Electric Field and Potential Questions and Answers

19 A small ball of mass m and charge q tied with a string of length is rotating in a vertical circle under gravity and a uniform horizontal electric field E as shown The tension in the string will be minimum for A 0 tan qE mg B 0 SP m E q C 0 tan 1qE mg D 0 tan qE mg

ES0016 7 20 C charge is placed inside a closed surface then flux related to surface is p If 80 C charge is added inside the surface then change in flux is given by ap Fill the value of a

Charge is uniformly distributed on the curved surface of hemisphere Potential at P Q and T is V V and V respectively A V V 2V R 2R LO B 0 V V V R T V V R P C V V V X D V V V

Two identical pendulums A and B are suspended from the one point The bobs A and B are given positive charges Q and Q respectively If mass of A and B are m and m m m and angles from vertical of A and B are 0 and 02 respectively 1 0 0 2 0 0 3 0 0 4 0 0

An electric dipole is placed close to a plastic block as shown a 5 points Draw the charge polarization on the plastic block due to the electric dipole 5 points Explain your answer b 5 points Which of the arrows a j best indicates the direction of the net electric plastic block and electric dipole field at location B Plastic block q q B b d i zero magnitude

Two positrons et and two protons p are kept on four corners of a square of side a as shown in figure The mass of proton is much larger than the mass of positron Let q denote the charge on the proton as well as the positron then the kinetic energies of one of the positrons and one of the protons respectively after a very long time will be 1 1 A 47 2 2 4 22 1 1 4 a 2 24T q B 2 Eo a 4 2 a q C 4 a 4 E a q D 2 Eo al 2 1 q a 1 4 2 8 2 a et P

Alpha particle is revolving around an infinitely long line charge of linear charge density at perpendicular distance r from it The centripetal force on the particle is 1 e 2 or e 3 4TET 2 4 e Teor e 2 TTS r

Wire is cut off Find the electric field at the centre due to the remaining wire Three point charges q 2q and q are located along the x axis as shown in figure Show that the electric field at P a along the y axis is 1 3qa 4 P y

A particle of mass m and charge q moves diametrically through a uniformly charged sphere of radius R with total charge 92 If 9 SHM then its time period is performs 1 2 3 2 4TE MR 9192 9192 4TE MR 2 4 2 2 4TE MR 9192 28 mR 0 0

A deuteron and an a particle are placed in an electric field The force acting on them are F and F and their accelerations are a and a respectively then 1 F F 3 a a 2 F F 4 a a

viii When the distance between two equal charges is decreased to half and their magnitude of charge also decreased to half the force between them a Remains unchanged c becomes double b Reduces to half d becomes four times

4 1 A primitive model for an atom consists of a point nucleus q surrounded by a uniformly charged spherical cloud q of radius a Fig 4 1 Calculate the atomic polarizability of such an atom q 9 FIGURE 4 1 E d 9 FIGURE 4 2

48 A uniformly charged rod of length 4 cm and line shown charge density 30 C m is placed as figure Calculate the x component of electric fi at point P 4cm 1 36 x 105 N C 3 1 8 10 N C P 13cm 00 00 2 9 105 N C 4 27 x 105 N C

Four particles A B C and D of masses mA MB mc and mp respectively follow the paths shown in the figure in a uniform magnetic field Each particle moving with same speed QA QB Qc and Qo are the specific charge of particles A B C and D respectively assume that the motion of each particle is in the same plane perpendicular to the magnetic field A QA QB Qc Qo B QD QB Qc QA C charge on the particle B and particle D is of same nature D Work done by magnetic force on the particle C is minimum as compared to other particle x X X X X X X x X 2R X X X R X Xxx X x xx x B XX A B 00 XX C X R X X X Dx XX X X X X X X x XX x X X X X X X X

55 A cylindrical region of radius R is filled with a uniform magnetic field B as shown in the figure A metal wire AB of length L is placed inside the field such that its ends are symmetrically located with respect to the centre 0 of the circular cross section of the region If the magnetic dB field is changed at a rate the emf induced in the metal dt wire is Find change in value of if the wire is displaced by a small distance AL parallel to its own length Assume that the wire remains inside the field region K X X X X X X X X X X X XDX X X X X X X X X X X X X X O x X X X X X X X X X X X X X X X X X X X X X X XmX X X X X X

An electric dipole has fixed dipole moment P 3i j Cm It is subjected to an electric field E 2i 2 3j V m the magnitude of net torque experienced by dipole is Options O 4 Nm O 8 Nm O 6 Nm o 12 Nm

solid conducting sphere having a charge Q is surrounded by an uncharged conducting hollow e shell is now connected to earth then which of the following statements will be correct A Potential difference between solid sphere and shell will decrease upon earthing the shell B Potential difference between solid sphere and shell will not change upon earthing the shell C Outer shell will not acquire any charge upon earthing D Outer shell will acquire negative charge upon earthing Options O A D

There are 27 drops of a conducting fluid Each has a radius r and they are charged to a potential Vo These are combined to form a bigger drop Its potential will be Question Type Single Correct Type 1 Vo

Initially sphere A has charge of 50e and sphere B has a charge of 20e The spheres are made of conducting material and are identical in size If the spheres touch each other what is the resulting charge on sphere A a 15e c 30e 30e 15e AMU Med b d

If the potential at infinity is assumed to be zero then the electric potential at points A and B due to a point charge is 40 V and 35 V respectively If on changing the potential at infinity VA becomes 45 V then VA VB 5 V VA VB 10 V VA VB 5 V

Find electric field intensity at the centre of the square unit positive charge is pla ce and the corners have 1 coulomb 1 coulomb 1 coulomb 1 coulomb respe ctively the length of the square is 4 m etre

The work done in moving a charge of 1 C on the surface of a conducting sphere from one point to the diametrically opposite point is Assume charge on shell 4 mC and radius of shell 4 m 9 J 9 J Zero

The electric fields of two plane electromagnetic plane waves in vacuum are given by E E cos wt kx and E Ekcos wt ky At t 0 a particle of charge q is at origin with a velocity V 0 8c c is the speed of light in vaccum The instantaneous force experienced by the particle is

A spherical cloud of charged particles of radius Ro 1 km produces a known electric field intensity inside the cloud R Ro given as E R R N C Calculate the a total charge in the cloud b the charge density in the cloud

A metallic block has no potential difference applied across it then the mean velocity of free electrons is T absolute temperature of the block Choose only 1 answer A Proportional to T B C Proportional to T Zero

the dial A charge 109 C is located at the origin in free space another charge Q at 2 0 0 If the X component of the electric field at 3 1 1 is zero calculate the value of Q Is the Y component zero at 3 1 1 A circular wire loop of radius R carries a total charge q distributed uniformly over its length A small length x R of the wire is cut off Find the electric field at the centre due to the remaining wire

A cavity of radius A is taken out from a uniformly charged solid sphere with charge density p and radius 2R as shown Consider four points 1 2 3 4 at following positions 1 2R 0 0 2 R 0 0 3 0 0 0 4 3R 0 0 E1 E2 E3 E4 represents magnitude of net electric field at 1 2 3 4 respectively then the correct options s are 3 2 1 4 2R X

A ring of radius rhas given a charge Q and uniformly distributed over its length If a charge q is placed at the centre The electric potential energy of the charge q will be kqQ r kqQ r

Three charges q q and q are placed at th vertices of an equilateral triangle as shown in figure The net electric field at centroid of triangle is 9 1 3 1 q 4 o A 1 4q 2 q a a a q 1 29 2 4 1 6q

Q 14 Two infinite planes each with uniform surface charge density o are kept in such a way that the angle between them is 30 The electric field in the region shown between them is given by a 80 0 c 280 30 2015 12 a 1 3 y 3 y 2015 2 1 3 y b 280 10 O d 280 2 2 JEE Main 7th Jan 2020 Shift I Q

In the figure shown below the conducting shell A having radius R is given charge Qinitially The shell A is connected to shell B of radius 2R via switch S and a conducting wire The switch S is closed att 0 then charge density on the shell B is Assuming separation between A and B is very very large R A ANSWER S Show options B 2R

Each of the following figures shows electric field vectors at two points A and B in an electric field In which figure or figures can the illustrated field be created by a single point charge a A B c B A b A B d B A

Three charges and q are placed at the 2 corner of an equilateral triangle of side a as shown in the figure The net electric dipole moment of the system will be 9 q 2 a 3 qa 2 3 qa qa 2 a a q 2

a State the aspects in which a ring distribution system outperforms than the radial systems b Justify that the minimum potential is at the mid point for a uniformly loaded DC distributor fed with equal voltages

The figure shows three large parallel sheets carrying uniform charge densities of a1 5 00 nC m 02 10 0 nC m and 03 5 00 nC Which of the following statements is true regarding the electric field at points A B and C 1 The magnitude of the field is highest at point A 2 The field vanishes E 0 at point B 3 The field points upwards at point A 4 The field at point C can be made larger in magnitude when the sheets become closer to each other 3 and 4 sodd 01 0 0 Activate Wi

Two cells of equal e m f E but of different internal resistances r and r are connected in parallel and the combination is conneted with an external resistance R to obtain maximum power in R Find the value of R What is the largest voltage you can safely annly across a resistor marked 1960 1 57 922 Mi 77 472 E r l E r 6 W R

An electric dipole is placed at the centre of a sphere Mark the correct options 1 The electric field is zero at every point of the sphere 2 The flux of the electric field through the sphere is non zero 3 The electric field is zero on a circle on the sphere 4 The electric field is not zero anywhere on the sphere

A dipole is placed in uniform electric field such 36 that potential energy of dipole is minimum U The work done by external agent in rotating a dipole by 180 is 1 U 3 2U 2 2U 4 U AF

The potential at a point in space due to a surrounding charge distribution is V x y Z V then the electric field at point 1 2 3 is 21 4 6k V m 21 4 6k V m 1 2 3k V m 1 2 3k V m

Q4 Two small spheres each having the charge Q are suspended by insulating threads of length L from a hook This arrangement is taken in space where there is no gravitational effect then the angle between the two thread and the tension in each will be Choose the answer O 180 O O O 90 180 180 1 0 4 22 1 0 416022 1 0 4m 21 1 0 2

Two insulated charged copper spheres A and B of identical size have charges qa and 3q respectively When they are brought in contact with each other and then separated what are the new charges on them

10 m s 60 A small sphere of mass m 0 6 kg carrying positive charge q 80 C is connected with a light flexible and inextensible string of length r 30cm and whirled in a vertical circle If a horizontally rightward electric field of strength E 105 N C exist in space the minimum velocity of sphere required at highest point so that it just complete the circle is m s may

31 Two point charges q and 2q are placed at the vertices B and C of an equilateral triangle ABC of side a as given in the figure Obtain the expression for i the magnitude and ii the direction of the resultant electric field at the vertex A due to these two charges A 9 B a a a 29 C All India 2014 C 22 3

34 A positively charged sphere of mass m 5 kg is attached by a spring of force constant k 10 N m The sphere is tied with a thread so that the spring is in its natural length Another identical negatively charged sphere is fixed to the floor vertically below the posi tively charged sphere as shown in figure Initial separation between sphere is x 0 50 m Now thread is burnt and maximum elongation of the spring is 0 10 m calculate the charge on each sphere in C g 10 m s2 Fill 10 Q in OMR sheet 000000 CITAL CLA

Paragraph for Question No 9 to 11 A charged particle is suspended at the centre of two thin concentric spherical charged shells made of non conducting material Figure A shows cross section of the arrangement Figure B gives the net flux o through a Gaussian sphere centered on the particle as a function of the radius r of the sphere charged particle 2 0 What is the charge on shell A A 5 31 x 10 6 shal A O shall Is What is the charge on the central particle A 0 2 C B 2 C B 5 31 x 10 C 10 Nm C C 1 77 C C 3 54 x 10 C 1 In which range of the values of ris the electric field zero A 0 to r C for r IB Figure shows a charge enclo D 3 4 C D 1 77 x 10 B r to re D for no range of r electric field is zero

Two large identical plates are placed in front of each other at x d and x 2d as shown in the figure If charges on plates are Q and 50 the potential versus distance graph for the region x 0 to x 3d is d is very small and potential at x 0 is Vo O A V Vo Q 5Q d 2d 3d d 2d 3d Correct Answer X

Paragraph for Question no 24 and 25 Suppose the earth is a negatively charged sphere of radius R and charge Q Neglect gravity to answer the following questions 24 Minimum velocity imparted to a particle of mass m and charge q so that it escapes earth s electric field is A 2kQq Rm A C D 11 2 km s 25 Velocity of the particle of mass m and charge q when it reaches the bottom of the smooth DIGIT kQqh mR2 kQq Rm B mo h 4kQqh mR 3kQq Rm C 7kQqh mR2 D 2kQqh mR

15 Consider a spherical volume which has uniform charge density p from x R to x 2R There is no charge from x 0 to x R and from x 2R to inifinity The electric potential due to this charge A at x 0 is 0 C at x 2R is 7pR 6 2R B at x D at x AL CLASSR R 3pR is 2 3R 2 is 8pR 3 o

Two identical copper spheres carrying char ges Q and 9Q separated by a certain dista nce has attractive force F if the spheres are allowed to touch each other and moved to d istance of separation x so that the force be tween them becomes 4F 9 Then x is equal to

Two particle each of mass m and charge q are attached to the two ends of a light rigid rod of length 2R The rod is rotated at constant angular speed about a perpendicular axis passing through its centre The ratio of the magnitude of the magnetic moment of the system and its angular momentum about the centre of the rod is 9 m 9 2m 2q