Electric Field and Potential Questions and Answers

The conductor in the figure has an excess charge of 3 72 mC If a 2 5 mC point charge is placed in the cavity what is the net charge on the outer surface of the conductor a 6 220 uC b 1 220 mC c All answers are incorrect Od 6 220 mC e 1 220 UC Cavity

A uniform electric field of 100 N C exists in XY plane making an angle 60 with x direction Consider points A 1 2 3 m and B 3 2 1 m then V V is 1 100 volt 2 200 3 volt 3 283 volt 4 400 volt A B

E CAPS 08 A Physics 13 For the situation shown in the figure mark the correct statements A is a uniform thin conducting shell of radius R 3R B R A C H 2 3 ANSWERS

ree point charges lie in the x y plane as shown in the diagram below 91 65 5 and is located at the origin 42 and located at m ar 0 93 15 3 C and is located at x 1 41 m and y 2 61 m A force diagram showing the forces acting on q and a coordinate system are given in the agram y m F21 31 1 T 92 x m 9 Iculate the y component of the net electrostatic force acting on q due to charges q 2 and 93

41 Two charges of 25 x 10 9 coulomb and 25 10 coulomb are placed 6 m apart Find the electric field intensity ratio at points 4 m from the centre of the electric dipole i on axial line ii on equatorial line 1 3 1000 49 500 49 2 4 49 1000 49 500 it is a large d

1 Sheila is trying to write an equation for the equivalent resistance for the following circuit She comes up 1 Rtotal R1 with the following equation Is she correct If not what mistakes did she make and what is the correct equation R R www R R R

The electric field intensity produced by the radiations coming from a 100 W bulb at a 6 m distance is E The electric field intensity produced by the radiations coming from 25 W bulb at the 3 m distance is O2E O 3E OE OE

A point charge q is placed at the centre of a cylindrical surface of length 8 CM and radius 3 CM as shown ABCD is a part of curved surface which subtends an angle 0 60 on axis as shown Electric flux through the surface ABCD will be q A 0 D T B C 8cm

25 Three identical charges are placed at the corners of an equilateral triangle If the force between any two charges is F then the net force on any one charge will be 1 2 F 3 3 F 2 2F 4 3F

8a The electric potential at points in an xy plane is given by V 2 0 r 3 0 y2 In unit vector notation what is the electric field at the point 3 0 2 0

A non conducting solid sphere of radius r 0 5 m and mass m 2 5 kg has a charge of Q 10 C distributed uniformly over its volume If the sphere is rotated about a diameter with an angular speed of w 25 rad s Find the magnetic moment in Am and angular momentum in kgm s of the solid sphere m Solid sphere A 12 5 12 5 B 12 5 6 25 C 12 5 12 25

A small object of mass m and of charge q slides down along a frictionless slope of a elevation from a height h From the midpoint of the slope it enters into a region of uniform horizontal electric field and it decelerates and stops at the bottom of the slope m q E h e A The magnitude of E istana B The normal reaction on block before dotted line and after dotted line remains the same C The magnitude of acceleration before and after dotted line remains the same D The speed at height from bottom is V

19 A short electric dipole with dipole moment p 2qd is placed coaxially with a ring of radius R at a distance r from the center of the ring as shown in figure The flux of the electric field due to dipole through the area bounded by the ring is Ra 280 80 R 2d The product 3a is R

9 The total charge enclosed in an incremental volume of 2x10 9 m located at the origin is nC if electric flux density of its field is found as D e siny e cosy 3 2zk C m Given swer 4

Two identical particles of mass m carry a charge Q each Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large distance with speed v The closed distance of approach be A C 1 Q 4 mv 1 20 2 41 my B D 1 4Q mv 2 4 1 30 2 4 mv

1 44 27 Theory and Exercise Book Three point charges q 2 q and 2 q are placed a the vertices of an equilateral triangle of side a The work done by some external force to increase thei separation to 2 a will be A 1 2q a 4 zero B negative 1 3q

8 The equation of an equipotential line in an electric field is y 2x then the electric field strength vector at 1 2 may be A 41 3 C 81 41 B 41 81 D 8 41 The electric field in region is given by

The electric field in region is given by E 4axy z i 2ax z j ax y Z k where a is a positive constant The equation of an equipotential surface will be of the form A z constant x y B z constant xy C z constant x y D None

The magnitude of the electric field is 1000 N C at a point located at d 2 5 m away from a long uniform line of charge Find the distance in cm away from the line at which the magnitude of the electric field is 6000 N C 21 d E

4 If mass of the electron 9 1 x 10 31 Kg Charge on the electron 1 6 10 19 coulomb and g 9 8 m s Then the intensity of the electric field required to balance the weight of an electron is A 5 6 x 109 N C C 5 6 x 10 8 N C B 5 6 10 11 N C X D 5 6 x 10 7 N C

Two dipoles are oriented as shown Dipole 1 consists of point charges 22 nC and 22 nC separated by 6 mm Dipole 2 consists of point charges 29 nC and 29 nC separated by 2 mm Location A is at distance d 0 56 m from the center of each dipole Dipole 1 Dipole 2 A a 10 points What is the electric field vector at location A due to dipole 1 b 10 points What is the electric field vector at location A due to dipole 2 c 10 points What is the net electric field vector at location A due to both dipoles

The figure shows a closed Gaussian surface in the shape of a cube of edge length 1 50 m with one corner at x 4 20 m y 3 70 m 2 807 3 60 y 3 40 kN C with y in meters What is the The cube lies in a region where the electric field vector is given by net charge contained by the cube x X

A metal sphere is given charge Q as shown in the figure A point charge Q is placed at a distance 4R from the centre of the sph choose correct statement s ect Answer 4 Answer 1 is incorrect R Net electric field at point P is zero In absence of point charge field at O is non zero In presence of point charge field at P is towards metal sphere iv in presence of point charge field at O is zero 1 i iii iv are correct i ii are correct ii iii are correct iii iv are correct Metal sphere R 2R

A positive charged particle when moves from higher potential to lower potential O Its potential energy must increase Its kinetic energy must increase OIts potential energy may decrea

Which of the following is incorrect statement O Electric field is sometimes non conservative O Electric field due to a stationary charge is conservative O Electric field due to a varying magnetic field is non conservative O Electric field lines are always closed loops

Figure shows some of the electric field lines corresponding to an electric field The figure suggests that E electric field V potential O EA EB O VA VB B O EA EB O VA VB

Five charges each q are placed at five corners of a regular pentagon Distance from corner to the centre of pentagon is r Then K O Potential at centre is 470 5kq O Electric field at centre is non zero O Potential at centre is zero O None of these

Two concentric shells have radii R and 2R charges q and qB and potentials 2V and 3 2 V respectively Now shell B is earthed and let charges on them become and Then B A O 9A 9B 1 2 O Potential of A after earthing becomes 3 2 V 4 O None of these

Two point charges q each are fixed at a 0 and a 0 A third charge Q is placed at origin Electrostatic potential energy of the system will O Increase if Q is slightly displaced along x axis O Increase if Q is slightly displaced along y axis O O D crease if Q is slightly displaced along x axis Remain constant if Q is slightly displaced along y axis

A and B are two conducting concentric spherical shells A is given a charge Q while B is uncharged If now B is earthed as shown in figure Then which statement is incorrect O B The charge appearing on inner surface of Bis Q O The field between A and B is not zero O The field inside and outside A is zero The charge appearing on outer surface of B is

A point charge q is placed at origin Let E E and be the electric fields at three points A 1 2 3 B 1 1 1 B and C 2 2 2 due to charge q Then O ELEB O E 8 Ec O E Ec O None of these

An electric dipole moment p 201 30 C mis placed in a uniform electric field 301 20k 10 NC X mark incorrect statement O The torque that exerts on is 0 67 0 47 0 9k Nm O The potential energy of the dipole is 0 6J O The potential energy of the dipole is 0 6J If the dipole is rotated in the electric field the maximum potential energy of the dipole is 1 3J

b How much work is required to separate the two charges infinitely away from each other c Suppose that the same system of charges is now placed in an external electric field E A 1 r A 9 x 105 C m2 What would the electrostatic energy of the configuration be Solution a U 4 1992 9 10 x r Scanned by TapScanner 7x 2 x10 2 0 18 0 7 J b W U U 0 U 0 0 7 0 7 J c The mutual interaction energy of the two charges remains unchanged In addition there is the energy of interaction of the two charges with the external electric field We find

A particle of charge q and mass m moves rectilinearly under the action of an electric field E a Ba Here and are positive constants and x is the distance from the point where the particle was initially at rest Ther B O The motion of the particle is oscillatory O The amplitude of the particle is 23 O The amplitude of the particle is O None of these

Three concentric conducting spherical shells have radii r 2r and 3r and charges q 92 and q3 respectively Innermost and outermost shells are earthed as shown in figure Select the correct alternative 93 92 91 2r 3r HI

a Determine the electrostatic potential energy of a system isting of two charges 7 C and 2 C and with no external field placed at 9 cm 0 0 and 9 cm 0 0 respectively b How much work is required to separate the two charges infinitely away from each other c Suppose that the same system of charges is now placed in an external electric field E A 1 r A 9 x 105 C m2 What would the electrostatic energy of the configuration be Solution 1992 9x10 x 4TE T b W U U 0 U 0 0 7 0 7 J c The mutual interaction energy of the two charges remains unchanged In addition there is the energy of interaction of the two charges with the external electric field We find q V q V 1 A and the net electrostatic a U 7 2 10 2 0 18 7 C 0 09m A 2 C 0 09m Scanned by TapScanner energy is ZUC 0 7 J RUC

2015 An electric dipole consists of two opposite charges each of magnitude 1 0 C separated by a distance of 2 0 cm The dipole is placed in an external field of 105 NC The maximum torque on the dipole is a 0 2 x 10 3 Nm c 2 10 Nm b 1 10 Nm d 4 10 Nm COMEDK

Charge 4 uc and 9 uc lies at 100 m distance find point on line joining charges where electric field zero Find out point where electric field is Zero but electric potential not zero Find out point where electric potential is zero but electric field not zero

A particle is moving in a three dimensional potential V x y z mo 2x y 42 If the mass of the particle is m then what is the energy of the particle in the lowest quantum State a b c 7 2 o 3 2 2 ho 3 3 re 3 d o

7 A solid conducting sphere of radius a having a charge Q is surrounded by a connectric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure Find the final potential of inner surface of shell when switch is closed a c kQ b 2a kQ 4a d kQ 3a kQ 6a 3a 2a

7 Following figure shows four situations in which positive and negative charges moves horizontall through a region and gives the rate at which each charge moves Rank the situations according t the effective current through the region greatest first i 7C sec ii 3C sec 1 i ii iii iv 3 i ii iii iv 4C sec iii 2C sec iv 5C sec 2 i ii iii iv 4 i ii iii iv 6C sec 1C sec

1 A ring of radius R has charge Q distributed uniformly over it A charge q is placed at the center of the ring such that the electric field becomes zero at a point on the axis at distance R from the center of the ring If the value of q is Q x find the value of x

54 Lenz s law is a consequence of the law of conservation of 1 momentum 2 charge 3 mass 55 In general a current carrying copper wire is 4 energy

1 Two point charges 4e and e are at a distance d apart What should be the sign of a third point charge q to be placed between them so that a q is in equilibrium h the entire system is in equilibrium

There is a cubical cavity inside a conduct ing sphere of radius R A positive point charge Q is placed at the centre of the cube and another positive charge q is placed at a distance R from the centre of the sphere The sphere is earthed A Charge induced on the inner surface of cavity is B C B R D Q uniformly distributed Q non uniformly distributed q Q q non uniformly distributed None of these

The number of free electrons per 10 mm of an ordinary wire copper wire is about 2 1021 If the average drift speed of the electrons is 0 25 mm sec then the electric current flowing through the wire is O 80 A O 0 08 A O 0 8 A O 8A Marks 4 1

Three concentric spherical shells have radii a and c a b c and have surface charg densities o o and o respectively If V V and Vc denote the potential of the three shells the for c a b we have A 1 Vc V VB 2 Vc VB VA V V

length is included in a circuit as shown in figure Given are the emf of the current source its internal resistance r and the distance d between the plates An electron with a velocity u flies into the capacitor so that the electron flies out of the capacitor at an angle of 37 to the plates Find the value of Rin ohm Assume that circuit is in steady state and neglect relativistic effect Take 91 cm 3 V r 2 Q d mm u 4 x 107 m s m 9 1 x 10 1 kg and e 1 6 x 107 19 C ax A d yg a2 l T Fuka h fa zefy xguz qkqy umfa 6 1 ua zata g fa a 3 R qu 54 dkg ufadu a tar 1 v ia uka 34 GR na Geal fc s azia cu uz mka agz Aga jy g fukuu zum udfg u aya ch aqvq 817 9 91 cm 3 V r 2 Q d mm u 4 107 m s me 31 19 9 1 x 107 kg e 1 6 x 107 C E d www Correct Answer 10

Consider a square loop of wire of side length 1 lying in the xy plane as shown in figure Suppose a particle of charge q is moving with velocity v where v c in the xz plane at a constant distance zo from xy plane Assume the particle is moving in the positive x direction Suppose the particle crosses the z axis at t 0 Give the induced emf in the loop as a function of time

A disc is charged non uniformly with charge per unit area depending on distance x from the centre as o cx 1 5 0 The radius of disc is 3m and the electric field at a distance of 4m from centre on it s axis is in SI units Find the value of c in integer in SI units charge