Electric Field and Potential Questions and Answers

Gauss s law is valid only for uniform charge distribution Gauss s law is valid only for charge place in vacuum The electric field calculated by Gauss s law is the field due to all the charges The flux of electric field through a closed surface due to all the charges is equal to the flux due to the charges enclosed by the surface

Two particles A and B each carrying a charge Q are held fixed with a separation d between them A particle C having mass m and charge q is kept at the middle point of the line AB Assuming x d show that this force is proportional to x

5 On the X axis and at a distance x from the origin the gravitational field due to a mass distribution is given by Ax in the x a 2 x direction The magnitude of gravitational potential on the X axis at a distance x taking its value to be zero at infinity is JEE Main 2020 4 Sep Shift l b A x a 2 d A x a a c A x a A x a 2

A hollow sphere having uniform charge density p charge per unit volume is shown in figure If b 2a remans Se and potential difference between A and B is n o pa Then find the value of n condurre doubt A B

Two charges q m and q m are connected a massless rod of length and released in a region of uniform electric field as shown 1 21 60 q Find the maximum speed of the charges qEl 2m 3qEl q EI E 2 3qlE 2m aEl

Three charges are placed along x axis at x a x 0 and x a as shown in the figure The potential energy of the system is 9 9 1 3 x a 1 4TEO 1 4TE q a q a 9 10 x 0 x a 1 2 A EO 4 1 4 3q 2a 3q 2

Assertion Consider a current carrying wire whose cross sectional area decreases gradually along the direction of current as shown in figure As one goes from cross section A to cross section B the drift speed of electrons increases B AL Reason Electric field intensity at any cross ection in a current carrying wire is inversely roportional to its cross sectional area 101

Three point charges 0 5 C 0 25 C and 0 1 C are placed at the vertices A B and C of an equilateral triangle ABC The length of the side of triangles is 5 0 cm Calculate the resultant force acting on the charge placed at point C k 9 x 10 SI

Two particles X and Y are 4m apart X has a charge of Q and Y has a charge of 2 Q The force of X on Y O has the same magnitude as the force of Y on X has four times the magnitude of the force of Y on X O has twice the magnitude of the force of Y on X O has half the magnitude of the force of Y on X O has one fourth the magnitude of the force of Y on X

Two metal plates having a potential difference of 800 V are 2 cm apart It is found that a particle of mass 1 96 10 15 kg remain suspended in the region between the plates The charge on the particle will be e elementary charge Question Type Single Correct Type 1 3e 2 4e 3 6e

If the electric potential on the axis of an electric dipole at a distance r from it is V then the potential at a point on its equatorial line at the same distance away from it will be 1 2 V 3 O 2 4 N 2 V 8

4 Two point charges q 2 C and q2 4 C are placed in the xy plane at the points P and P2 whose position coordinates are 0 0 and 0 3 respectively i Find the electric potential at A 2 0 and B 0 2 due to the two point charges ii Find the potential difference between the points A and B iii How much energy need to be expanded to bring a third charge q3 3 C from infinity to the point B Use Eo 8 85 x 10 12 F m

34 The effective resistance between points P and Q of the electrical circuit shown in figure 2R 2R ww ww 2Rr R r Po www 2R ww wwwww 2R 2R 2 ww 2R ww 8R R r 3R R 5R 4 2r 2R 3 2r 4R 35 In the following circuit find current delivered by 10 V battery 292 20 V

A cone made of an insulating material has a total charge Q spread uniformly over its sloping surface Calculate the energy required to bring a small test charge q from infinity to the apex A of the cone The cone has a slope length L

O A metal ribbon of some thickness has width and area of cross section A It is placed in a magnetic field B directed normal to the ribbon If there are N conduction electrons per unit volume of the metal and current I flows through then there will be A zero potential difference across the width B potential difference given by IB NeA C the statement is incomplete D potential difference is given by across the width 2 IB NeA across the width

Three identical metallic plates A B and C are initially given charges Q 4Q and 2Q respectively Now the plates A and C are connected by a conducting wire and plate B is earthed then choose the incorrect option to A B C d 2d 1 Charge on the inner surface of plate A is 2Q 2 Charge on the inner surface of plate C is zero 3 Charge flown through the connecting wire from plate C to A is Q

A charge Q is uniformly distributed in a dielectric sphere of radius R having dielectric constant unity This dielectric sphere is enclosed by a concentric spherical shell of radius 2R and having uniformly distributed charge 2Q Which of the following graph correctly represents variation of electric field with distance r from the common centre A EA R 2R E M B R 2R 2Q 2R 39

19 There are four concentric shells A B C D of radii a 2a 3a and 4a respectively Shells B and D are given charges q and q respectively Shell C is now earthed The potential difference VA Vc is 1 3 kq 12a kq 4a 2 4 kq 3a kq 6a k 1 4 EO

33 A point charge Q is placed inside a conducting spherical shell of inner radius 3R and outer radius 5R at a distance R from the centre of the shell The electric potential at the centre of the shell will be 1 3 10 4 R 1 13Q ATS 15R 2 4 1 50 5Q 4 E 6R 1 70

2 A potential difference of V volts is applied on two parallel electrodes separated by a distance of 4 0 10 m The electrons of very low energy are injected into the region between the electrodes which contains argon at low pressure The average distance the electrons travel between collisions with argon atoms is 8 10 m The ionization energy of argon atom is 16 eV Estimate the minimum value of V in kV such that the electrons will cause ionization in argon atomo hu 11

a QFour charge particles each having charge Q 1 c are fixed at the corners of the base A B C and D of a square pyramid with slant length a AP BP BP PC a 2m charge Q is fixed at point P A dipole with dipole moment p 1 Cm is placed at the center of the base and perpendicular to its plane as shown in figure Force on the dipole due to the charge X particles is N Find x 4 EO A r r r C

i Two identical small non conducting balls are charged t rubbing against each other They are suspended from ceilin rod through two strings of length L 20 cm each The separatic between the suspension points being d 5 cm In equilibriu the separation between the balls is r 3 cm Find the mass m each ball and the tension in the strings The charge on each ba has magnitude 2 10 8 C 7 96g 7 72 x 10 2 N

As shown in the fig charges q and q are placed at the vertices B and C of an isosceles triangle The potential at the vertex A is A q a 1 1 4 EO 1 q 3 4 o b 2 EO a 2q 2 2 a b b C q 2 zero 1 4 4 EO q b 2 2 a

Two small spheres each carrying a charge q are placed r metre apart and they interact with a force F If one of the spheres is taken around the other once in a circular path the work done will be A B C F r F 2 r F 2 r My Answer

5 Neutral metal sphere of radius R is connected to earth through a switch S which is initially open Two charges 3Q and 2Q are kept at 9R and 3R distances from the centre of the sphere as shown When switch is closed the charge flown from the sphere to the earth is S A Q 2 C 0 3R 9R 2Q D B Q 3Q 20

Question 20 1 point Two charged objects with mass are 1m apart if we increase the mass by 2x then a Gravitational Force between the 2 objects increases by 2x and the Electrostatic Force between them increasees by 2x Ob Gravitational Force between the 2 objects increases by 4x and the Electrostatic Force between them increases by 4x c Gravitational Force between the objects increases by 2x but Electrostatic force is not affected d Electrostatic Force between the objects increases by 2x but the Gravity Force is not affected

A piece of wool is rubbed against a PVC strip What will be the charge on the strip if approximately 2 x 10 2 electrons are transferred from the wool to the PVC strip gold pin Given Molar mass

Your friend is negatively charged and walks up and touches you to give you a shock What type of charging did you receive Positively charged by induction Negatively charged by conduction Positively charged by conduction Negatively charged by induction

A long wire placed along z axis has linear charge density X for z 0 and o for z 0 If magnitude of electric field intensity at a point 5 2 5 2 in x y plane is 2 N TEO then find the value of N 4 Answer 00 01 02 03 04 05 06 07 8

1 In a rectangular coordinate system a charge of 25 x 10 C is placed at the origin coordinates and a charge of 25 x 10 C is placed at a point x 6 cm y 0 What is t electric field at a x 3m y 0m b x 3m y 4m

1 An infinitely long tube of semicircular cross section is given some electric charge One half of the tube is given a surface charge density o and the other half of o If lol 2neo coul m find the magnitude of electric field at point O on the axis The point 0 is some where near the centre on the axial line in volt m Given R 0 25 m O 6 R D

A point charge of 5 C is located at 3 4 0 while line y 1 z 1 carries uniform linear charge density of 2 nC m use 1 48 9x10 Sl unit Magnitude of force experienced by 5 C charge is 510 N Magnitude of force experienced by 5 C charge is 18 10 N Electric field by line charge only at origin 0 0 0 0 is 18 k N C Electric field by the line charge only at origin 0 0 0 0 is 9 k N C

Plane x 2y 10 carries uniform surface charge 3 density nC m Resulting electric field at a A point near to the plane makes an angle 0 with X Find the value of A Here A JA B and Bare integers in their simplest form axis and sin Answer 00 01 02 03 04 05 06 07

Three point charges are kept at points 4 0 4a 0 0 0 and B 0 4a as shown in the figure A 0 4a 15Q 5Q O 0 4a B 3Q P 3a 0 X Work was done on the external agent who assembled these charges in moving them from infinity to the point

Four charges of 2q q q and 2q are at the corners of a square ABCD of side 20cm find the magnitude and the direction of the electric field at the centre of the square Take q 5 C Page 4 of 6

37 On the x axis and a distance x from the origin th gravitational field due to a mass distribution is given b Ax x 1 2 2 a in the x direction The magnitude of gravitation potential on the x axis at a distance x taking its value to be zer at infinity is 4 Sept 2020 Morning A 1 2 x a C A x a 2 A A x a 2 D A x a 1 2 B

Electric field at any point P x y z in space is given by Exi where Eo is a positive constant and all physical quantities are given in S I units Select the correct statements out of the following Potential at points on y axis must be zero Potential difference between any two points along z axis must be zero Potential changes linearly with positive along x axis A cubical volume of edge 1 m with one of the edges along x axis placed in this electric field encloses a charge of E coulomb

35 Charges are given to three large parallel plates as shown in figure Now the switch S is closed The value of electric field between the plates 2 and 3 is each plate has surface of Area A 10 C 30 C 1 A ED 20 C 3 A EO 2 20 C 3 30 C S 25 C 2 A EO 4 zero of n sides each corner

Two horizontal parallel long wires each carrying charge of linear charge density Ao are placed at distance 2d In the symmetry plane of this system located between the wires a charge particle q m is held in equilibrium n 3d g Find value of 12 Minimum value of m is

An infinitely long thin non conducting wire is parallel to the z axis and carries a uniform line charge density It pierces a thin non conducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120 at the centre o of the spherical shell as shown in the figure 1 P Z R 120 O The permittivity of free space is eo Which of the following statements is are true a The electric flux through the shell is 3R E0 b The z component of the electric field is zero at all the points on the surface of the shell c The electric flux through the shell is ZRA E d The electric field is normal to the surface of the shell at all points 2018

2 One end of an insulating rigid rod of negligible mass and length pivoted to a fixed point O A small ball of mass m having a negat charge of modulus q is attached to the lower end of the rod Anot small ball carrying a positive charge Q is fixed at a height h above point O as shown in the figure What should the range of values of m m of the lower ball be so that the rod remains in a state of sta Qqh equilibrium Acceleration due to gravity is g my 47 E 9 h l

EA and dB and t these correct 97 1 Four charges of maghl the vertices of a square of side length a with origin O at centroid Find the electrostatic potential at point P given OP r r a qa 41 ED r O O 45 2 qa 2 0 r

0 Three objects are brought close to each other two at a time When objects A and B are brought together they attract When B and C are brought together they repel From this we conclude that 1 Objects A and B possess charge of same sign 2 Objects A and C possess charges of opposite sign 3 All three of the objects possess charges of the same sign 4 Either A and Care of opposite signs or A may

A spherical conductor having a charge of 100 C is brought near another metallic sphere of mass 36kg resting on earth s surface What minimum distance of separation should be maintained so as to lift up the metallic sphere with uniform Separati speed What happens if the separation is more or less than the calculated value

1 The electric dipole potential falls off at large distance as 1 r 2 The electric potential due to dipole in the equatorial position is zero 3 The electric potential due to dipole has axial symmetry about dipole moment vector P 4 Electric potential on dipole axis is

A stationary tuning fork is in resonance with an air column in a pipe If the tuning fork is moved with a speed of 2 ms 1 in front of the open end of the pipe and parallel to it the length of the pipe should be changed for the resonance to occur with the moving tuning fork If the speed of sound in air is 320 ms the smallest value of the percentage change required in the length of the pipe is

Three identical charged particles are suspended E three insulated threads of equal length I from a po on ceiling If the strings make angle with vertica equilibrium then find the specific charge on the particles 72

41 A charge q moves from points A 0 1 E C cted then as shown in figure If Ip Ip l then work done by electric force in moving charge q from A to B in the vicinity of two short dipoles placed at the origin with their dipole moments as shown will be 1 Positive 2 Negative 3 Zero A P P B of radius R is charged to Int a distance r R nt be determined

Two parallel large thin metal sheets have equal surface charge densities o 26 4 x 10 12 C m of opposite signs The electric field between these sheets is 1 1 5 N C 3 3 N C 2 1 5 x 10 10 N C 4 3 x 10 10 N C

Problem 223 Two small metal balls of mass m 0 1 g are suspended at the same point by insulating threads of length 30 cm One of the balls is loaded with twice as much electric charge as the other Pushing the balls towards each other by insulating materials we move them to a position where both threads make an angle of a 20 with the vertical and the threads remain in a common vertical plane After releasing the two balls from this position at the same time the angle between the two ds reaches the largest value of 3 84 Determine the charge of the balls a m 2Q