Electric Field and Potential Questions and Answers

24 Two pith balls carrying equal charges are from a common point by strings of equal length the equilibrium separation between them is r Now the strings are rigidly clamped at half the height The equilibrium separation between the balls now becomes NEET 2013 a 1 2 b 3 2 c 2r 3 y 2 d 2r 3

In static electricity which notion is right about the flow of electrons Is it due to electric charge gradient like how air flo ws from higher pressure to lower press ure or is it due to the property of attract ion and repulsion of the charges Are t he charges distributed between the bod ies so as to maintain the highest level o f neutrality

In the figure mi has mass 5kg and my has mass 10kg The coefficient of friction between mi and my is 0 5 and the mass my is on the smooth horizontal floor If a force F is applied on the string such that it makes angle 37 with the horizontal then the maximum force F that can be applied so that there is no slipping between masses mj and m2 is 100 x N Find the value of x smooth ITT Q m m 37

A large metallic plate is facing a large charged sheet having charge density per unit area a placed parallel to the plate at a distance from the plate Potential at point P at a distance x from the sheet is kb A 200 C 0 1 x 1 x O A OB O C D 1 x B 260 D 1 x 0

q a a 2 P X 9 211 200 ZAPOJ 2q 1 What is the electric potential at point P midway between the line connecting the q and q charges assuming that V 0 at infinity ii What is the potential energy U of this configuration of three charges What is the significance of the sign of your answer iii A fourth charge with charge 3q is slowly moved in from infinity to point P How much work must be don in this process What is the significance of the sign of your answer NG

1 Two identical charged spheres are suspended by strings of equal lengths The strings make an angle of 30 with each other When suspended in a liquid of density 0 8 g cm the angle remains the same If density of the material of the sphere is 16 g cm the dielectric 3 3 constant of the liquid is

120 Wggo e as od 50 550 od as 58s 500 550 5g esso de todos 9 10 Nm C po 506 58 3 108 ms Options 2x10 7 2 3x10 7 3 4 10 7 4 0 100 cm rdos mis Dex T

There is a uniform electric field of strength 103 Vm along the Y axis A particle of mass 1 g and charge 106 C is projected into the field from the origin along the ve X axis with a velocity of 40 ms Then the magnitude of its velocity after 30 seconds will be neglect gravitation 10 Vm 35 x 2568 Doogee Y ego 3oad 305kj 1 t 558 106 C5 65 X go 866 40 ms o a 20 35 30 55e dobr 3x 3050 55 Options 1 40 ms 1 50 ms 1

A particle A having with a charge q 5 x 107C is clamped in vertical wall A small ball B of mass 100 g and having equa charge is suspended by an insulating thread of length 30 cm from the wall The point of suspension is 30 cm above the particle A as shown in figure 1 30 Find the angle 0 which the thread makes with the wall in equilibrium Take g 10 m s 30 cm 30 cm BO

A and B are two concentric metallic hollow spheres If A is given a charge q while B is earthed as shown in figure then B A x 1 charge density of A and B are same 2 field inside and outside A is zero 3 field between A and B is not zero 4 field inside and outside B is zero

Which of the following is incorrect about electrostatic force Only one correct answer A B C D It is conservative It is a central force Electrostatic field lines never intersect It also depends on mass content of body

53 A short dipole of dipole moment p is placed with axis perpendicular to a long thin uniformly charg rod with linear charge density at a distance r F the force acting on the rod due to field of dipole 1 p 2 EO p 3 r 2 AY p TEO 3 po p

A small sphere of mass mand having charge qis suspended by a silk thread of length in a uniform horizontal electric field If it stands at a distance x from the vertical line from point of suspension then magnitude of electric field is Only one correct answer A B C C mg q mga 77 mgx 9 2 2 mgl

you certainly draw Answer A B C D Your Attempt Correct answer Rate this question If Fe Fm for like charges and F Fm for unlike charges both the spheres must be made of insulating materials If Fe Fm for like charges and Fe Fm for unlike charges both the sphe must be made of conducting materials Irrespective of their materials Fe Fm for like charges and Fe Fm for unlike charges Irrespective of their materials Fe Fm for like charges and F Fm for unlike charges

Lines of a electrostatic field can t have sudden break in charge free region because A B C D It can t be discontinuous It is imaginary line Gauss s theorem will not be true These line can t exist in charge free region

A cube of side a has charge q at two diagonally opposite vertices as shown in the igure The net electric potential at the centre of the cube will be 4q 3 a q 3 a Read More O4q na

The electric fields from three coherent sources are described by E Eo sin wt Eo sin wt E2 Eo sin wt and E3 Eo sin wt 20 Let the resultant field be repre sented by Ep ER sin wt a Use phasors to find ER and a when a 20 0 b 60 0 and c 120 d Repeat when 3 2 rad d

Displace current is given by 1 dE dt 2 3 4 AHO HOEO dE dt Correct Answer 3 Status unattempted dE dt EOA A dE 140 0 dt

78 Positronium is like a H atom with the proton re by positron a positively charged antiparticle of the electron which is as massive as electron The ground state energy of positronium would be b 5 2 eV a 3 4 eV c 6 8 eV d 10 2 eV energy that must be given to ctron in al to tron

12 If electric field in a region is given as 3 k 1 1 Exi E0 E0 E 5 x 10 N C 1 2 cm then calculate the flux of electric fie passing through a rectangular plane 2 cm x 1 cr at y 2 cm N m C 1 2 Nm N m C 2 3

Let three be a spherically symmetric charge distribution with charge density varying as p r Po 5 r 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 4 R

An electromagnetic wave of frequency 1 10 4 hertz is propagating along z axis The amplitude of electric field is 4 V m If 8 8x10 12 C N m then average energy density of electric field EE 160E it 2014 will be A 35 2 10 13 J m C 35 2 10 11 J m Thi CH B 35 2x10 12 J m D 35 2 10 10 J m C

Two point charges of 0 1mc and 0 05m c are kept at points A 2m 0 0 B 2m 0 0 respectively Calculate the electros tatic potential energy of the system if t he whole system is placed in a region o f electric field E C r 2 where C 7 5x1 0 5 N C and r is distance of a point fro m origin 0 0 0

Charge 2Q and 3Q are given to inner and outer plates of a spherical capacitor having inner radius a and outer radius 2a Total electrostatic potential energy stored in the spherical region a 2a is 2a O Ta a 2Q 3Q Q 2 a

Infinite number of alternate charges q and q are arranged on a straight line with separation a Find interaction energy of each charge with all others ka O q q q q q q 9 9 O q 27a 2q In 2 In 2 39 Ta In2 o 9 9 9

point fre charge A charge Q is uniformly distributed over a large plastic non conducting sheet The electric field at a point close to the centre of the plate near the surface is 20 V m If the plate is replaced by a copper plate of the same geometrical dimensions and carrying the same charge Q then what is the electric field at that point 3x 101NG 1 through a cube of side 20 cm oriented field

28 Two charges each equal to q are kept at x a and x a on the X axis A particle q of mass m and charge q is placed at 2 the origin If charge qo is given a small displacement y a along the Y axis the net force acting on the particle is

1 11 Three identically charged small spheres each of mass m are suspended from a common point by insulated light strings each of length 1 The spheres are always on vertices of an equilateral triangle of length of the sides x 1 Calculate the rate da dt with which charge on each sphere increases if length of the sides of the equilateral triangle increases slowly according dx a dt to law Ans 3reomga

Figure shows three concentric thin spherical shells A B and C of radii R 2R and 3R The shell B is earthed and A and C are given charges q and 2q respectively Find the charges appearing on all the surfaces of A B and C B C

vii A leaky parallel capacitor is filled completely with a material having dielectric constant K 5 and electrical conductivity o 7 4 x 10 22 m If the charge on the plate at the instant t 0 is q 8 85 C then calculate the leakage current at the instant t 12s 0 2 Al

1 26 A non conducting hollow sphere having inner and outer radii a and b respectively is made of a material having di electric constant K and has uniformly distributed charge over its entire solid volume Volume density of charge is p Calculate potential at a distance r from its centre when

Three short dipoles each of dipole moment of magnitude p are placed on a circle of radius Ras shown The magnitude of electric field intensity at centre will be 1 4kp kp 120 120 120 2 2kp

onsider the charge configuration and a Gaussian surface as shown in figure If 2 and 3 are net electric flux due to charges 9 92 and q espectively then Here 91 92 and 93 all are different and non zero charges q 93 Gaussian surface

Two balls of same mass and carrying equal charge from a fixed support of length 1 At electrostatic equilibrium assuming that angles made by each thread is small the separation x between the balls is proportional to 2013 A I C 12 3 B 1 D 11 3

n 1 n 3 n 1 5 A total charge of 20 C is divided into two parts placed at some distance apart If the charges experience maximum coulombian repulsion then the charges should be 1 5 C 15 C 2 10 C 10 C 3 12 C 8 C 40 20

Figure shows an imaginary cube of edge L 2 A uniformly charged rod of length L moves towards left at a small but constant speed u At t 0 the left end just touches the center of the face of the cube oppositei it Which of the graphs shown in figure 30 Q2b represents the flux of the electric field through the cube as the rod goes through it flux G L 2 V a L b L 2 d b V L a C time

3 4 Electric charges are distributed in a small volume The flux of the electric field throught a spherical surface of radius 10 cm surronding the total charges is 25V m The flux over a concentric sphere of radius 20 cm will be A 25 V m D 200 V m B 50 V m C 100 V m Figure shows an imaginary cube of edge L 2 A uniformly charged rod of li at a small but com

Two small equal point charges of magnitude q are suspended from a common point on the ceiling by insulating massless strings of equal lengths They come to equilibrium with each string making angle 0 from the vertical If the mass of each charge is m then the electrostatic potential 1 k at the centre of line joining them will be 41 0 A 2 kmgtano L C 4 kmg tan0 B kmgtan0 D kmgtan0 2013

2013 Consider a finite insulated uncharged conductor placed near a finite positively charged conductor The uncharged body must have a potential A less than the charged conductor and more than at infinity B more than the charged conductor and less than at infinity C more than the charged conductor and more than at infinity D less than the charged conductor and less than at infinity

A solid metallic sphere has a charge 3Q Concentric with this sphere is a conducting spherical shell having charge Q The radius of the sphere is a and that of the spherical shell is b b a What is the electric field at a distance R a R b from the centre 4Q A 2 R 3Q B TEOR 4 ER C 3Q 2 R Q D 2TEOR

22 Two similar small balls of mass m and charge q each are suspended by silk strings having length l according to the figure If in the figure 0 is a very small acute angle then for equilibrium the distance between centre of balls is 1 3 q l 2TE mg 9 3 Ema 2 4 edical 117 Divisions of q l 21 mg q l 4 mq 2 12 2

13 It is observed that as one moves along posit x axis the electrostatic potential reduces One n conclude that the direction of electric field 1 Must be along x axis 2 Must be perpendicular to x axis 3 May be perpendicular to x axis 4 May be along x axis

3 90 V 4 60 V 16 In a certain region potential is given by V k 2xy The electric field at 1 1 has magnitude 1 2 k 2 2 2 k 4 k k 2 17 The variation of electrostatic potential as a function 3 Medical

25 A beam of cathode rays is subjected to crossed electric E and magnetic fields B The fields are adjusted such that the beam is not deflected The specific charge of the cathode rays is given by AIPMT Prelims 2010 1 B 2VE 2VE 2 2VB E E

SolveLancer Test In a hypothetical situation a small spaceship having charge q approaches a massive planet which has a charge Q Initially the distance between them is very large as shown Q Spaceship d 221 q 2u 5u O Planet What is the final velocity of spaceship when it again at a large distance from the planet Ignore effects of gravity SolveLancer Test a Data insufficient b 7u c 12u

1 42 A solid non conducting hemisphere of radius R has a uniformly distributed positive charge of density p per unit volume A negatively charged particle having charge q is transferred from centre of its base to infinity Calculate work performed in the process Di electric constant of material of hemisphere is unity Ans 9pR 480 1

A spherically symmetric change distribution is characterised by a change density having the following variation 2014 p r Po 1 R p r 0 for r R The radial electric field is given by A C Po 480 Po 380 r r 3 4R r 3 for r R 4R B D Po r 80 3 4R Po r 12 3 4R

1 20 Find the electric field strength vector at the centre of a Vball of radius R with volume charge density p ar where a is a constant vector and r is a radius vector drawn from the ball s centre Ans E 1 6a R

Two batteries of emf s 5V each and internal resistance R R R R respectively are connected in series with wires having negligible resistance Then A V V V Ve 0 V V 0 B V V 0 V Vc 0 VA VB 0 R

In a space electric field is acting parallel to x axis wherever it is present Variation of electric potential v s position x as shown Choose the correct statement s n 5 volt 2m 4m 5m 10 volt A if an electron is released from x 5 then it can reach to x 0 B if an electron is released from x 0 then it can reach to x 5 C if a proton is released from x 5 then it can reach to x 0 D if a proton is released from x 0 then it can reach to x 5