Electric Field and Potential Questions and Answers

8 Examine the charge distribution shown 9 4 0 x 10 C 9 2 4 0 x 105 C 4 0 m 3 0 m a What will the net force be on the third charge of q3 3 0 x 10 C placed at the point P T I 4 O P b What will the total electric potential energy be if the third charge of q3 3 0 x 105 C is placed at the point P T I 4

3 The electric field due to a spherically symmetric charge distribution is given to be E Q A cor2 r R Qp 4 R5 0 r R Find the potential at a point inside and out side the charge distribution which vanishes at spatial infinity Also find the charge distribution that produces the above field 8

12 The amount of current through R is use junction rule a 1 A c 3 A b 2 A d 4 A A source R 4 A 3 A

In a Millikan type experiment there are two oil droplets P and Q between the charged horizontal plates as shown in the diagram Droplet P is in rest while droplet Q is moving upwards The polarity of the charges on P and Q is 1 2 3 PO P Neutral O Q Q I

2 Two small balls A and B of positive charge Q each Q m and masses m and 2m respectively are connected by a non conducting light rod of length L This system is released in a uniform electric field of strength E as shown Which one of the following is are incorrect Assume no other force acts on the system a Rod has zero angular acceleration b Rod has angular acceleration clockwise direction c Acceleration of point A is L 2QE 3m QE BO Q 2m 2QE 2mL E in anti towards right

An uniform electric field of magnitude E is set up is a region of gravity free space in upward direction An electron of mass me is projected at an angle 0 with the field with a speed u at time t 0 If the electron is at same height at t and t The value of t t will be 2m usine eE mousine 1 0 2 LAY meu cose eE 2m ucose

case A rod of mass M 10 kg is hinged at its midpoint on top of a pedestal of height h 50 cm and mass m 250 g The ends of the rod are connected to a ceiling with the help of two springs of equal relaxed length lo 40 em and unequal force constants k 25 N m and k 15 N m In equilibrium the rod stays at an unknown angle from the horizontal and the springs are vertical as shown in the figure If height of the ceiling above the floor is H 1 5 m find the force of normal reaction between the pedestal and the floor

3R at a distance of R from the centre of the shell outer radius The electric potential at the center of the shell is 1 1 41 0 q 2R 1 5q 3 47 6R 2 1 4TE 4q 3R 1 2q 4T 3R The potential V of an electrostatic field E a yi xi where a is a constant is c is Vm is direc 30 with the positive x axis as shown in OA 2m and OB 4m The potential di VB VA is Fift constant here 1 axy c 2 axy c 3 axy 4 axy 15 Oharges q Q and q are placed at an equa distance on a straight line If the total potentia energy of the system of three charges is zero Then the ratio Q q is 1 100 2 3 V 3 100 2 3 v A solid sphere of radius what distance from its potential half of the p 1 R 3R 3 2 Inducting sph

Q 102 The electric field at X due to dipole P is Q 102 perpendicular to P then the angle 0 is equal to figure correction 1 0 3 tan 2 r 2 tan 2 4 90 PR 8 figure correction 1 0 3 tan 2 P 2 tan 2 4 90

3 Two identical point charges are placed at a separation of I P is a point on the line joining the charges at a distance from any one charge The field at Pis E E is plotted against x for values of x from close to zero to slightly less than L Which of the following best represents the resulting curve H M N E C D E

1 What is the total charge on an infinite wire carring a charge density to where a is a cosntant Find electric potential at a point whose perepndicular distance from the wire at x 0 is R

3 2 148 There is a conducting shell of inner radius 8 Q 148 cm and outer radius 10 cm Inside this shell there is a charge of 5 C at a distance of 5 cm from the centre of the shell then the force experienced by a charge 10 C at a distance 12 cm from the centre is k 40 5 cm 10 cm 1 F kx 5 8 cm 5 C x 10 C Repulsing 13 102 12 cm 10 C 2 F kx 5 C x 10 C Repulsing 12x10 2 4 F kx 3 Fkx 5 C x 10 C Repulsing 2x102 Attracting 5 C x 10 C 12x102 Ep 5 cm fa a 10 C 1 460 k 5 cm 10 am 5 8 cm 60 af 8 cm 10 cm araferer 12 cm 5 12 cm fra 4 F kx 10 C 1 F kx 5 C 10 uc 13 10 2 2 F kx 5 C x 10 C f 12x10 3 F kx 5 C x 10 C saferaff 2 10 5 C x 10 C 142 10 2 311

There are two concentric metallic spherical shells A and B as shown in figure If a charge Q is given to shell B and A is earthed then the potential at r 1 Q a b C D B b A 1 Q 4 b 1 Q 4 EO r 1 Q a 4 1 a 9 b B A a

outside then there must be charges on the surface or in there cannot be any charge in the body of the c there must be charges only on the surface there must be charges inside the surface X

Example 3 4 The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 2 and at steam point is 5 23 2 When the thermometer is inserted in a hot bath the resistance of the platinum wire is 5 795 2 Calculate the temperature of the bath Solution R 5 2 R100 5 23 22 and R 5 795 22 R Ro x100 R R 1 at R100 Ro Now 5 795 5 5 23 5 0 795 023 x100 x100 345 65 C

Four points charges Q q 2q and 2Q are placed one at each corner of the square The relation between Q and q for which the potential at the centre of the square is zero is 1 Q q 3 Q 9 2 4 Q 1 AIPMT 2012 q

A very narrow tunnel is formed along the diameter of a spherical uniformly charged non conducting body Its radius is R and total charge is Q If an electron is released from rest from one end of the tunnel then kinetic energy of electron at centre of sphere is k 3 1 4 0 kQe 2R kQe AR 2 kQe 2R kQe 4 Tag

Two point charges q1 and q2 of equal mass m are initially at rest at an infinite distance It move towards each other due to their mutual attraction find their speeds when they are at a distan apart

If J and are current density and electric field inside a current carrying conductor at an instant then Jx is O Positive O Negative O Zero May be positive or negative

If the charge on a capacitor is increased by 2 C the energy stored in it increase by 21 The original charge on the capacitor is 1 10 C 2 20 C 3 30 C

3 Two identical charged spheres of mass m and charge q are suspended by strings of equal lengths T from a common point of suspension The strings make an angle of 60 with each other Find the value of q in terms of m 1 and e Find the tension in the strings 4 Two charges q and q are fixed at a 0 a 0 respectively

A uniformly charged hollow non conducting spherical shell of radius R is having charge Q The magnitude of work done in moving any charge q from centre of sphere to a distance 2R from its centre will be 1 2 Qq 8 R Qq 4 ER na

2 An insulating shell of radius R with its center at the origin has a charge Q that is uniformly distributed on its surface An infinite line of charge density is located at x 2R parallel to y axis Find the magnitude of the electric field at the origin 2 2 2 2 E R D 87 R 4TE R TER A B C

A charge Q is kept at a perpendicular distance from the centre of a square plate of sides a The electric flux through the square surface is Only one correct answer A B C 0 Q 280 4 0

A circuit involving five ideal cells three resistors R R and 200 and a capacitor of capacitance C 1 F shown At steady state match the proper entries from celumn 2 to column 1 using the codes given below the columns 30V LOCT 300E 2012 10V A Column I P K is open and K is in position C O K is open and K is in position D R K is closed and K is in position C S K is closed and K is in position D P Q R S R 224 H 1 F 20V R B Column II 1 Potential at point A is greater than potential at B 2 Current through R is downward 3 Current through R is upward 4 Charge on capacitor is 10 C

3 150 cm 4 200 cm Q 124 If potential in volts in a region is expressed Q 124 as V x y z 6xy y 2yz the electric field in N C at point 1 1 0 is 1 6i 9j k 3 6i 5j 2k 2 3i 5j 3k 4 21 3 k 3 150 cm 4 200 cm Para atce f fareit a V x y z 6xy y 2yz 1 1 0 1 6i 9j k 3 6i 5j 2k RT faz men 2 3i 5j 3k 4 2i 3j k

1 Find the magnitude of the electric field at a point that is at a distance x x R away from the center of two concentric shells with radius r and R r R and with charge q and Q uniformly distributed on their surfaces B C A Q 9 4 Ex Q 4 TEX Q q 4 EX D Q 47x 9 4 R

BL 29 nathor q 0 1 mathon Q8 27 July 2021 Shift 2 What will be the magnitude of electric field at point O as shown in figure Each side of the figure is I and go perpendicular to each other mathange mathongo mathongo mathango mathongo mothongo A q q A 1 24 1 9 E mathongo 1 q Ameo Phongo mathonge mathonge Hmathongo mathongo mathongo mathongo mathongo G 24 mathongo mathongo mathongo mathongo mathongo mathongo mathongamathongo mathongs mathongo mathonga mathongs 1 2 42 2 2 1 21 3 mathongo Amathongamathongo mathongo mathongo mathongo 4m6o 21 1 2q 5 mathongo mathongo mothonge mathonga

NEET PHYSICS All India Major Test Series Phase I II Major Test 28 22 03 06 2020 Q 102 A semicircular ring of radius R is given a Q 102 R fan af vasarafgarantera at uniform charge Q Then the electric field and amer Q fra en farge electric potential at its centre will be faga f 2 4 R 4n R Q Q 2 R 4 R Q Q 4x R 2 R 4 zero zero 1 2 3 4 4t R 4 R Q Q 2 R R 4 R Q Q 4t R 2n R

27 If a magnet is kept in a magnetic field B then the potential energy of the system is P E MB cos M B where is the angle between M and B a When 90 P E is minimum and is equal to MB b When 9 90 P E 0 i e the potential energy associated with the magnet when it is kept perpendicular to the field is zero c When e 180 P E is maximum and is equal to MB d When e 90 P E is maximum and is equal to MB A B

View In English Electric charge on sphere A is equal to electric charge of sphore B The spheres are joined by conducting wire Then the wire is removed the common potenti on each sphere is found to be v The charge on each sphere before joining is 1 3 Vr 2K 2K 11 12 2K 1 12 11 1

Which among the following statement is incorrect regarding a uniform spherical shell Inside the shell the gravitational potential is zero Inside the shell the gravitational field is zero Inside the shell the gravitational potential is same everywhere Inside the shell the gravitational field is same everywhere

A dipole of dipole moment p is placed at a distance 2R from the centre of a neutral conducting sphere of radius R The direction of dipole is towards the centre of the sphere A tangent is drawn from the dipole to the sphere which meets the sphere at point A A The potential at point A is p 16 R 2 B The potential at point A is 3p 24 R 2 C The potential at point A due to induced charges is 3 2 3 p 48R D The potential at point A due to dipole is 3p 24 R

Electric flux emanating element ds E 41 41 4k is 1 10 unit 3 30 unit through a surface 5 placed in an electric field 2 60 unit 4 20 unit 2

Two non conducting solid spheres of radii R and 2R having uniform volume charge densities p and p2 respectively touch each other The net electric field at a distance 2R from the centre of the smaller sphere along the line joining the centres of the spheres is P P2 zero The ratio 1 4 3 T 32 OF can be 2 4 4 32 25

13 An electrostatic field line leaves at an an gle a from point charge q and connects with point charge 92 at an angle 3 91 and 92 are positive as shown schematically in the figure We have q 292 and a 60 Then 60 0 9 29 0 A a test charge placed at the midpoint O will be in equilibrium B B 90 92 C the magnitude of the electric field at a distance r far away from O see figure is 92 4 cor D for a negative test charge the electrostatic potential energy is lower near q as compared to that near 92

If J and are current density and electric field insid a current carrying conductor at an instant then JxE is O Positive O Negative O Zero O May be positive or negative

The galvanometer shown in figure has resistance 50 2 and current required for full scale deflection is 1 mA are resistances R R and R required to convert it into ammeter having ranges as indicated Then G A a R b R R w 1 198 1 198 T 10 A Q R Q R R 5 Y 1 A 11 1 Q 22 R3 Z 0 1 A

b 4 69 10 d 3 69 104N Among two discs A and B first have radius 10 cm and charge 106 C and second have radius 30 cm and charge 105 C When they are touched charge on both 9A and q respectively will be s rat a 9A 2 75 C q 3 15 C 6 9A 1 09 C q 1 53 C GROSENE d c 9A 9B 5 5 C a 3 69 10 N c 2 69 10 3 N ts

A potential is given by V x k x a 2 for x 0 and V x k x a 2 for x 0 The schematic variation of oscillation period T for a particle performing periodic motion in this potential as a function of its energy E is A C T E L B T D T 5 E E

Two small objects A and B are fixed in place and separated by 2 69 cm in a vacuum Object A has a charge of 1 27 C and object B has a charge of 1 27 C How many electrons must be removed from A and put onto B to make the electrostatic force that acts on each object an attractive force whose magnitude is 59 6 N Number 5 75e12 Units No units

In a vacuum two particles have charges of 91 and 92 where q1 2 8 C They are separated by a distance of 0 23 m and particle 1 experiences an attractive force of 2 7 N What is the value of 92 with its sign Number 5 7e 6 Units C

Four identical metallic objects carry the following charges 1 47 6 49 4 56 and 9 79 C The objects are brought simultaneously into contact so that each touches the others Then they are separated a What is the final charge on each object b How many electrons or protons make up the final charge on each object a Number 1 6e 6 Units C

A thin rod of mass m carrying uniform negative charge q is placed symmetrically along the axis of a thin ring of radius R carrying uniformly distributed charge Q The ring is held fixed in free space and length of the rod is 2R Find period of the small amplitude oscillations of the rod along the axis of the ring q Q R

A conducting sphere of radius R and charge Qis placed near a uniformly charged non conducting infinitely large thin plate having surface charge density o Then potential at point A on sphere due to charge on sphere Here k 0 O 1 4180 Q 00 11 T 3

Two charges of plus two point 4 microc oulomb and minus 2 4 microcoulomb a re at a distance of 2 5 into 10 raise to t he power minus 3 metre apart from eac h other determine the magnitude of ele ctric field in the broadside on position a t a distance of 0 30 m from this type all of the dipole be rotated through 90 deg ree then what will be the intensity of th e field

J 4 Two concentric hollow conducting spheres of radius a and b b a contains charges Q and Q respectively If they are connected by a conducting wire then find out following Final charges on inner and outer spheres Heat produced during the process g 17

Two identical small insulating balls are suspended by separate 0 25 m threads that are attached to a common point on the ceiling Each ball has a mass of 8x10 4 kg Initially the balls are uncharged and hang straight down They are then given identical positive charges and as a result spread apart with an angle of 36 between the threads Determine a the charge on each ball and b the tension in the threads

0 Three infinitely long line charges having linea charge density 22 and 32 are placed along x axis y axis and z axis respectively The work done by electric field in moving a unit positive charge from 2 2 2 to 2 2 0 will be 1 3 3 ln 2 4 TEO In 2 4 TE 2 4 3 ln 2 4 TEO In 2

If we consider solid conductors then of course the atoms are tightly bound to each other so that the current is carried by the negatively charged electrons There are however other types of conductors like