 cm

An electric flux of 6 x 10 Nm C passes normally through a spherical Gaussian surface of radius 10 cm due to a point charge placed at its centre a b What is the charge enclosed by the Gaussian surface If the radius of the Gaussian surface is doubled how much flux would pass through the surface

If E 2x then find volume charge density inside le cube 1 8 85 x 10 1 C m 2 1 77 x 10 1 C m 3 8 85 x 10 7 C m 4 1 77 x 10 7 C m S 61

A point charge is placed at centre of a disc now it is moved away from centre along axis then graph between flux related to the disc and distance x from centre of disc is d q 2 1 3 Z X 10 9 28 X 2 q 280 o 9 28 X

All are true 26 A charge Q is placed at the corner of a cube of edge length L The electric flux linked to one of the face not touching the charge Q is 3 2480 Q 8E0 2 680 4 Zero charos

A charge q is placed at a distance x from the flat surface of the cone as shown in figure i Flux through the curved surface of cone due to this charge is 39 Now if the same charge is placed at a 780 distance x inside the cone as shown in the figure ii then flux through the curved surface of cone would be 1 9 EO 4q 3 78 9 i ak 2 X 3q 780 4 Can t be determined

A rectangular loop of area 20 cm x 30 cm is placed in a magnetic field of 0 3 T with its plane i normal to the field ii inclined 30 to the field iii parallel to the field Find the flux linked with the coil in each case for coil of 2000 turns is 10 cm Its plane is ke

A given charge is situated at a certain distance from an electric dipole in the end on position experiences a force F If the distance of the charge is doubled force acting on the charge will be 1 2F 2 F 2 3 F 4 4 F 8

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 1 4 3 TS 4 A 9 1 A 2 41 A 4 20

A point charge q is placed at a distance on the y axis vertically above the surface which lies in the xz plane as shown in the figure The flux of electric field passing through the plate is A B C D q 6E0 1880 q 2480 q 480 q 0 2 0 0 1 0 1

Qr sphere is given by p TR4 where Q is total charge on sphere and R is its radius r is distance from centre of sphere Magnitude of electric field at a distance I from centre of sphere R will be 1 Q1 8 E R4 QI 2 Q1 4 R4

53 Above an infinitely large plane carrying charge density o the electric field points up and is equal to What is the magnitude and direction of the electric 260 field below the plane a o 260 down c o so down b o 280 up d o so up

Charge is distributed inside a long cylindrical volume of radius R such that charge density inside the volume varies as P ar where a is a constant and the distance from the axis of the cylinder If the magnitude of electric field E inside the cylinder is independent of r the value of is 2 2 1 1 Check all that apply A B C D 3 2 4 1

A point charge q is placed at a normal from one edge of a semi infinite large plate as shown in figure Find net electric flux passing through this plate 1 q 280 Semi infinite plate A 9 480 W 2 24

35 A small spherically symmetric charge q is placed at one vertex of a cube as shown The flux through the faces ABCD and HGFE are respectively 9 a H 9 24 9 9 0 1 G 9 240 E D B FIGURE 13 122 b 0 F C 9 880 9 0

9 A square of side d is placed horizontally A particle having charge q is held at a height d above one comer of the square The electric flux passing through the square is 1 Eo q td Fo d q 2 48 9

In a region of space the electric field E Exi Eoyj Consider an imaginary cubical volume of edge a with its edges parallel to the axes of coordinates Now A the total electric flux through the faces 1 and 3 is Ea B the charge inside the cubical volume is 28 Ea 3 C the total electric flux through the faces 2 and 4 is 2E a D the charge inside the cubical volume is Ea 3 1 Z y 2 5 4 3

Consider a gold nucleus to be a sphere of radius 6 9 fermi in which protons and neutrons are distributed Find the force of repulsion between two protons situated at largest separation Why do these protons not fly apart under this repulsion

A circular loop of radius 0 3 cm lies parallel to a much bigger circular loop of radius 20 cm The centre of the small loop is on the axis of the bigger loop The distance between their centres is 15 cm If a curretn of 2 0 A flows through the smaller loop then the flux linked with bigger loop is 2 R r 10 1 weber 2 3 3x10 weber 10 11 weher

will change B If Q changes E will change b D If Q 0 and Q 0 then E 0 but 0 electric flux passing through the cube A charge q is placed at the centre of a cube whose top face is open it has only 5 faces Calculate the total A point charge of 2 0 C is at the cente C If Q 0 and Q 0 then E 0 but 0 What is the net electric

An electric field E 4x y 1 N C passes through the box shown in figure The flux of the electric field through surfaces ABCD and BCGF are marked as and respectively The difference between 1 1 is in Nm C L 3 5 9E Two infinite planes each with unifor depois 0 2 2 y D A H 0 2 0 Z 0 0 2 E 0 0 0 G B 3 2 2 3 2 0 3 0 2 3 0 0

This question has Statement 1 and Statement 2 Of the four choices given after the statements choose the one that best describes the two statements AIEEE 2012 An insulating solid sphere of radius R has a uniformaly positive charge density p As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere at the surface of the sphre and also at a point out side the sphere The electric potential at infinity is zero Statement 1 When a charge q is taken from the centre to the surface of the sphere its potential energy changes by qp 3 Eo pr 3 0 Statement 2 The electric field at a distance r r R from the centre of the sphere is 1 Statement 1 is true Statement 2 is true and Statement 2 is the correct explanation of Statement 1 2 Statement 1 is true Statement 2 is true and Statement 2 is not the correct explanation of statement 1 3 Statement 1 is true Statement 2 is false 4 Statement 1 is false Statement 2 is true

24 The electron is projected from a distance d a with initial velocity u parallel to a uniformly charged flat conducting plate as shown in figure It strikes the plate after ravelling a distance 1 along the direction The surface charge density of conducting plate is equal to

15 The radius of a gold nucleus Z 79 is about 7 0 10 m Assume that the positive charge is distributed uniformly throughout the nuclear volume Find the strength of the electric field at a the surface of the nucleus and b at the middle point of a radius Remembering that gold is a conductor is it justified to assume that the positive charge is uniformly distributed ver the entire volume of the nucleus and does not come o the outer surface

1 Variation of electric potential V due to a charge spherical conducting system is shown in the figure V 10 volt A electric energy density is zero from r 0 to r 10 cm region B Electric flux through a spherical surface 2x10 C of radius r 12 cm is 980 1 C Electric potential energy of the system is 9 1 D Electric potential energy of the system is 3 1 104J 10 4 J 10 hyperpola 20 30

The adjacent diagram shows a charge Q held on an insulating support S and enclosed by a hollow spherical conductor O represents the centre of the spherical conductor and P is a point such that OP x and SP r The electric field at point P will be S O Q 1 4x 2 3 0 Charge Qon Insulating support X P SP r OP x Q 2 An of 4 None of the above

31 An uncharged conductor has two spherical cavities of radius r and r two point charges q and q are placed at centres of cavities Potential at the surface of conductor is vo then potential at point P will be 1 zero 2 3 92 91 1 4 o 1 r 9 KU r P Vo 91 92 4 22 418 Vo

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

Find the electrostatic force of interaction between two halves of a spherical conductor of radius R carrying a charge Q

a sph erica symme distribution with charge density varying as p r Po upto r R and p r 0 for r R where r is the distance from the origin The electric field at a distance r r R from the origin is given by a 5 r 4 R 4 r 5 r 380 3 R 4er 5 r b Por 5 480 513 r R por 5 r

gure shows in cross section two Gaussian spheres and two Gaussian cubes that are centered on a positively charged particle Rank greatest first and indicate whether the magnitudes are uniform or variable along each surface q i 111 iv 1 net flux through all the four Gaussian surfaces will be equal 2 the magnitudes of the electric fields on the surfaces i and iii will be constant 3 the magnitudes of the electric fields on the surfaces ii and iv will be variable 4 the magnitudes of the electric fields on all the surfaces will be constant

2 3 1 4 Shown in the figure are two point charges Q and Q inside the cavity of a spherical shell The charges are kept near the surface of the cavity on opposite sides of the centre of the shell If o is the surface charge on the inner surface and Q net charge on it and a2 the surface charge on 2 the outer surface and Q net charge on it then 1 0 Q 0 0 0 Q 0 0 0 Q 0 0 0 Q 0 0 0 Q 0 02 0 0 Q 0 0 0 O

A spherically symmetric system shown in the figure below consists of a conducting spherical core and a conducting spherical shell These conductors carry some unknown charges which you are asked to find based on the two measurements of the resulting radially directed electric field The field at point A distance a 7 4 cm away from the center equals to E 170 KN C The field at point B distance b 27 cm away from the center equals to E 61 kN C Positive values of radially directed fields refer to the outward direction negative values to the inward direction C Find the total charge on the surface of the spherical core including its polarity Qu What is the total charge on the inner surface of the spherical shell Qever C What is the total charge on the outer surface of the spherical shell K C

A cube has sides of length L 0 330 m It is placed with one corner at the origin as shown in Figure 1 The electric field is not uniform but is given by E 4 79 N C m zi 2 32 N C m zk Figure S left side L L S top L S back S right side y 1 of 1 Y Part A Find the electric flux through each of the six cube faces S1 S2 S3 S4 S5 and S6 Enter your answers in newtons per coulomb times meter squared separated by commas 2 3 4 5 6 Submit Part B 97 Find the total electric charge inside the cube Express your answer in coulombs Submit Request Answer VAZO Provide Feedback 6 VAZO Request Answer 22443 5 C BHER N C m

A charge q is placed at a point exactly above the centre of square of side a at a distance The flux passing through square will be The value n o of n is equal to Answer 01 02 03 04 05 06 07 08 09 00 01 02 03 04 05 06 07

A neutral aluminum pie plate is brought near to a positively charged foam board When it is held near what does the charge distribution on the aluminum pie plate look like Tap on object to toggle through Charge Distribution options In this situation the aluminum pie plate is Tap to select or deselect answers Select all that apply electrically neutral polarized negatively charged positively charged