Electric Field and Potential Questions and Answers

In absence of electric field there is only random motion of electrons but path is straight line In present of electric field there is random motion of electron but path curved a Only i is correct b Only ii is correct i c i ii both correct d None of these

Charges Q and Q lie inside and outside respectively of a closed surface S let E be lectric field at any point on S and be the flux of E over S a If Q changes both E and will change b If Q changes E will change but not change c If Q 0 and Q 0 then E 0 but 0 d If Q 0 and Q 0 then E 0 but 0

ssage A sphere of charge of radius R carries a positive charge whose volume charge density depends only on the distance r from the balls centre as S So 1 where So is a constant and is permittivity of free space The magnitude of electric field as a function of the distance r inside the sphere is given a E b E So E So d rm E So c E Se 12 E a rm b m c rm 1 3 So d E 2 4R G 4 3R E The value of distance rm at which electric field intensity is maximum R 3 3R 2 2R 3 4R

A charge of value 50 C is distributed uniformly on the surface of an equilateral triangle of side length 30 cm and which lies on the x y plane A uniform electric field of magnitude 1000 N C acts along the Z axis direction Find the magnitude of the net force acting on the ring

the angle of 180 12 a charge 200 micro coulomb is placed at a distance 20 cm from a point P find electric potential at point P 13 derive an expression for the capacitance of a parallel plate capacitor when a dielectric slab 1 2 but of same area as that of the plates is inserted

Consider two points 1 and 2 in a region outside a charged sphere Two points are not very far away from the sphere If E and V represent the electric field vector and the electric potential which of the following is NOT possible 1 E HE V V 2 E E V V 4 E E I V V 3 F V V F

Answer is given 2 but I am getting 3 And how to determine the positive and negative sign Three infinitely charged sheets are kept parallel to x y plane having charge densities as shown in figure The electric field at P is Z 3a Z 2a 11 2 3 Aok 4ok 20 U 1 Z 0 P 20 0

ed to a stored 4 2Q towards plate The ratio of field energy stored inside and outside a uniformly charged solid sphere of radius R and volume charge density p is fou 4Q towards plate grameetquation 1 11 5 3 1 5 2 4 566 5

A thin metal shell enclosed by concentric thick hollow metal sphere then potential at point P is 1 2 3 Question Type Single Correct Type KQ C KQ C P 20 2KQ b Q KQ KQ KQ a C a

1 From a ring of radius 10 cm that has a uniform charge density and a total charge of 15 C an arc that makes an angle of 30 is cut out If the remaining charge is again redistributed to form a complete uniform ring of radius 10 cm find the new charge density

Two long thin charged rods with charge density each are place parallel to each other at a distance d apart The force per unit lengt exerted on one rod by the other will be where k a kz d b k2 d k2 c d d k2 d 1 4 0

3 A cylinder of radius 6 cm and height 20 cm has a coil wound around it The total number of windings is 12 and the wire has a uniform charge density of 420 C m Find the total 22 charge on the wire Assume the wires are tight with no gap in between and 7

e q are rge that lates of w Then Aakash Institute 66 Equipotential surfaces in a region are shown Magnitude of electric field in the region is y m 1 2 V m 2010 10 V 30 20 V 30 V 40 V 50 V 10 20 X m 2 10 V m

48 If electrostatic potential at a distance r from the centre of a small dipole in axial position is V ther potential at a distance 2r from the centre on the same line is 1 V 180 3 8V 2 4V 4 V

Aakash Institute 35 Figure shows three spherical and equipotential surfaces A B and C around a point charge q at their common centre The potential difference V VB VB VC If t and to be the distances between them then 1 t 1 2 1

57 Four identical charge particles having charge q are placed fixed at the vertices of a square of side length a A negative charge Q having mass m is situated at the centre of the square The minimum velocity given to Q so that it can escape from there is 1 3 Qq2 2 4 ma 7 2 Qq2 27 1 2 TE ma 2 4 8Qq 27 2 TE ma Qq 2 7 1 2 4T ma 61

Two insulated charged spheres of radii 6 cm and 19 cm are having same charge are connected by conductor then they are separated Which will have greater charge Metallic sphere is placed in uniform electric field Which path is followed by lines of force 3

2 A conducting sphere of radius R is charged potential V The electric field at a distance r 1 from centre of the sphere is 1 RV 2 R V

2 Two point charges 8q and 2q are located at x 0 and x L respectively The location of a point on the x axis at which the net electric field due to these two point charges is zero is a 8 L b 4 L c 2 L d L 4

3 Two concentric conducting thin shells of radius al and b a b carry charges Q and 3Q respectively The net charge on the outer surface of the outer shell is 1 4Q 3 20 2 3Q 4 Q

1 Starting from rest an electron moves through a small distance in an uniform electric field of magnitude 2 x 104NC 1 The direction of the field is reversed keeping the magnitude unchanged and a proton moves through the same distance The time of motion will be b More in the case of an electron d Independent of charge a Same in both cases c More in the case of proton

Electrostatic Potential and Capacitance 62 Two conducting spheres each given a charge q are kept far apart as shown The amount of charge that crosses the switch s when it is closed is 1 q 3 q 2R 2 2q 3 9 66

4 0 72 J m 19 A charge is q kept in front of neutral metallic sphere as shown in the figure The value of electric field at the centre of sphere due to induced charge on surface of sphere is R 1 3 9 4 eo d EO q 4 Eo R d d q 2 4 q 4 R 3q 4T 41 0 R 23

Point charges 4q q and 4q are kept on the X axis at point x 0 x a and x 2a respectively Then a only q is in stable equilibrium b all the charges are in stable equilibrium c all of the charges are in unstable equilibrium d none of the charges is in equilibrium 1988

1 2 3 4 Two charges of equal magnitude q are placed in air at a distance 2a apart and third charge 2q is placed at midpoint of the line connecting identical charges The potential energy of the system is 1 3 8ma 5q 8 a 1 2 3 2 3q 2 8 a 4 The electrical potential on the surface of a uniformly charged sphere of radius r due to a charge 3 x 10 C on it is 500V The intensity of electric field on the surface of the sphere is in N C 1 10 2 200 3 between 10 and 20 7q 8 a 1 3Q 1 42R 2 1 4 0 Charge Q is uniformly distributed throughout the volume of a solid hemisphere of radius R Then the potential at center O of the hemisphere is 3 Rate of change of potential with position on them is zero 4 They can be spheres 6 Two charged conducting spheres of radil R and R potential at their surfaces is A non conducting ring of radius 0 5 m carries a torpeelquesve equal surface charge density The ratio of charge of 1 11 10 10 C distributed non uniformly on its circumference producing an electric field everywhere in space The value of line integral J Ede 0 at the center of the ring in volt 1 0 is given potential at infinity is zero Q R 1 4 TUD 5 3Q 4R 7 3 8 1 Q 47 4R Which of the following is not true about equipotential surfaces 1 They do not cross each other 2 They are concentric spheres for uniform electric field 3 1 1 Q 4E8R 20170 The work done by battery to charge an uncharged parallel plate condenser of plate separation d and plate area of cross section A such that the uniform electric field between the plates is E is Ad 30 20 1 3 2U Ad 3 E Ad 4 E Ad A capacitor is charged by a battery and the energy stored is U The battery is now removed and the separation between the plates is doubled The energy stored now is 2 U 4 4U

The work done by battery to charge an uncharged parallel plate condenser of plate separation d and plate area of cross section A such that the uniform electric field between the plates is E is Ad 3 E Ad 2 Ad 4 E Ad

Electrostatic Potential and Capacitance 9 The plates in a parallel plate capacitor are separated by a distance d with air as the medium between the plates In order to increase the capacity by 66 67 a dielectric slab of dielectric constant 5 is introduced between the plates What is the thickness of dielectric slab 1 3 Ala 94 5d 4 d 10 In the figure shown the equivalent capacitance between A and B is 10 F 10 F 3 A 1 3 75 F 3 6 5 F 2C 1 20 X 3C 5 HH 5 F 2 5 25 F 4 10 5 F 11 Equivalence capacitance between the points X and Y in the circuit is 2 1 100V 3 80 V 3 F B 0 b JIN 15 F HH 6 F 6uF N 5C 3 A a 0 Y 4 None of these 12 A capacitance of 10 uF is charged to a potential of 50V with a battery The battery is now disconnected and an additional charge 200 C is given to positive plate of the capacitor The potential difference across the capacitor become B 2 70 V 4 60 V 13 A charge q is placed at the origin O of X Y axes as shown in the figure The work done by external agent in taking a charge Q from A to B along the curved line A B is 3 Qq a l 4TE ab 3 Qq b 4 TE a Q 4RE L 3ms L Telegram neelquestion n 2L 14 A charged Q is uniformly distributed over a thin rod AB of length L as shown in the figure The electric potential at the point O lying at distance 2L from the end A is 0 N W 2 4 en 3 2 4 Aakash Institute Qq b a 4 ab Qq 2m 4 3Q 4 L a Q 4xL 10 C b B 15 In the arrangement of two concentric conducting shell as shown in the figure charge on the outer shell is 10 C and the inner shell is grounded Then charge q on the inner shell is n WIN 1 Zero 3 q 20 C 16 2 q 10 C 4 q 5 C Two identical capacitors have the same capacitance C One of them is charged to potential V and other to V The negative end is joined with the positive end of other capacitor When the other two remaining ends are connected the change in energy of combined system is 1 C v v C V V 3 C V V 4 C V V

A metal rod of radius a is concentric with a metal cylindrical shell of radius b and length The space between rod and cylinder is tightly packed with a high resistance material of resistively p A battery having a terminal voltage V is connected across the combination as shown Neglect resistance of rod and cylinder If I is the total current in the circuit then Question Type Single Correct Type 1 2 1 ev 2nlV p enb na 11 1 4nev

A 3 F capacitor is charged to a potential of 300 volts a 2 F capacitor is charged to 200 volts The capacitors are connected in parallel plates of opposite polarity being connected together The final potential difference between the plates of the capacitor after they are connected is now equal to A 700V B 240V

Question 2 A Hemispherical Bowl Of Inner Radii R And Outer Radii 2R Is Charged With Density R P P Fin 2 A hemispherical bowl of inner radii R and outer radii 2R is charged with density P Po 1 4 2p R 38 3p R 48 P R 3 28 Find the electric field at point 0 3p R 28 P RO 2R

A certain charge Q is divided into two parts q and Q q How should the charges Q and q be divided so that q and Q q placed at a certain distance apart experience maximum electrostatic repulsion 1 Q 4q 2 Q 3q 3 Q 2q 9 2

4 An electric dipole is located at the origin of the zy plane and generates an electrostatic potential given by V x y x y Here Vis measured in volts and z and y are measured in meters a What is the gradient of the potential V at the point z y 1 2

36 In a uniformly charged solid sphere of radius Rit found that electric field at distances R and R from the centre of the sphere is same Then the corre relation is R R R 1 R R R 3 R R 2R 2 R R R 4 R R R

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

Electric Charges and Fields 41 Variation of electric field intensity due to charged ring along axis with respect to distance measured from centre is given as 1 2 3 stionpaper E E 5 25

4 A long cylindrical wire carries a positive charge of linear density An electron e revolves around it in circular path of radius r The speed of the electron is proportional to the distance r 2 r 4 1 3 2 4 Telegramneeta

53 Variation of magnitude of electric field intensity due to uniformly charged non conducting solid sphere with respect to distance from centre along x axis is best represented by 2 3 X 0 J 57 Telegram neetquest

Aakash Institute 46 An electric dipole is placed at the origin and is directed along x axis At a point P far away from dipole the electric field is parallel to y axis OP makes an angle with x axis 1 tane 3 2 tano 2 3 0 45 4 tan 1 7 2

3 EA Es Ec 28 Electric field due to an electric dipole at a distance r from its center in axial position is E If the dipole is rotated through an angle of 90 about its perpendicular axis the electric field in magnitude at the same point will be 1 E 3 E 2 2 E 4 4 2E

24 Electric field at a distance x from the centre of uniformly positively charged ring having radius R is given by R x 1 3 kQx 1 2 x R 2 kQ 2 kQx R 4kQ 3 3 R

In moving from A to B along an electric field line the electric field does 1 28 x 10 18 J of work on an electron If 91 92 are equipotential surfaces then difference VE VD is equal to potential 1 8 volt 2 8 volt B Question Type Single Correct Type 3 zero F 42 E

16 If is the linear charge density of wire bent in form of semicircular shape as shown Then electric field intensity at the centre will be 1 3 2k R y axis x axis 2 2k R 1 k R Telegram neet

A particle of mass m and charge Q is placed in an electric field E which varies with time t as E Eo sinwt It will undergo simple harmonic motion of amplitude Question Type Single Correct Type 1 2 3 QEZ mw QEo mw QEo mw

A certain charge is divided in a ratio x y so that when kept at a finite distance the electrostatic force of repulsion is maximum The ratio xy is 1 2 1 2 4 1 3 1 1 4 1 2

4 With a uniform potentiometer wire AB of resistance 100 an electric cell of negligible internal resistance is connected A voltmeter of resistance 360 is connected between A and the mid point C of the wire If the reading of the voltmeter be 1 0 V determine the emf of the cell 2 28 V in what ratio

wo co axial rings of same radius R 10 cm are placed parallel to the y z plane such that x axis is the axis of the rings Ring 1 carries a current of 2 Ampere and ring 2 arries a current of 1 Ampere as shown in the figure The separation between the rings is d 50 cm Find the magnitude of Bdx where is the net magnetic field Ho any point on the axis Current in both the rings are in opposite sense Ring 1 Ring 2 010 50 cm 54 11 16 21

A fixed non conducting spherical shell of radius R has a charge Q spread uniformly on its surface projection speed is u R 2 A particle having mass m and charge qis projected towards the shell from a large distance at a speed u Impact parameter is see figure The particle passes the shell grazing its surface If the R 2 find n Neglect gravity nQq TE MR R

V Vxi Vyj the stick is at an angle to the x axis and is spinning around its centre at angular velocity w A 0 uniform magnetic field B is applied along the positive z axis Then q Xe Answer A B C D Your Attempt Correct answer Fnet on the dipole wqBL cos 01 sin 01 F net on the dipole wqBL cos 01 sin 03 7cm qBL vx cos 0 vy sin k 7cm qBL vx cos 0 vy sin 0 k Rate this questio L

20 points Upload your handwritten solution in the box below the question Two positive charges q 3 10 C and q2 3 10 9 C are separated by a distance of d 0 09 m At location P between the two charges the net electric field is found to be zero a 5 points Which of the following is correct at location P OE1 E 0 O E 0 OE E2 b 10 points The distance between charge q and location P is considered to be x Find the value of x in cm X 4 5 cm c 5 points A charge qo 5 109 C is placed at location P What is the net electric force on charge qo due to q and 4 Fnet N

Body Uniformly volume charged nonconductor sphere of radius R 2nd Body Uniformly surface charged conductor spherical shell of radius R distance of a point P from the centre of either 1 body or 2nd body Q Total charge of either 1st body or 2nd body E Electric field at point P Column I a 1st body and R b 1st body and R c 2nd body and R d 2nd body and r R A a s b p c q d r B a q b r c p d r C a r b R c p d r Column II p E 0 4 E 2 46 R T E 10 48 r s E 4ne R t E