Electric Field and Potential Questions and Answers

Two positive charges Q and Q are fixed at A and B A unit positive charge is taken from A to B along the line joining AB The force experienced by unit charge Decreases continuously Increases continuously Increases first and then decreases Decreases first and then increases

A dipole with dipole moment 3 x 10 9 C m is placed in external uniform field of E 4 x 105 N C 1 Calculate amount of work done by field in rotating the dipole from 0 60 to 0 0 is angle between electric field E and dipole moment vector NCERT Pg 66 1 200 J 2 600 J

9 An uncharged solid spherical conductor of radius R centered at origin has a cavity of some arbitrary shape is formed as shown in the figure Somewhere within the cavity charge q lies as shown A A kq The field at P outside the sphere due to induced charge on the outer surface of sphere is k r T r T2 3 B kq 3 B kq q 1 1 T T 10 The potential at point P due to induced charges is 1 H 1 12 P T T C kq C kq 1 4 4 2 12 1 Space for Rough Work D D kq kq ri r T r

The plot given LRC circuit versus frequency The quality factor of the circuit is I amp 1 0 7 4 6 8 kHz f

An infinitely long uniform charge distribution of charge per unit length lies parallel to the 3 y axis in the y z plane at z a If the 2 magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x y plane with its centre at the origin is L then the value of n is ne A B L 3 2 a S

Two charges are located on the x axis q 6 5 C at x 4 7 cm and q2 6 5 C at x2 4 7 cm Two other charges are located on the y axis q3 4 4 C at y3 4 2 cm and q4 11uC at y4 6 5 cm Find a the magnitude and b the direction of the net electric field at the origin a Number i 1e12 Units N C

A particle of mass m and charge q is moving around a 4 fixed charge q in a circle of radius r under electrostatic and force of attraction The total energy of system is 1 2 8 3 q 4TEO q q STED 4 Zero fre after fra en qu 1 2 8 3 4 r fac d q 4TE OF q 8E

0 19 10 A thin spherical conducting shell of radius 2R has charge q Another charge 2g is placed at the centre of the shell The electrostatic potential at point Pat distance from the centre of the shell is 5q 82 R 3q 82 R 9q 82 R 3q 4R Solution Answer 3 Hint V O 48 R P 9 R2

3 Given a uniform electric field E 2 x 10 NC find the flux of this field through a square of side 20 cm whose plane is parallel to the YZ plane What would be the flux through the same square if the plane makes an angle of 30 with the X axis Foreign 2014

Consider a uniformly charged solid cube of side a and volume charge density p The centre of cube 1 41E0 O and one of vertex is A The potential at one of the vertex is given by cx p ay Where c is dimensionless constant Select correct alternatives A x 1 B y 2 D M 1 2

3 A battery maintains the electrical potential difference of 60N BE arallel metal plates separated by 10 mm What is the strength of the A 8 0 V m B 600 V m C 6000 V m

shell with inner ing sph A small conc radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d as shown The charge 2q and the inner shell has total outer shell has charge 4q Calculate the electric field in terms of q and the distance r from the common centre of the two shells for i r a ii a r b iii b r e is x times of 1 q 2 4 Find x r d

36 180 The distance of closest approach of an a particle fired towards a nucleus with momentum Pis ro If momentum of a particle is 2p the corresponding distance of closest approach is To

A charge q is placed along a line segment joining two charges Q and 4Q The system of the three charges will be in equilibrium if q is equal to A Q 2 B Q 4 C 2Q 9 D 4 Q 9 Calculate the electrostatic potential energy for the system in problem 1 if the distance between Q and 4Q is R A Q 4 R B Q 16 ER C Q 36 ER D Zero

13 A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V A hole with a small area a4R a 1 is made on the shell without affecting the rest of JEE Adv 2019 Paper 1 the shell Which one of the following statements is correct A The potential at the center of the shell is reduced by 2aV Vo B The magnitude of electric field at the center of the shell is reduced by 2R C The magnitude of electric field at a point located on a line passing through the hole and shell s center av on a distance 2R from the center of the spherical shell will be reduced by D The ratio of the potential at the center of the shell to that of the point at R from center towards the 1 1 20 hole will be 2R One or More Option s Correct Type Questions

There are two current carrying planar coils made each from identical wires of length L C is circular radius R and C is square side a They are so constructed that they have same frequencies of oscillation when they are placed in the same uniform magnetic field B and carry the same current I The relation between a and R is 1 a 2R 3 3a R 2 a 3R 4 a 4R

17 An oil drop carrying charge of 2 electrons has mass 3 2 10 kg It falls freely in air with terminal velocity The electric field required to make drop move upwards with same speed is 4 x 10 V m 3 x 10 V m O 2 x 10 V m 8 x 10 V m

28 An uncharged conducting ball is suspended by a thread A charged conducting ball is brought very close to it The uncharged conducting ball will A Not be attracted or repelled B Will be attracted C Will be repelled D Will initially be attracted and after touching the charged ball it will be repelled MIDADH D C 5

A long straight metal rod has a radius of 4 60 cm and a charge per unit length of 21 0 nC m Find the electric field at the following distances from the axis of the rod where distances are measured perpendicular to the rod s axis a 3 40 cm magnitude direction Select b 16 0 cm magnitude direction Select c 160 cm magnitude direction Select N C V N C V N C

2 A particle of mass 2 gm and charge 1 C is held at a distance of 1m from a fixed charge of 1 mC If the particle is released it will be repelled The speed of the particle when it is at a distance of 10m from the fixed charge is 1 100 m s 2 90 m s 3 60 m s 4 45 m s

an electron with an initial velocity of 3 2 x 106 m s is projected into a uniform electric field in the direction of the field If at the time of being at rest to travel 2 3 cm what should be the electric field in what displacement

A Q 87 R B 167 R 3Q 167 R D 3Q 32 R 17 A uniform rod of length 2L is carrying a linear charge density and is placed along the X axis between x L and x L Calculate the potential at point P 0 y Calculate the electric field at P 18 Two rings of radii R and 2R are carrying equal linear charge density and are placed co axially with their centres

Two charges of equal magnitude q are placed in air at a distance of 2a apart and third charge 2q is placed at mid point The potential energy of the system is q 8 39 8 5q 8

x L Calculate the potential at point P 0 y Calculate the electric field at P 8 Two rings of radii R and 2R are carrying equal linear charge density and are placed co axially with their centres at a separation R Find the position of the points where the electric field is zero use a graphical solution if necessary Is this a stable equilibrium position for a charged particle placed at this point Discuss the nature of the equilibrium 9 A semicircular ring of radius R is carrying a charge a uniformly distributed over its length Calculate the magnitude

Two charges of magnitude 5 nC and 2 nC are placed at points 2 cm 0 0 and x cm 0 0 in the region of space There is no external field If electrostatic potential energy of the system is 0 5 J The value of x is 10 20 30 40

A thick spherical shell with inner radius 2R and outer radius 4R has uniform charge density p The shell also has a spherical cavity of radius R centered at B see figure Select the correct statement s 1 E PR 980 PR R B 4R 2R A 1 2 E 4 F 16pR 27 19pR I

5 For point charges q and q separated by a distance 2a the field on their equatorial plane at a distance r from their mid point is a c 2qa 4TE p b 2qap 47 r 213 2 d 2qap 4 r 2ga 2 2 3 2 D

Consider a non spherical conductor shown in the figure which is given a certain amount of positive charge The charge distributes itself on the surface such that the charge densities are 0 o and at the regions 1 2 and 3 respectively Then 3 1 3 1 0 0 03 3 03 0 0 Which of the following 2 0 03 0 4 0 0 03 is true

44 180 Two charges of equal magnitude q are placed in air at a distance of 2a apart and third charge 2q is placed at mid point The potential energy of the system is q 8 3q 2 88a Mark for Review 5q 8

108 Two concentric conducting spheres having rad a and b are charged to q and 92 respectively The potential difference between 1 and 2 will b 92 91 a 4ne 4ne b b c 4TE b b 91 41 0 2 b d none of these

2 radius TL Figure shows a neutral metal ball of mass 50 kg and m placed on an insulating horizontal surface An upward electric field of strength 5 10 N C exists in the space A stream of light ions is switched on at 0 The ions are incident on the ball from left side at a speed 2 10 m s The charge density of ion beam is 5 10 2 C m All charges incident on the ball are absorbed Friction is large enough to prevent any horizontal movement of the ball Neglect any effect of the electric field on the ion beam The time in second at which ball will rise up from the surface is 12 a 25 R E b 15

The charge density on the surface of a conducting sphere is 64 10 7 C m and the electric intensity at a distance of 2 m from the centre of the sphere is 4T X 104 N C The radius of the sphere is A YOU B 0 83 m 0 4 m c 0 6 m

A solid conducting sphere of radius 10 cm is enclosed inside a thin metallic shell of radius 20 cm A charge of 1 C is given to inner sphere How much heat is generated in process when inner sphere is connected to shell by a conducting wire 22 5 mJ 2 25 J 9 0 mJ

An oil drop has a charge 9 6 x 10 C and has a mass 1 6 x 10 5 g When allowed to fall between horizontal plate of uncharged parallel plate capacitor due to air resistance force it attains a constant velocity Then if a uniform electric field is to be applied vertically to make the oil drop ascend up with the same constant speed which of the following are correct g 10 m s Assume that magnitude of air resistance force is same in both cases A The electric field must be directed upward B The electric field must be directed downward C Intensity of the electric field must be 100 3 N C D Intensity of the electric field must be 100000 6 N C

16 180 Mark for Review 02 57 hr min Figure shown are imaginary cube of side a A uniformly 3a charged rod of length moves towards right at uniform 2 speed of v At t 0 the right end of the rod first touches lef face of the cube The correct plot of graph between electric flux through cub versus time is 2

A ring with uniform distribution of charge q and radius a is placed in Y Z plane with its centre at origin The electric field at origin is Potential at origin is 9 4 9 4 a The electric field at x 0 0 is 9 4 80x The electric field at point x 0 0 is 9 4 o a x

between them is X 10 m 7 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 The intensity of the electric field at origin is 9 1 3 Eo 2 9 6TE 3 9 2TE q 4 ATE

The electric potential at a region varies with position as V x y z x y z A positive charged particl placed in this region will A experience a force towards the origin B experience a force away from the origin C remain in equilibrium at the origin D experience maximum force at the origin

Two charged spheres are kept at a finite centre to centre spacing as shown in the figure The force of electrostatic interaction between them is first calculated assuming them point like charges at their respective centres and then force is measured experimentally If the calculated and the measured values are F and Fm respectively which of the following conclusion can you certainly draw A If Fc Fm for like charges and Fc Fm for unlike charges both the spheres must be made of insulating materials B If Fc Fm for like charges and Fc Fm for unlike charges both the spheres must be made of conducting materials C Irrespective of their materials Fc Fm for like charges and Fc Fm for unlike chares D Irrespective of their materials Fc Fm for like charges and F Fm for unlike charges

720 N 240 N point charges 16 nC and 8 nC are situated at the corners B and C of an equilateral triangle of side 0 03 m Find the magnitude and direction of the resultant electric field at the vertex A of the triangle 21 2 104 NC 140 532 ncl Two nith halls of

2 5 Figure represents a square carrying charges 9 9 9 q at its four corners as shown Then the potential will be zero at points inucins q q A t 1 I 1 B C 9 1ST 1 8 9 111 Q 1 A B C P and Q 2 A B and C 3 A PC and Q 4 PBand O

Polar molecules are the molecules 1 2 3 A acquire a dipole moment only when magnetic field is absent having a permanent electric dipole moment having zero dipole moment acquire a dipole moment only in the presence of electric field due to displacement of charges

1 a An electric field E E X i uniformly increases in magnitude but has a constant direction The uniform rate of increase of the field is a volt m A dipole of dipole moment p makes an angle 0 with the x axis What is the force experienced by the dipole

Assume that an electric field E 30x iN Cexists in a space Then the potential difference V V between the point A 1 m 0 m and B 0 m 1 m is 20 V 10 V 20 V 10 V

The volume charge density of a solid sphere varies with distance r from its centre as p Por where po and R are positive constants The electric R field at a distance r from the centre of the sphere and inside the sphere is O O Por2 4 R Por 38 Br 3 R

A point charge Q is placed at the centroid of an equilateral triangle When a second charge Q is placed at a vertex of the triangle the magnitude of the electrostatic force on the central charge is 0 1 N The magnitude of the net force on the central charge when a third charge Q is placed at another vertex of the triangle is a zero c 0 12 N b 0 2 N d 0 1 N

Two charges q and q2 are placed 30 cm apart as shown in the figure A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D The change in the potential energy of the system is AIPMT Prelims 2005 93 k where k is 4 EO 1 892 2 89 3 692 93 Co 40 cm 92 9 1 A 30 cm B D

2 Two identical positive charges are fixed on y axis from origin O A particle with a equidistant negative charge starts on the negative x axis at a large distance from O and moves along the positive x axis passes through O and moves far away from is taken as positive along O Its acceleration a its direction of motion The particle s acceleration a is plotted against its x coordinate Which of the following best represents the plot a b c O d

3 If atmospheric electric field is approximately 150 volt m and radius of the earth is 6400 km then the total charge on the earth s surface is 1 6 8 x 105 coulomb 2 6 8 x 106 coulomb 3 6 8 x 104 coulomb 4 6 8 x 10 coulomb

Six charges are placed at the corner of a regular hexagon as shown If an electron is placed at its centre O force on it will be a Zero b Along OF c Along OC d None of these 24 E 9 39 29 D