Electric Field and Potential Questions and Answers

Note that volume of conductor and hence weight required is less in case of 3 phase 3 wire system Example 7 6 A sub station supplies power at 11 kV 0 8 pf lagging to a consumer through a single phase transmission line having total resistance both go and return of 0 15 The voltage drop in the line is 15 If the same power is to be supplied to the same consumer by two wire d c e by a new line having a total resistance of 0 05 and if the allowable voltage drop is 25 calculate the d c supply voltage

6 If is the linear charge density of wire bent in form of semicircular shape as shown Then electric field intensity at the centre will be y axis 1 XX CR 2k Reforla x axis 2k R 2 1 prilbu kastelb a ta blait bhi k 4

R two parallel conducting rails as shown in the figure X X X X B R Two resistors R and R are connected across the ends of the rails There is a uniform magnetic field B pointing into the page An external agent pulls the bar to the left at a constant speed V The correct statement about the directions of induced currents I and I flowing through R and R respectively is 1 Both I and I are in anticlockwise direction 2 Both I and I are in clockwise direction 3 I is in clockwise direction and I is in anticlockwise direction 4 I is in anticlockwise direction and I is in clockwise direction

A spherical conductor of diameter 20 distributed uniformly What is the magnitude of electric field at a p cm from the centre of the sphere O 3 2 10 N C O 6 4 10 N C 6 4 x 102 N C O 3 2 x 104 N C

2 A block of mass m having charge q is hung by a spring of spring constant k in a vertical electrostatics field E The string extension in equilibrium will be E a mg k b qE c d mg qE k mg qE k m q

An electric dipole is placed in an external electric field as shown in figure which varies with x in m as E E xi where Eg 10 NC m Force acting on dipole is lal 10 C x 10 m 1 Zero 2 20 UN 3 207 N 4 10 UN O q x 10 m

A conducting balloon of the radius a is charged to potential V and held at a large height above the earth ensures that charge distribution on the surface of the balloon remains unaffected by the presence of the earth It is connected to the earth through a resistance R and a valve in the balloon is opened The gas inside the balloon escapes from valve and the size of the balloon decreases The rate of decrease in radius of the balloon is controlled in such a manner that potential of the balloon remains constant free space 0 and charge cannot leak to the surrounding air hor massume the electric permittivity of the surrounding air equals to that of mo ang matho

Two charges of 25 x 10 coulomb and 25 x 10 coulomb are placed 6 m apart Find the electric field intensity ratio at points 4 m from the centre of the electric dipole i on axial line ii on equatorial line 1000 49 a b c 49 500 49 d 1000 49 500

O 45 A dipole with dipole moment Pis aligned with uniform external electric field E The work done by an external agent to rotate the dipole by 180 so that finally dipole moment is opposite to the electric field Eis PE 2PE PE 2 Mark for Review Zero

7 Two point charges Q are kept fixed on XY plane at points A 0 d and B 0 d Another point charge q with mass m is held at a point on the positive side of X axis that is at the distance 2d from both the fixed point charges What will be the magnitude of acceleration of the negative point charge just after it is released from its location ii at an instant it crosses the origin 8 In the previous question calculate the maximum possible force that the negative charge may experience if it is to be placed somewhere on X axis What will be the distance of negative charge from origin where it experiences the maximum electrostatic force

16 Displacement current is same as 1 conduction current due to flow of free electron 2 conduction current due to flow of positive ions 3 conduction current due to flow of both positive and negative free charge carriers 4 is not a conduction current but is caused by time field as

A non conducting solid sphere of radius 30 cm and relative permittivity 1 has the volume charge r 5 C m 1 3 where r in cm is the radial distance of any point in the 2 density p 30cm space from the centre of the sphere Then choose the correct statement s A Density of electric field lines is maximum at r 25 cm B Density of electric field lines is maximum at r 20 cm C Electrical energy stored in the space r 30 cm to r is same as that of a solid non conducting sphere carrying charge of 0 0225 C and radii 30 cm having uniform volume harge density in the same space r 30 cm to r D Variation of magnitude of electric field due to the sphere with respect to radial distance r is rectangular hyperbola in the region r 30 to r

A solid sphere of radius 4R is charged with volume charge density as p r kra here k and a are positive constant r is the distance from the centre If electric field at r R is 1 2 times the electric field at r 2R then find the value of a Answer 0 1 809 2 3 4 5 6 7

Consider a point charge q The equi potential surface whose potentials differ by a constant amou say 1 0 volt are A equally spaced B unequally spaced separation increasing one goes away from q C unequally spaced separation decreasing as one goes away from q D none of the above

219 Charge Q is uniformly distributed on a dielectric rod AB of length 21 The potential at P shown in the figure is equal to Q A a c Q 4 21 Q ATE 21 21 In 3 B b In 2 4 1 d None of these P 1 138 r

When a negative charge is released and moves in electric field it moves towards a position of A lower electric potential and lower potential energy B lower electric potential and higher potential energy C higher electric potential and lower potential energy D higher electric potential and higher potential energy

Let E 2xyi xj be the electric field distribution in the space All are in SI units Then which of the following options is are correct Electric field is zero on y axis Electric field will makes an angle of 60 with ve x axis at point 2 1 Volume charge density py 2 oy Volume charge density pv oy

Pre Med 02 For a uniformly charged sphere the electric field from its centre 1 increases linearly upto the surface 2 decreases linearly upto the surface 3 remains zero upto the surface 4 first increases and then decreases upto the surface inclosed by a Gaussian spherica

A dipole having dipole moment p is place at the axis of a charged ring having charge Q and radius R at a distance x from the center as shown in figure Find the force experienced by the dipole of dipole moment p pi placed along the axes of the uniformly charged ring 2 R K y B Lex

Two charges q and 2q are placed at heights a 2 and a respectively from plane of the square surface ABCD Then flux through the square surface is 1 2 3 q 3 0 q 4 0 A 5q 24 0 a Question Type Single Correct Type B a 2 Center D a 2q a

Mark the correct statement 1 Displacement current is produced only by varying magnetic field 2 Displacement current is produced by varying electric field only 3 Displacement current is produced by varying electric field as well as varying magnetic field 4 Displacement current can be produced neither by varying electric field nor by varying magnetic field

An electric dipole is fixed along y axis with its centre at origin At a given instant a charge particle is moving along x axis then q m O V 0 Power of electric force on charge particle is zero Acceleration and velocity are perpendicular Time rate of change in velocity is zero If charge is free to move it always moves along x axis to

An electron is projected from a distance d and with initial velocity u parallel to a uniformly charged flat conducting plate as shown It strikes the plate after travelling a distance along the direction of projection The surface charge density of the conducting plate is equal to 2da mu A C e d mu B D 2d mu el de mu Al m

Plane x 2y 10 carries uniform surface charge density 3 nc m Resulting electric o T field at a point near to the plane makes an angle 0 with x axis and sine Find the B value of A Here A and B are integers in their simplest form Answer 00 8 1 2 3 4 5 6 7 9

The electric potential V at any point x y z in meters in a space is given by V 10x volt The magnitude of electric field at the point 1 0 2 in V is E A B C D 16 20 4 2

1 If N is number density of acceptor atoms added and N is number density of donor atoms added to a semiconductor n and n are the number density of electrons and holes in it then 1 ne N n NA 2 n N n N e A 3 n N n NA ne 4 n N n ND A

The velocity of a particle m 10 mg q 4 0 C at t 0 is 20 m s in the positive x direction If the particle moves in a uniform electric field of 20 N C in the positive x direction what is the particle s velocity in m s at t 16 2 s Select one A 109 60 B 149 60 C 84 80 D 44 80 E 52 40

9 A thin spherical shell of radius R carries uniform surface charge density o It is cut into two parts by a plane from centre as shown To hold two parts together force F from both side has to be applied R at a distance 2 3 R The minimum force F is Value of n is n o F R

Two non conducting solid spheres of radii Rand 2R having uniform volume charge densities p and P2 P1 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 zero for where k is positive integer find k P k P Answer 00 01 02 03 04 05 06 07

78 A thin metallic spherical shell contains a charge Q over it A point charge q is placed inside the shell at point T separated from the centre by distance a Another point charge q is placed outside the shell at a distance b from the centre as shown in the adjacent figure Now select the correct statement s from the following q JO T a 9 A R 91 91 A Electric field at the centre due to charge over outer surface of the shell is zero B Electric field at the centre due to charge over outer surface of the shell is 9 9291 4 b 1 4 La 1 91 4 La R b C Electric potential at the centre due to all charges in space is D Electric potential at the centre due to all charges in space is 9 Q 2 b

D A charged particle of mass m 1 kg and charge q 2 C is thrown from a horizontal ground at an angle 0 45 with speed 25 m s In space a horizontal electric field E 2x107 v m exist The range of charged particle on ground is closest to Take g 10m s 1 216m 2 298m 4 322m

Choose the Correct Answer Q1 Two long thin rods with linear charge densities A1 6 5 nC m and A2 3 5 nC m lie parallel to each other and separated by 15 cm as shown in FIGURE 2 Determine the position of the point along the x axis where the net electric field due to the two rods is zero Figure 2 A 175 cm B 125 cm C 25 cm D 75 cm

0 Two infinite planes each with uniform surface charge density 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 1 0 6 0 2 20 3 20 4 260 30 3

For an electric dipole Piat origin find the value of tand at point A 3 4 Here S is the angle made by resulting electric field at point A with ve x axis Answer 1 9 0 8 0 1 2 3 4 5 2 3 4 LO 5 6 7 6 7

I wo large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference X A proton is released at rest midway between the two plates It is found to move at 45 to the vertical JUST after release Then X is nearly A 1 x 105 V C 1 10 V B 1 x 107 V D 1 10 10 V 20

making 90 with CB and 30 with AC when produced ABC is a right angled triangle the right angle being at point B Charges of 10 24 11 52 3 24 puC are placed at points A B and C respectively If AB 4 cm and BC 3 cm calculate the magnitude and direction of the resultant electric field at the foot D of the perpendicular drawn from point B on the side AC Ans 180 2 NC 1 inclined equally with both DA and BD when produced

wo charged spheres are kept at a finite centre to centre spacing as hown in the figure The force of electrostatic interaction between them first calculated assuming them point like charges at their respective entres and then force is measured experimentally If the calculated and he measured values are F and Fm respectively which of the following onclusion can you certainly draw a If F Fm for like charges and F Fm for unlike charges both the spheres must be made of insulating materials b If Fe Fm for like charges and F Fm for unlike charges both the spheres must be made of conducting materials c Irrespective of their materials F Fm for like charges and F Fm for unlike charges d Irrespective of their materials Fe Fm for like charges and F Fm for unlike charges

The graph shows the electric potential as a function of x in a certain region What is the x component of the electric field in this region if V 50 V Select one O a 40 V m O b 250 V m O c 10 V m O d 250 V m O e 40 V m V V 0 V 02 x m 0 4

3 Consider a current carrying wire AB placed on a smooth inclined plane as shown A steady current of 1 Aa being maintained in the wire At t 0 inclined plane starts accelerating in rightward with 6 m s acceleration and at the same time a vertical magnetic field of magnitude 6 T is switched on Magnitude of acceleration of wire with respect to inclined plane is 2x m s Find the value of x Given that length of wire AB 2 m mass 9 sin 37 3 0 of wire 2 kg cos 37 45 a 6 m s A 379 B B

Two small non conducting spherical objects each of mass 5 kg carry the same amount of identical charges uniformly distributed over them If the electrostatic force between the two objects is exactly balanced by gravitational force of attractie between them then the magnitude of the charge approximately is Take G 20 10 SI units 0 43mc 4mc 40mC O 4 3 10 C

A small block having charge Q placed on a frictionless horizontal table is attached to one end of a spring of force constant k The other end of the spring is attached to a fixed support and the spring stays horizontally in relaxed state Another small block carrying a negative charge q is brought very slowly from a great distance towards the former block along the line coinciding the axis of the spring Find extension in the spring when both the blocks collide

A small ball of mass 2 x 10 3 kg having a charge of 1 C is suspended by a string of length 0 8 m Another identical ball having the same charge is kept at the point of suspension Determine the minimum horizon tal velocity which should be imparted to the lower ball so that it can make complete revolution IIT 01

Paragraph for Question Nos 12 to 14 Three concentric spherical conductors A B and C have radii R 2R and 4R respectively A and C is shorted and B is uniformly charged charge Q 12 Charge on conductor A is 13 14 A Q 3 C 2Q 3 Potential at A is Q 4 R Potential at B is A A 4 R B Q 3 D None of these B B 16 R 16 R C C 20 R 50 48 R D None of these D None of these

Four charges are arranged as shown in figure A point Pis located at distance from the centre of the configuration take r A Then electric field at Pis 1 9 q P Electric field at Pis of magnitude Electric field at Pis of magnitude 2 5 ql 4 5 ql 4 Electric field at Pmakes an angle of 8 tan 2 with positive x axis Electric field at Pmakes an angle of 8 tan 1 with positive x axis

The work done by the electric field in terms of 10 25 J to turn an electric dipole 1920 in a uniform electric field of magnitude E 19 N C if the electric dipole moment P 3 02x10 25 C m and the initial angle 66 with E O 80 O 57 O 36 O 80 O 36

insulating threads When the pith balls are given equal positive charge Q they hang in equilibrium as shown in figure 1 3 Q Now the charge on the left pith ball is increased from Q to 2Q while leaving its mass essentially unchanged Diagram best representing the new equilibrium configuration is 0 2Q 0 0 0 0 40 Q 2Q Tsind fe sine 2Q Q

A ring of insulating material is situated at one end of a semi infinite long line of charge If is charge per unit length for ring as well as line charge and R is radius of ring Plane of ring is perpendicular to line charge Tension 2 in ring is nie Find n Answer O R

Four charges particles each having charge Q are fixed at corners of base at A B C and D of a square pyramid with slant length a AP BP DP PC a A charge Q is fixed at point P A dipole with dipole moment P is placed at the centre of base and perpendicular to its plane as shown in fig 3 63 Find a Force on dipole due to charge particles b potential energy of the system C

7 There is spherical symmetric charge distribution around origin The electrostatic potential at a Kr distance r from origin is given as V where K is a positive constant The slope of 1 tangent to density vs r graph at r m is aK Then find value of a

A charge of e is located at the origin and a charge e is located on the x axis at x 1 00 m The electric potential energy of an these charges is minimum when these charge are located in O independent of orientation of electric field an electric field in positive y direction an electric field in negative y direction O an electric field in negative x direction an electric field in positive x direction