Electric Field and Potential Questions and Answers

qis placed in a spherical cavity made in a positively charged sphere with uniform volume charge density The centres of sphere and cavity are displaced by a small distance 7 Force on charge qis A B C D do midt in the direction parallel to vector 7 in radial direction with respect to centre of cavity in a direction which depends on the magnitude of charge density in sphere direction cannot be determined

sing Thomson s model of the atom consider an atom consisting of two electrons each of charge e embedded in a sphere of charge 2e and radius R In equilibrium each electron is at distance d from the centre of the atom What is equilibrium separation between electrons P R 2 e d R d e R 3 palis D R 4

36 Eight charges having the values as shown in fig are arranged symmetrically on a circle of radium 0 1 m in air Potential at center O will be 7 C 15uC 7 C 1 252 1010v 3 252 106V 5 C 11uC 5 C 7 C 5 C 2 252 104V 4 zero

218 56 Two charges each equal to q are kept at x a and x a on the x axis A particle of mass m and charge qo q 2 is placed at the origin If charge qo is given a small displacement y a along the y axis the net force acting on the particle is proportional to JEE Main 2013 d 1 y a y b y c 1 y

A charge q is placed at rest on ve x axis at the point a 0 and another charge aq is placed at the point a a 0 Find a Coordinates x y of the point where the electric potential is zero b Nature of the equipotential surface through a general point x y in the plane c Components of forces Fx and Fy acting on an unit positive charge placed at some general point x y

9 Two identical positive charges are fixed on the y axis at equal distances from the origin U A negatively charged particle starts from negative x axis at a large distance from O moves along the x axis passes through O and moves far away from O Its acceleration a is taken as positive along its direction of motion The best graph between the particle s acceleration and its x coordinate is represented by A J a 0 B ta C a 11 D s 8

electric force experienced by any charge Ans 4 21 The electric field in a region is given by E ai bj Here a and b are constants Find the net flux passing through a square area of side L parallel to y z plane Ans aL A hollow spherical shell of radius r has a uniform charge density a It is

An infinite number of charges each of magnitude q are placed on x axis at distances of 1 2 4 8 meter from the origin respectively Find intensity of the electric field at origin Ans q 3RE towards origin

A clock face has negative charges q 2q 3q 12q fixed at the position of the corresponding numerals on the dial The clock hands do not disturb the net field due to the point charges At what time does the hour hand point in the direction of the electric field at the centre of the dial Ans 9 30

23 An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown The radius of the loop is a and distance of its centre from the wire is d d a If the loop applies a force F on the wire then a Fo d3 JEE Main 2019 9 Jan Shift 1 d b F 0 51

In a uniform electric field E a conductor in the form of a sphere is introduced How will the intensity of the field at points A B and C change A Field at A will increase B Field at B will decrease C Field at C will increase D Field at all points will remain same X Tox E uniform B 1 1 C

Examp 14 Consider the charges q q and q placed at the vertices of an equilateral triangle f each side 1 What is the force on each charge NCERT Solved Example Solution As is clear from Fig 1 a 16 force on g q at A FIQUD546 S

Ihree charges are placed at the vertices of an equilateral triangle of side 1 m as shown in fig An electron is placed at the centre of the triangle What is the magnitude of the net force on the election IC A 1 74 x 10 8 N C 8 6 x 10 9 N Im IC 18 B 4 3 x 10 9 N D Zero

Two free point charges 4e and e are placed a distance a apart Where should a third point charge q be placed between them such that the entire system may be in equilirbium What should be the magnitude and sign of q What type of a equilibrium will it be Suppose the charges are placed as shown in fig

In the basic CsCl crystal structure Cs and Cl ions an arranged in a bcc configuration as shown in the figur The net electrostatic force exerted by the eight Cs ion on the Cl ions is Cst Cst a b c 1 4e 4 o 3a 16e 4 o 3a 1 32e possono 1 Cst d zero CIT Cs Cst a Cst Cst Cs

Six point charges are kept at the hexagon of side L and centre O as shown in figure which of the following 1 q 4 co L statement s is are correct Given that K A 29 q S B q IIT JEE Multiple Correct Choice E 9 C q D 29 1 The electric field at O is 6K along OD 2 The potential at O is zero 3 The potential at all points on the line PR is same 4 The potential at all points on the line ST is same

Two point charges Q and 3Q are placed at some distance apart If the electric field at the location of Qis E then field at location of 3Q is 1 E E 3 3 3E 4 E 3

Four point charges each of charge 4 C are placed at the four corners of a square such that they are in equilibrium when a charge q is placed at its centre Find q

A solid sphere of radius R has charge q uniformly distributed over its volume The distance from its surface at which the potential is equal to half of the potential at the centre 1 R 2 2R 3 R 3 4 R 2 are of radius B and unifrom volume charge

5 Four charges each equal to Q are placed at the four corners of a square and a charge q is placed at the centre of the square If the system is in equilibrium then the value of q is 1 1 2 2 2 1 2 2 3 1 2 2 4 1 2 2

In section PQ of a circuit P is at higher potential than 9 by 40 V The potential difference in volt across the battery A is A 6 V C 2 V B D 4 V 8 V 592 A Pw 6V 202 852 w www B 12V 252

1 Faraday s laws are consequence of conservation of a energy b energy and magnetic field c charge d magnetic field 1991

A conducting sphere of radius r having charge Qo is connected to earth through an ideal inductor of inductance L and a switch S The switch S is closed at t 0 Find the charge on sphere and TW 4mcorL take Qo 10 C and TL 2 4 current through S at t Qo r L

42 A straight wire of a diameter 0 5 mm carrying a current of 1 A is replaced by another wire of 1 mm diameter carrying the same current The strength of the magnetic field far away is 1 One quarter of the earlier value 2 No change 3 Twice the earlier value 4 One half of the earlier value

Consider a sphere of radius R with charge density distributed as p r kr For r R 0 for r R a Find the electric field as all points r b Suppose the total charge on the sphere is 2e where e is the electron charge Where can two protons be embedded such that the force on each of them is zero Assume that the introduction of the proton does not alter the negative charge distribution

Fig 1 52 6 Find the magnitude and direction of electric field at point P in Fig 1 53 A 99 9 a B Ec a P EB EA q C

A non conducting rod of AB having uniformly distributed positive charge of linear charge density is kept in x y plane The rod AB is inclined at an angle 30 with positive y axis The magnitude of electrostatic field at origin due to rod AB is Eo N C and its direction is along line OC If line OC makes an angle 0 10a b degree where a and b are the positive integer less than 9 with negative x axis as shown in the figure calculate the value of a b OB 2m and 10 C m C y A 30d O B X

Two identical conducting spheres one having an initial charge Q and the other initially uncharged are brought into contact a What is the new charge on each sphere b While the spheres are in contact a positively charged rod is moved close to one sphere causing a redistribution of the charges on the two spheres so the charge on the sphere closest to the rod has a What is the charge on the other sphere

Two point charges q and 4q are separated by a distance of 6a Find the point on the line joining the two charges where the electric field is zero Ans At a distance 2a from charge 4

3 Find the magnitude of dipole moment of the following system 9 1 21 aq 3 4 ag 4q 60 60 a 5q 2 Zero 4 10 ag

Iwo short dipoles each of dipole moment p are placed at origin The dipole moment of one dipole is along x axis while that of other is along y axis The electric field at a point a 0 is given by 1 2p 1 4 a 3 3 3 1 1 5p 1 2 4 a 3 A Zor 2

If the electric field in a region varies according to yi xj Assuming the potential at the origin to be zero the potential at point 3m 4m is Et t 1 8 volt 3 12 volt 2 12 volt 4 10 volt 2 18 1

1 Two spheres have radii 10 cm 20 cm One of the sphere is given 150 C charge and connected by a wire Their common potential will be 1 9 x 106 volts 2 4 5 x 106 volts 4 1 35 x 10 volts 3 1 8 x 106 volts

The electrostatic potential existing in the space is given as V density in coulomb m at x 2m 3 x 680 2 volts Find the charge

3 N fundamental charges each of charge q are to be distributed as two point charges seperated by fixed distance then the maximum to minimum force bears a ratio N is even and greater than 2 2N N 4 N 1 N 1 1 N 1 4N 2 4N N 1 3 4

B 10 Find out electric field intensity due to uniformly charged solid non conducting sphere of volume charge density p and radius R at following points i At a distance r from surface of sphere inside 3 At a distance from the surface of sphere outside

Find the electric field at point O due to the segment of a ring whose linear charge density is 8 C cm XXX 1 9 x 1013 V m 3 8 x 1013 V m 4 cm 60 O 2 16 1013 V m 4 18 x 1013 V m

3 f and E are current density and electric field respectively inside a current carrying conductor then relation is Arn 4 11 1 j 1 3 j E 0 2 jxE 0 4 All of these

A charge Q is placed at each corner of a cube of side a The potential at the centre of the cube is 2008 M 1 8Q 40 2 40 3 Br a 4 20

Electric field inside a conducting sphere with distance from its centre E versus 1 r where E is electric field due to a point charge and r is the distance from the ch

In figure two points A and B are located in a region of electric field The potential differenc VB VA is 1 Positive 2 Negative 3 Zero 4 None of these e B

S and S are two conducting surfaces Between S and S and inside S is air S is spherical with A 2 its centre S has total charge Q S is uncharged Find if possible 2 i Charges induced on inner and outer surface of S ii Total electric field at A B 0 bes 0 iii Electric field at B due to induced charges on S iv Electric field at C due to induced charges on inner surface of S G A S B S v Electric field produced by induced charges on outer surface of S inside the body of S vi Can you find electric field at C easily take the required distances from A Which charge will produce electric field here

le 1 6 x A circular plane sheet of radius 10 cm is angle of 60 with the field Calculate electric flux through the sheet You are given a charge Q at the origin O Refer to Fig 1 90 Consider a sphere S with centre 2 0 0 of radius 2 m Consider another sphere of radius 2 m centered at the origin Consider the spherical caps i PSQ ii PRQ iii PWQ with normals outward to the respective spheres and iv the flat circle PTQ with normal along the x axis a b c What is the sign of electric flux through each of the surface i iv What is the relation between the raagnitudes of fluxes through surfaces i iv Calculate the flux through the surface ii directly Assume that the area of the cap ii is A NCERT y 1m S 0 0 0 0 P 1 6 IT 2 0 0 CLASS W

2 A parallel plate capacitor having plate area 20 cm and separation between the plates 1 00 mm is connected to a battery of 12 0 V The plates are pulled apart to increase the separation to 2 0 mm a Calculate the charge flown through the circuit during the process b How much energy is absorbed by the battery during the process c Calculate the stored energy in the electric field before and after the process d Using the expression for the force between the plates find the work done by the person pulling the plates apart e Show and justify that no heat is produced during this transfer of charge as the separation in

the same 1 A charge q is moved from A to B in the region of a fixed ideal dipole p Find the work don on the charge Assume gravity free space B

3 4 60 cm 14 An electric dipole having charges q and q are at a separation r At distance d ralong the axis of the dipa the field is proportional to 1 3 2 4 qr d qr 3

If a positive charge is shifted from a low potential region to a high potential region then the electric potential energy a increases c remains the same b decreases d may increase or decrease

Three charged particles their sign are shown move along the path in a uniform electric field as shown In each of three cases state whether the potential energy increases or decreases A B

C Both A and B The relative permitivity of vacuum is A 0 B 1 C 1 D 1 A B dx D Only A Attempt all questions 2 marks each Define electric potential energy and give its Sl unit Convert 1eV and 1keV into J

A point dipole is located at the origin in some orientation The electric field at the point 10 cm 10 cm on the x y plan is measured to have a magnitude 1 0 103 V m What wil be the magnitude of the electric field at the point 20 cm 20 cm a 5 0 10 4 V m b 2 5 10 4 V m c It will depend on the orientation of the dipole d 1 25 x 10 V m