Electric Field and Potential Questions and Answers

c 1 5 x 10 ms d 1 6 x 10 ms 28 The acceleration for electron and proton due to electrical force of their mutual attraction when they are 1 apart is a 3 1 x 1022 m s 1 3 10 9 ms b 3 3 x 10 m s 3 2 x 10 ms c 2 5 x 1022 ms 1 4 x 10 ms2 d 2 5 x 10 8 ms 1 3 x 106 m2 34 35

c 4 TE 31 A charge Q is placed at the centre of the line joining two point charges q and q as shown in figure The ratio of charges Q and q is q e b 1 4 12 Four point charges are at the corners of a c 4 q d 1 4 4 C 3 CC 40

ance eing 3 5 10 N 24 Two point charges of 3 C and 4 C rep each other with a force of 10 N If each is given an additional charge of 6 C the new force is a 2N b 4 N c 5 N d 7 5 N

0 A conducting sphere of radius 10 cm has unknown charge If the electric field at a distance 20 cm from the centre of the sphere is 1 2 x 10 NC and points radially inwards The net charge on the sphere is a 4 5 x 10 C b 4 5 x 10 C c 5 3 x 10 C d 5 3 x 10 C 1 A particle of mass 103 kg and charge 5 C is thrown

c 4 a 4 b 1 4 32 Four point charges are placed at the corners of a square ABCD of side 10 cm as shown in figure The force on a charge of IAC placed at the centre of square is a 7N b 8 N 4 C 3 C 0 3 CC 4 C d zero B c 2 N of qual magnitude q is placed at the

2 The nucleus of helium atom contains two that are separated by distance 3 0 x 10 magnitude of the electrostatic force that each pr m The prote exerts on the other is a 20 6 N b 25 6 N c 15 6 N d 126 3 Two insulated charged metallic protoce c 30 C vea su

21 The force between two small charged spheres h charges of 1 x 107 C and 2 x 10 C placed 30 apart in air is a 4 5 x 10 2 N c 5 4 x 10 N 2 The nucleus of helium jective NCERT P b 4 5 x 10 N d 5 4 x 10 N atom Prices

and a 20 6 N b 25 6 N c 15 6 N d 12 6 23 Two insulated charged metallic spheres P Q have their centres separated by a distance f 60 cm The radii of P and Q are negligible compared to the distance of separation The mutual force of electrostatic repulsion if the charge on each 3 2 x 10 7 Cis b 2 5 x 10 N d 3 5 10 N a 5 2 x 10 N c 1 5 x 10 N protam 30 C ve SU 3 C 31 A th

If energy of incident a particles in a scattering experiment decreases by 50 then distance of closest approach ba A B 4 times 3 times 2 times same

9 A homogeneous non conducting rod RS rotates about an axis passing through O and perpendicular to its length The length of OR and OS are respectively a and b Charges Q and 2Q are uniformly distributed on OR and OS respectively It the magnetic moment is zero then the relation between a and b is SE 21 00 k ba MTA 1 a 2b R 2 b 2a pir 4 a 2b el eisinis M 8

SolveLancer Test The given figure shows 3 metal shells placed concentrically B is earthed If A and C are given charge Q and Q then find the energy stored in the system a b 3R 110 288 R 1102 144MER 110 72MER 70 R B SolveLancer Test

A cylindrical region contains a uniform electric field that is along the cylinder axis and is changing with time If r is distance from the cylinder axis the magnitude of the magnetic field within the region is 1 Uniform 2 Proportional to 1 r 3 Proportional to r 1 0 1680 5

39 If linear charge density of a bent wire as figure is A a potential at the centre is R b electric field at the centre of the loop is 11 AT c electric field at the centre of the loop is f th 2 280 hove 2 2 R 2 2 ER 2ER

10 C charge is uniformly distributed over a thin ring of radius 1m A particle mass 0 9 gm charge 1 C is placed at the centre of ring It is displaced along the axis of ring by small displacement then time period of SHM of particle A 0 6 sec C 0 3 sec B 0 2 sec D 0 4 sec

4 gr 29 An electric field in space is is given b 10i 33 4k unit then electric flux through surface of area 1 unit lying in yz plane is 1 10 units 2 17 units 3 30 units 4 40 units 30

In a uniform positively charged spherical region there is a cavity as shown in figure The electric field the cavity is Option A B C P greatest at point A and along OA greatest at point P and along OP Least at point B and along BO Rate this quest

Which of the following systems of charges have zero electrostatic potential energy A l C TI luc C 2cm 1cm luc 1cm 2 C e 2cm luC 2cm luc B 2 C 1cm l C 1cm D None of these 1cm 2 C

A charge of 40 pC is distributed on an isolated spherical conductor that has a 4 0 cm radius Point A is 1 0 cm from the center of the conductor and point B is 6 cm from the center of the conductor Determine the electric potential difference VA VB A 3 V B 30 V C 30 V D 3 V E OV

We have two concentric conducting sphere S of radius Rand S of radius 2R and charge Q 20 respectively as shown in the figure Switch S is opened initially The amount of heat generated after S is closed A Q 16 R B Q 8 R Q S S C 2Q S Q 4 Eo R D 2 E R

A 144 sphere of radius 2R has uniform charge density p The difference in the electrostatic potential at r R and r 0 from the centre is a PR o c p 6 R b 2pR d pR 680

28 Just outside a sharp point on a conductor we will have a larger gradually curving places on the conductor 1 Electric field 3 Both 1 2 2 Voltage 4 Neither 1 2 than just outside

28 A spherically symmetric gravitational system 1 PO for FSR 0 for r R of particles has a mass density p where po is a constant A test mass can undergo circular motion under the influence of the gravitational field of particles Its speed v as a function of distance r 0 r cc from centre of the system is represented by VA 1 3 R r R 2 R 9 Gravitational field at the centre of the semicircle formed by a thin wire AB of mass M and length is Y R

Ex Two concentric coplanar circular loops made of wire resistance per unit length 10 m have d 0 2 m and 2 m A time varying potential difference 4 2 5 t volt is applied to the larger loop Calo current in the smaller loop Sol The magnetic field at the centre O due to the current in the larger loop is B Mol 2R Il p is the resistance per unit length then I potential difference 4 2 5t resistance 2nR p r R so the field B can be taken almost constant over the entire area of the smaller loop the flux linked with the smaller loop is Bx xr Ho 4 2 5t nr 2R 2nRp Induced emf e de Mox2 5 dt 4R p The corresponding current in the smaller loop is l then x2x R 4R p 1 2nrp 2 5 or R p B Ho 4 2 5t 2nRp 2R 8nRp 2 5x4x 10 0 1 8nx 1 104 1 25A V 4 2 51

32 Two charges q and 2q are placed along the x axis in front of a grounded infinite conducting plane as shown in the figure They are located respectively at a distance of 0 5 m and 1 5 m from the plane The force acting on the charge q is 1 1 7q 0 5m q 1 5m 2q 85 45 A ei tot 1 b 29 c q d 2 1 q ATC 2 138 24

Figure shows a uniformly charged hollow spherical shell having total charge Q and radius R Consider two point A 0 Y 0 and B 0 Y 0 If electric field vector at A is E then electric field vector at B is y R A E B E C E D E Q 4 R Q 4 R 1 Z y B A

1 Mass density of a solid sphere is p Radius of the sphere is R The gravitational field at a distance r from the centre of the sphere inside it is 4p G r 3 4pGr b 3 4p GR 3 3r PGR Tr a c d 3

plat m 2 face each other 5 0 cm apart with equal charge magnitudes q but opposite signs The field magnitude E between them neglect fringing is 55 N C What is the closest value of q Max score 1 Neg score 0 1 10 Coulombs None of the rest 3 Coulombs 105

68 not to scale The variation of potential with distance x from a fixed point is shown in figure The electric field at 13 m is X V volt 60 45 30 20 10 6 0 2 4 1 7 5 volt meter 3 5 volt meter x m 2 7 5 volt meter 4 5 volt meter 8 10 12 14 16 70

25 A sphere of mass M and radius R has a concentric cavity of radius R as shown in figure The force F sphere on a particle of exerted by mass m located at a distance r from the centre of sphere varies as 0 r the a c R R N Kh b d

11 The electric field due to a charge configuration with total charge zero is not zero but for distances large compared to the size of the configuration its field falls off faster than 1 r typical of field due to a single charge An electric dipole is the simplest example of this fact

Two point charges are placed on the x axis as shown in the figure q1 6 20 C is placed at the origin and q2 4 92 C is placed at distance d 20 cm from the origin Find the position in cm of the point A at which the electric field vanishes E 0 9 A x axis

Q 5 Moderate O 400 V An oil drop with charge q is held stationary between two plates with an external potential difference of 400 V If the size of the drop is doubled without any change of charge the potential difference required to keep the drop stationary will be O 1600 V C 4 1 3200 V 01 14

016 part 1 of 2 10 0 points Several light bulbs are connected in series across a 112 V source of emf What is the equivalent resistance if the cur rent in the circuit is 1 50 A Answer in units of N 017 part 2 of 2 10 0 points If each light bulb has a resistance of 10 0 how many light bulbs are in the circuit Answer in units of bulbs

The additive property of charge is not an obvious property It is related to the fact that electric charge has no direction associated with it charge is a scalar 6 Charge is not only a scalar or invariant under rotation it is also invariant for frames of reference in relative motion This is not alway true for every scalar For example kinetic energy is a scalar unde rotation but is not invariant for frames of reference in relativ motion

12 i Using Gauss Theorem derive an expression for electric field intensity at a point due to an infinitely long straight charged wire 2 ii ABCD is a square of side 5m Charges of 50 C 1C 50C and 50 C are placed at A B C and D respectively Find the resultant electric force on charge at B 3 A B

A test charge qo is slowly moved from point A to B perpendicular to the uniform electric field as shown in figure The work done by the agent to move the charge from point A to B against the electric field will be B E q Ed 90 Ed 9 Ed 9 A

10 a Draw equipotential surfaces corresponding to the electric field that uniformly increases in magnitude along with the z directions b Two charges q and q are located at point 0 0 a and 0 0 a What is the electrostatic potential at the points 0 0 z and x y 0

D Power factor is zero Two point charges A 3nC and B InC are placed 5 cm apart in the air The work done to r charge B towards A by 1 cm is A 2 0 10 J B 2 7 10 J C 12 1 10 J D 1 35x10 J

A ring whose inner radius is a and whose outer radius is b lies in the xy plane The ring contains positive charge with uniform charge density o Determine the electrostatic potential at the point P located along the axis of the ring a distance z from the xy plane assuming that V 0 as z 00 Select one OA O B OC 2 6 a G 4 b 2 a 460 b a P

Electric field in region is give Eo If particle of mase and charge is thrown with inital eed u from the origin the total oken by particle to return to origi a

An electric dipole dipole moment p is placed at a radial distance r a where a is dipole length from a infinite line of charge having linear charge density 2 Dipole moment vector is aligned along along radial radial vector force experienced by dipole is 1 2 3 p 2 p 2 or 2 ap 2 or an attractive attractive repulsive

The variation of electric field between two charges Q and Q along the line joining the charges is plotted against distance from Q as shown in figure below then correct statement is taking right side as positive field direction E a Q b a Q and Q are both positive and IQ l IQ l Q and Q are both positive and IQ IQ l Q is positive and Q is negative and IQ Q Q Q are both negative and IQ IQ 2 1

A circle of radius R is drawn in a uniform electric field E as shown in the fig VA VB Vc and VD are respectively the potentials of points A B C and D on the circle then 1 VA Vc VB VD 2 VA VC VB VD 3 VA Vc VB VD 4 V V VB VD A A B

134 Two spherical conductors of radii 4 cm and 5 cm are charged to the same potential If o and o2 be respective value of surface density of charge on both the conductors then the ratio of o 02 will be a 25 5 c 16 25 b 10 5 4

1 An electron charge e is placed at each of the eight corners of a cube of side a and an a particle charge 2e at the centre of the cube Calculate the potential energy of the system 10 21 1

Three charges 2q q q are located at the vertices of an equilateral triangle At the centre of the triangle 1 the field is zero but potential is non zero 2 the field is non zero but potential is zero 3 both field and potential are zero 4 both field and potential are non zero

If electrical force between two charges is 200N and we increase 10 charge on one of the charges and decrease 10 charge on the other then the electrical force between them for the same distance becomes 1 200 N 2 202 N 3 198 N 4 199 N

A generator uses 2600 joules to increase the electrical potential of a 2 coulombs arge What difference in potential will result if all of the generator s energy is onverted to electrical energy

per the are nits 18 The electric potential due to an infinite sheet of positive charge density o at a point located at a perpendicular distance Z from the sheet is Assume Vo to be the potential at the surface of sheet 1 Ve 2 Vo 3 Ve GZ 40 oz 20 Z 4 Vo 20

Three wires AB BC CD of equal length are charged uniformly with linear charge density and are placed as shown P is a point which lies at a distance from the wire BC on its perpendicular bisector Then the electric field at P is A C 2k 5e k 5e 2 5 1 2 5 3 B B 5 1 2k 5 D None of these C