Electric Field and Potential Questions and Answers

In an uncharged conducting spehre of radius R a spherical cavity of radius R 3 is made as shown in the figure It is given that OC and PX R A point charge q is placed at c and another point charge Q is palced at x Find the potential of point P due to charges at the outer surface of the sphere Options k Q q 2R 1 2 3 4 k Q 2q R P k q Q R k 2q Q 2R

vi What are the colour codes of carbon resistor Explain its significance vii Derive an expression for electric field due to electric dipole at axial point viii Explain the force between the two parallel current carrying conductor ix Write the properties of charge Explain

xi yj zk The electric field intensity in a region of space can be given as C x y z charge enclosed by a sphere of radius a centred at origin Options 1 470 C 2 4 o 3 4 4 470 where c is a constant of appropritae dimension Find the

100 If 343 droplets each of charge q and radius r are combined to form a big drop then the potential of big drop as compared to small droplet will be a 343 times b 49 times c 7 times d none of the above

31 A particle of mass 2 g and charge 1 C is held at rest on a frictionless horizontal surface at a distance of 1 m from the fixed charge of 1 milli coulomb mC If the particle is released it will be repelled The speed of the particle when it is at a distance of 10 m from the fixed charge is a 100 m s b 90 m s d 45 m s c 60 m s 69

97 Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of cm and are uniformly charged If the spheres are connected by a conducting wire then equilibrium condition the ratio of the magnitudes of the electric fields at the surfaces spheres A and B is a 4 1 d 1 4 b 1 2 c 2 1

83 When a charge of 3 C is placed in a uniform electric field it experiences a force of 3000 N The potential difference between two points separated by a distance of 1 cm within this field is a 10 volt b 90 volt d 3000 volt c 1000 volt 84 A uniform electric field having magnitudo

Find the electric field at a distance from a linear plus charge with a constant linear charge density infinite length and a distance from a linear plus charge

Q 21 Compare the current in the given circuit in the two cases 2KJ2 10 V SOUR 7 ww 3k 2 i when an ideal ammeter is used ii when an ammeter with internal resistance of 500 is used for the measureme as shown in the above figure

Consider three particles with positive charges Q 1C Q2 2C and Q3 4C placed in vacuum Find the minimal possible magnitude of the force between Q and Q3 if you know that the force between Q and Q2 is F12 8 N and the force between Q and Q3 is F23 16N

Two identical balls each having density p are suspended from a common point by two insulating strings of equal length Both the balls have equal mass and charge In equilibrium each string makes an angle with the vertical Now both the ball are immersed in a liquid As a result the angle e does not change The density of the liquid is o Find the dielectric constant of the liquid

A small particle of mass m and charge qis placed at point P on the axis of uniformly charged ring and released IfR x the particle will undergo oscillations along the axis of symmetry with an angular frequency that is equal to A qQ 476 R 3 qQ C 4 mR qQx B 4TE R 4 D qQx 47cmR

An electron is revolving around a long line of charge having charge density 2 Find the kinetic energ of the electron assuming that it is independent of radius of electron orbit e 2 2 1 4780 4 s 2 s 2 3 4 e 278

Two charges of magnitudes 3Q and 2Q are located at points a 0 and 4a 0 respectively What is the electric flux due to these charges through a sphere of radius 5a with its centre at the origin

Figure shows three point charges 2q q and 3q Two charges 2q and q are enclosed within a surface S What is the electric flux due to this configuration through the surface S Delhi 2010 39 29 9 S

06 A uniform but increasing with time magnetic field exists in a cylindrical region The direction of force on an electron at P is a towards right b towards left c into the plane of paper d out of the plane of paper x Px X X XX X L X X xx X X X XX X X XXX X XX

Consider the situation shown in figure The work done in taking a point charge from P to A is W from P to B is WB and from P to C is Wc A B 1313 atuatio C Q point charge 1 WA WB Wc 3 W W Wo R P A R 2 WA WB Wc 4 None of these

A ring of radius R is charged uniformly with a charge Q The electric field at a point on its axis at distance r from any point on the ring will be KQ 1 KQ r R KQ 3 K 1 R 2 www 3 KQr R ES0020

28 A 3 0 nC charge Q is initially at rest at a distance of r 10 cm from a 5 0 nC charge q fixed at the origin The charge Q is moved away from q to a new position at r 15 cm In this process work done by the field is a 1 29 x 10 5 J c 4 5 x 10 7 J b d 3 6 x 105 J 4 5 x 10 7 J

The volume charge density inside and outside a spherical charge distribution is as follows a p r a Po b 0 c Calculate the total Electrostatic energy r d for 0 r a for r a 16 Q 6 20 6 Q 67

37 Four objects W X Y and Z each with charge q are held fixed at four points of a square of side d as shown in the figure Objects X and Z are on the midpoints of the sides of the square The electrostatic force exerted by object W on object X is F Then the magnitude of the force exerted by object W on Z is W a 7 F N 5 857115

51 Four charges q q q and q are placed at the corners of a square of side 2 L is shown in figure The electric potential at point A midway between the two charges q and q is qp a c 2q 4 EO L 1 4 0 q 2L TA q 1 2 L b 4 0 d 15 35745 857 2q zero

23 The magnitude of electric field due to a point charge 2q at distance r is E Then the magnitude of electric field due to a uniformly charged thin spherical shell of radius R with total charge q at a distance r R will be a c b 0 d 4E

The sphere of charge 6 24 uC distributed uniformly throughout its volume The radie the sphere is 2 0 cm Find the electric field at distances 1 0 cm 2 0 cm and 3 0 cm 4 a 7 02 10 N C 14 0 10 N C and 6 24 10 N C b 9 31 10 N C 1 25 10 N C and 7 14 10 N C c 2 33 10 N C 12 0 10 N C and 23 1x10 N C d 4 31 10 N C 25 1 10 N C and 25 7 10 N C

The magnitude of electric field due to a point charge 2q at distance r is E Then the magnitude of electric field due to a uniformly charged thin spherical shell of radius R with total charge q at a distance r R will be a 0 O b 0 d 4E 38

49 Two equal point charges Q each are kept at the two corners of an equilateral triangle Another charge q is kept at the centre of the triangle as shown in figure The distance between the centre and vertex is r The resultant force on q is 1 Qq Teor 299 Q q 2 Q Qq 2mer Qg

P Q is a uniform wire of resistance 2000 2 and M is the mid point of PQ A voltmeter of resistance 1000 2 is connected between P and M The reading of the voltmeter when the potential difference applied between PQ is 150 volt will be 91 1 150 volts 3 75 volts 1 P MQ 1 2 100 volts 4 50 volts 8

The final answers and plots 1044 04x1 Q3 6 marks In the figure shown a rod of length L has a uniform linear charge density A Write a code to find the potential at point P using Mathematica x oS x5 70X 3 S x d Bonus 2 marks Find the electric field at point P Q4 10 marks Choose the correct answer for the following 1 The output of the following ling olve fxt X5 95 99dd

q1 92 93 d If q1 2 nC q2 3 nC and d 0 01 mm what is the magnitude of the charge q3 that would be in equilibrium at the position shown 8 nC 12 nC 16 nC 24 nC None of the other answers is correct

2 Find the electric field at a point 1 1 1 due to two uniformly charged infinite non conducting plates which are placed perpendicular to the x axis at I 2 and r 3 and a infinite thin wire passing through r 0 2 2 and parallel to the plates The surface charge densities of the plates are 10nC m and 15nC m and the line charge density of the wire is 10 nC m respectively Use 9 10 10 1 00

An electron enters in a horizontal electric field of strength 105 V m Assuming the weig of electron to be negligible its acceleration would be A 1 7x10 7 ms2 B 1 7x10 6 ms 2 C 1 7x1020 ms D 1 7x1024 ms 2

246 Current Electricity 15 Two metal wires of indentical dimensions connected in series If o and 2 are conductivities of the metal wires respectively effective conductivity of the combination is Re AIPMT 2 1 3 01 02 0 02 01 02 2 4 20 02 01 02 01 02

b Figure shows two charges q 21 3 C and q2 21 3 C held a fixed distance d 1 52 m apart a Find the strength of the electric force that acts on q b A third charge q3 21 3 C is brought in and placed as shown in Fig b Find the strength of the electric force on q now 9 d 91 a d as in d d 93

44 180 Mark for Review Across a metallic conductor of non uniform cross section a constant potential difference is applied The quantity which remains constant along the conductor is Electric field Current density 02 48 hr mir Current

Three charges Q q and 2q are placed at the vertex of equilateral triangle of side length L If potential at centre is zero then correct relation is NCERT Pg 57 1 Q q 3 Q 0 2 Q 2q 4 Q 2q

2 Two conducting plates P and Q with large surface area A are placed as shown in the figure A charge q is given to plate P The electric field between the plates at any point is P Q 10 9 h q c 9 d 29 Ac

10 An electric dipole of dipole moment p is placed parallel to the uniform electric field E The work done by external force to rotate it perpendicular to the field is NCERT Pg 67 1 pE im 3 2pE Tb 2 pE amen 4 2pE

2 4 x 10 9 Nm 0 60 3 7 101 Nm 8x10 11 Nm E x104 Two point charges of equal magnitude but opposite polarity are kept at points A 0 0 3a and B 0 0 3a respectively The work done by the electri field when another positive point charge is moved from P 2a 0 0 to Q 0 2a 0 is 1 Positive 2 Negative 3 Depends on the path followed 4 Zero 1 2 3 32

59 Two infinitely large charged planes having surface charge density to and o are placed along xy plane and yz plane respectively as shown in figure Then the nature of electric field lines is best represented in 1 3 Z X AZ O X 6 2 4 Z X

Equipotential surfaces are shown in figure Then the electric field strength will be cm 10V 30 Hobb 10 20 30 20V a 100 Vm along X axis b 100 Vm along Y axis c 200 Vm at an angle 120 with X axis d 50 Km at an angle 120 with X axis 30V cm X

Four identical charges i e q each are placed at the corners of a square of side a The charge that mus be placed at the centre of the square such that the whole system of charges is in equilibrium is 2 2 2 1 4 3 3 1 1 4 3 2 2 1 4

d is not zero any where on the SECTIONARE Objective Type Questions Four expressions for an electrostatic field appear below Select the incorrect one E in N C x y z in m 1 3i 4j 5k 2 xi yj zk 3 E y i z x k 4 E yzi xzj xyk Electric field at point 30 cm 30 cm 0 due to a

An electron increases in speed when it moves from location A y 10 cm to location B y 1 cm The speed at position Ais 4 70 x 10 m s and at position B va 7 95 x 10 m s Neglect gravity a Which point has a higher potential Point A Point B both points have the same potential Choose one b What is the electric potential difference between these two points 10 cm A 1 cm B Write your answer the following way a Higher potential is b Potential difference is Explanation Volts Explanation dation with the values you used to earn a partial credit in case your answer is incorrect

Consider a strip of charged copper that runs vertically upward from the floor to the ceiling There is a 1 m long string with one end attached to the middle of the strip and the other end attached to a 0 1 kg rubber ball with 1 x 10 6 C As you let the rubber ball hang you want the string to rest at an angle of 0 15 rad as measured from vertical How many C m must there be along the length of the copper strip

wo thin rings each having radius 3R are placed at distance 4R apart with their axis coinciding The harges on the rings are Q and Q The potential difference between the centres of two rings is

29 Electric field at centre O of semicircle of radius a having linear charge density is given as 1 3 2 a a O a 2 2 Eo a 4 a

E ax 2 E E Problem 1 The electric field components in Fig 3 26 are 0 in which a 800 N C m 2 Calculate a the flux through the cube and b the charge within the cube Assume a 0 1 m

During lighting a current pulse shown in figure flows from the cloud at a height 1 5km to the ground If the breakdown electric field of humid air is about 400 kVm 1 the energy released during lighting would be in unit of 10 J I KA 150 0 A 0 2 ms

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 3R 9R 2Q 3Q

Dipole having dipole moment 4C m is placed on origin along x axis Point charge of 8 C is fixed at 4 0 0 m Now dipol rotated by an angle of If the work done in kJ in rotating the dipole is 6x then fill the value of x