Electric Field and Potential Questions and Answers

ch veen Equivalent resistance between points A and B is A R R www R EX R R R www B an

Illustration 3 The region in between charge Q and Q2 has three different media Find out the force between Q and Q2 the total distance between the charges is r Figure is given below Q Vacuum Dielectric Dielectric medium medium 11 1 K2 K 1 4 1 4 Q K and ko are dielectric constant

A charged particle of mass m and charge e has velocity u when at a distance d from a conducting plate crosses it at point B The length of the plates AB is Then the charge density of the plate is 1 A 2domu e 2 2 m K u I B 2 X 2dcomu el

3 a 8 4 a a 12 Three equal charges Q each are at the corners of an equilateral triangle as shown The intensity of electric fie at O will be Q 1 4 er 3 Zero 2 4Teor Q 4

wo identical small bodies each of mass m and charge q are suspended from two strings each of m a fixed point This whole system is taken into an orbiting artificial satellite then find the tension in strings Kq 2 mg 12 2 Kq 2 mg 4 3 Kq 1 4 Kq 41 placed

Short answer questions 1 Two similarly charged pith balls are suspended from a point The balls repel each other If a mica sheet coulomb s to introduced between them what will be the effect on the positions of balls reduces the kind of charge attract each other between them 21 3

15 Electric field lines about a negative point charge are 1 Circular anticlockwise 2 Circular clockwise 3 Radial inwards 4 Radial outwards An electric dipole placed in a uniform electric field experiences in general A force only G

24 A point charge of 6 uC is placed at a distance 20 cm directly above the centre of a square of side 40 cm The magnitude of the flux through the square is 1 3 10 6 1 2 0 4 1x10 6 En

19 A loop of irregular shape of conducting wire PQRS as shown in figure placed in a uniform magnetic field perpendicular to the plane of the paper changes into a circular shape The direction of induced current will be 4 X X X X X X 1 Clockwise 2 Anti clockwise 3 No current 4 None of these Xx X X X X X X X X X X X X X

27 Which of the following statements is correct regarding electrostatics of conductors a The interior of a conductor can have no excess charge in the static situation b Electrostatic potential is constant throughout the volume of the conductor c Electrostatic potential has same value inside as that on its surface d All of these

Two spherical cavities of radii a and b are hollowed out from the interior of a neutral conducting sphere of radius R At the centre of each cavity a point charge is placed Call these charges qa and qb a Find the surface charges a b and OR b What is the field outside the conductor c What is the field within each cavity d What is the force on qa and qb e Which of these answers would change if a third charge qc were brought near the conductor 9a R b ab

Two positive charges q and q are located at the points with position vectors and 72 Find the magnitude of a negative charge q and the position vector 73 of the point at which it is 93 to be placed for the force acting on each of the three charges to be equal to zero

5 A ring with a uniform charge Q and radius R is placed in the yz plane with its centre at the origin 1 The field at the origin is zero 2 The potential at the origin is k R Q 3 The field at the point x 0 0 is k x 4 The field at the point x 0 0 is Q 2 R x Choose the correct answer 1 a and b are true k 2 c is true

Two similar spheres having Q and Q charges are kept at a certain distance F force acts between the two If in the middle of two spheres another similar sphere having Q charge is kept then it experiences a force in magnitude and direction as a Zero having no direction b 8 F towards Q charge c 8 F towards Q charge 1 towards charge

17 Electric field due to a uniform positively charged arc AB of radius R at O is Q 1 A E DR 0 101 0 160 R 3Q 2 A It it 8 B 3Q 04 3Q

14 A charge Q is placed at the origin The electric potential due to this charge at a given point in space is v The work done by an external force in bringing another charge q from infinity up to the point is V b Vq c V q d V a 9

shell of same mass Shell is free to move on the is placed on the top of a hemispherical smooth ground If particle is given a gentle push and reaches to angular position q as shown in fig ure then for an observer fixed on a shell ratio of re action force exerted by shell to pseudo force as observed from shell acting on particle is 1 sin e 3 cos 0 m m R 2 cosec 0 4 sec 0

The force between two point charges in air is 100 N Calculate the force if the distance between them is incre Ev 50 Ans 4

The electric intensity due to a dipole of length 10cm and having a charge of 500 C at a point on the axis at a distance 20cm from one of the charges in air is 1 6 25 107N C 2 9 28 107 N C 3 13 1 10 1 N C CC 4 20 5 107 N C f focal length

An electric dipole of moment p is placed in a uniform electric field E The i The torque on the dipole is px E ii The potential energy of the system is p E V iii The resultant force on the dipole is zero 1 i ii and iii are correct 2 i and iii are correct and ii is wrong 3 Only i is correct 4 i and ii are correct iii is wrong

8 C is at rest in 127 A pendulum bob of mass 80 mg carrying a charge of 2 x 10 uniform horizontal electric field E 20000 V m Find the tension in the thread of the pendulum and the angle it makes with the vertical A 9 1 2 2 x 10 N B 18 2 4 4 x 104 N C 27 3 6 6 x 10 N D 27 3 8 8 10 N

1 Two particles carrying charges q and q and having equal masses m each are fixed at the ends of a light rod of length a to form a dipole The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field The rod is slightly tilted and then released Neglecting gravity find the time period of small oscillations

A conducting spherical shell is given charge 2Q A point charge Q is kept inside the shell at point O as shown Now if charge Q is shifted from point O to point P then magnitude of electric field at point A outside the shell will 2Q O P Conducting shell 26 2 fr 26 5 26 Action Y W 335 20 1 Increase 2 Decrease 3 Remain constant AY Ipproppo or decrease depending on distance

20 Three charges Q q and q are placed at the vertices of a right angle triangle isosceles triangle as shown If the net electrostatic potential energy of the configuration is zero value of Qis 1 3 q 2 2 2q 2 2 a q a 9 9 2 2 2 4 2q 2 2

equilateral triangle with the ends of the piece 6 A long straight wire carries a current i Let B be the magnetic field at a point P at a distance d from the wire Consider a section of length 1 of this wire such that the point P lies on a perpendicular bisector of the section Let B be the magnetic field at this point due to this section only Find the value of d l so that B differs from B by 1

Two free positive charges 4q and q are a distance apart What charge Q is needed to achieve equilibrium for the entire system and where should it be placed from charge q 4 1 Q q negative at 3 4 2 Q q positive at 3 3 Q q positive at 4 Q q negative at 1 3 1 3

0 Three concentric metallic shells A B and C of radii a b and c a b c have surface charge densities o o and o respectively i Find the potentials of three shells A B and C ii It is found that no work is required to bring a charge q from shell A to shell C then obtain the relation between the radii a b and c O

30 Equal charges q are placed at the four corners A B C D of a square of length a The magnitude of the force on the charge at B will be MP PMT 1994 DPMT 2001 1 b a 39 4 4q 2 4 2 q X 1 2 2 1 2 2 d 2 2 24 a

Answer the following questions in brief A glass rod is rubbed against a silk cloth Which object s gets get charged in this process 1 3 4 5 neither between two opposite charged clouds nor between a charged cloud and the ground 6 Name two objects a that can be charged by rubbing b that do not get charged on rubbing State the main difference between a conductor and an insulator Name the device used for protecting tall buildings from lightning strikes Give the meaning of the term earthing List down two precautions that a person can take if he is caught outside in the open during a lightning strike stions the dod plastic straw that

ILLUSTRATION 3 51 Figure shows three thin concentric spherical shells A B and C with initial charges on A B and Cas 30 20 and Q respectively The shells A and C are connected by a wire such that it does not touch B Shell B is earthed Determine the final charges 9 9 and a 3 R R 20 30 2 R Q B

5 placed at vertex A due to the other charges Four charges each of Q Coulomb are situated at the four vertices of square of side length a Find the net force on the charge placed at vert A due to the other charges

2 Two infinitely long uniformly charged non conducting sheets of charge density o 2 x10 each are placed perpendicular to each other as shown in figure What is the resultant electric field intensity at point P O at Isitms P O 0153 976 rito8 odt noiget al AV

1 ABC is an equilateral triangle of side 2m If E 10NC then V V is A A 1 10Y 2 10V B 3 20V 4 20V Ya and x 2a If the potential energ

11 Positive and negative point charges of equal magnitude are kept at 0 0 a 2 and 0 0 a 2 respectively The work done by the electric field when another positive point charge is moved from a 0 0 to a 0 0

A short dipole of dipole moment pj is the centre of a spherical cavity inside a solid metal sphere as shown Electric field at point P as shown on the x axis due to charges induced on the surfaces of the metal sphere is of 1 koj 3 2kn V A iO R P X 2 k ng 3 r

Take g 10 m s Two like charged infinitely long parallel wires with the same linear charge density of 3 10 C cm are 2 cm apart The work done against electrostatic force per unit length to be done in bringing them closer X by 1 cm is 100 J m Find the integer closest to x Corporate Office CG Tower A 46 52 IPIA Near City Mall Jhalawar Road Kota Raj 324005 in IF mail contact resonance ac in ADVES 122

2 Two opposite and equal charges 4 108 coulomb when placed 2 102 cm away form a dipole If this dipole is placed in an external electric field 4 x 108 newton coulomb the value of maximum torque and the work done in rotating it through 180 will be a 64 104 Nm and 64 104 J b 32 10 Nm and 32 104 J c 64 104 Nm and 32 104 J d 32 104 Nm and 64 104 J

An electric potential difference will be induced between the ends of the conductor shown in the figure when the conductor moves in the direction A P B Q C L 3 4 6 D M N

A point charge of 6 x 10 9 coulomb is placed at a distance of 30 cm from another point charge of 4 x 10 coulomb Determine the force on the charges due to each other Also find out the intensity of electric field at a point between the charges on the line joining the charges and at a distance of 20 cm from the bigger charge

41 In a certain region of space with volume 0 2 m the electric potential is found to be 5 V throughout The magnitude of electric field in this region is 1 E V 2 3 4 zero 0 5 N C 1 N C 5 N C Vid SZEX

An electron gun fires an electron beam of kinetic energy E with a very small divergence angle 0 To focus all the electrons to one point a magnetic field induction B is applied along the direction of propagation of the electrons If the mass and charge on a electron are m and q respectively then minimum distance x shown in figure at which the ME electrons focus is nx aR then value of n is X

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 2 e coul m2 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 D 0

15 Consider a metal sphere of radius R that is cut in two along a plane whose minimum distance from the sphere s centre is h Sphere is uniformly charged by a total electric charge Q What force is necessary to hold the two parts of the sphere together R 65145

Two equally charged identical metal spheres A and B repel each other with a force 3 x 10 5 N Another identical uncharged sphere C is touched with A and then placed at the midpoint between A and B Net force on C is a 1 10 5 N b 2 10 5 N c 1 5 10 5 N d 3 10 5 N e C

www 4V 6V a 10 2 A b 10 A c 10 A d 0 A 6 A n p n transistor is connected in common emitter configuration in a given amplifier A load resistance of 800 2 is connected in the collector circuit and the voltage drop across it is 0 8V If the current amplification factor is 0 96 and the input resistance of the circuits is 192 2 the voltage gain and the power gain of the amplifier will respectively be NEET 2016 a 3 69 3 84 c 4 3 69 b 4 4 d 4 3 84

From A conducting sphere of radius R a cavity of radius R 2 is cut out as shown in the figure At the centre of cavity a point charge q is placed then the field and potential at point P as shown in the figure is A V C V 9 2 d q 4 d 9 E E q 2 d 9 4 d B V D V q 4 d q 2 d P d E E R q 2 d q 4 d 9 R 2

A solid sphere of radius R with its center at the origin is uniformly charged with density p in its volume A spherical cavity of radius is made in the sphere as shown The electric potential at the 278 1 41 0 coordinate 2R 0 is k 5 K 1 7 kpR 3 kpR O Y R X 2 kpR T 4 kpR 27

Two infinite nonconducting sheets of uniform charge density 8 and 8 are parallel to each other as shown Electric field at the 8 8 1 midpoint in the space between the sheets is and is directed towards right 28 2 midpoint in the space between the sheets is 0 and is directed towards right 3 midpoint between the sheets is zero 4 points to the left or to the right of the sheets is

3 Two point charges q 0 2 C and q2 0 4 C are 0 1 m apart Find the electric field at i mid point between the charges ii a point on the line joining q1 and q2 such that it is 0 05 m away from q2 and 0 15 m away from q Ans i 7 20 x 10 1 N C towards 1 1 12 both

15 In the given electric field E d x i E j N Ca hypothetical closed surface is taken as shown in figure The total charge enclosed within the closed surface is Keo Then find the value of k a 2 m b 3 m and c 2 m a 0 0 0 b E E E d