Electric Field and Potential Questions and Answers

60 In the rectangle shown below the two corners have charges 91 5 C and q2 2 0 C The work done in moving a charge 3 0 C from B to A is take 1 4 TEO 1010 N m C2 a 2 8 J c 4 5 J 91 b 3 5 J d 5 5 J B 234 15 cm A 5 cm 92 42M

Three pairs of large conducting plates are charged to different potentials as shown in figure The separation between each pair of plates is same Rank the pair of plates according to the magnitude of the electric field between them from highest to the least 30V 80V 20V 70V 10V 90V 1 2 3 1 3 1 2 2 1 2 3 3 3 2 1 4 1 32

Figures below show regular hexagons with charges at the vertices In which of the following cases electric field at the centre is not zero Question Type Single Correct Type 1 2 3 4 E 2q 2q 2q 29 2q q 2q

A solid conducting sphere of radius a is surrounded by a thin uncharged concentric conducting shell of radius 2a A point charge q is placed at a distance 4a from common centre of conducting sphere and shell The inner sphere is then grounded The potential of outer shell is 9 9 32 16 a A 4 B Y 2a 9

An electric dipole consists of charges 2 10 8 C separated by a distance of 2 mm It is placed near a long line charge of density 4 0 10 4 Cm as shown in Fig such that the negative charge is at a distance of 2 cm from the line charge Calculate the force acting on the dipole 2 cm 9 2 mm

The electric field in x y plane is given by E x i y2j Potential at point 3 3 is taken as zero Then A Work done in moving a test charge q slowly from a point a b to a point b a is zero B Potential at any point on x y plane can t exceed 18 unit for x y in 1st quadrant C Potential can t be defined as field is non conservative in nature D Equipotential curve are concentric circles with centre 3 3

A long straight wire Wire 1 carries a current such that a magnetic field is created around it as shown below in Figure Q2a You may assume that its length continues indefinitely Magnetic Field Lines Figure Q2a Magnetic field lines around Wire 1 The magnetic field strength is 42 nT at a distance of 150 mm from the wire a i Calculate the magnitude of the current in the wire ii In which direction do the electrons flow in the wire upwards or downwards State the name of the rule you have used to determine this Another wire Wire 2 of length of 348 mm is positioned 150 mm from Wire 1 and oriented parallel to it as shown in Figure Q2b A current flows through Wire 2 and the two wires experience a repulsive magnetic force of magnitude 768 pN b Calculate the current in Wire 2 Wire 1 S Wire 2 Figure Q2b Wire 1 and Wire 2 3 2

on the sides of an equilateral 8 A charge Q is spread uniformly in the form of a line charge density COR 3a triangle of perimeter 3a Calculate the potential at the centroid C of the triangle It moves from point A where the electric

8 A spherical charge distribution with a volume charge density p and radius R contains a spherical cavity where there are no charges as shown in the figure If the radius of the cavity is R 4 determine the force experienced by a point charge Q placed along the line joining the centres of the sphere and the cavity at the following points i at any point r R and ii at any point where 0 r R 4 R p R 2 R 4

Two parallel infinite line charges with linear charge densities C m and C m are placed at a distance of 2R in free space What is the electric field mid way between the two line charges 120191 A C REOR zero N C B D 2 ER 2 TEOR N C N C

In a certain region of space electric field is given by 21 3j 4k The change in potential of a point charge which is moved from point 1 0 5 to the point 4 2 6 is x volts Find the value of x Electric field is in N C and coordinates are in meter

A cathode ray tube is shown in Figure Q3a Electrons increase speed due to the accelerating voltage before emerging through a hole in the anode and then travel into a region between the parallel deflecting plates which have a length of 12 cm and a separation of 4 5 cm In addition a uniform magnetic field can be applied to this region with magnetic field lines passing directly into or out of the diagram Deflecting Plates 0 Cathode Anode Figure Q3a A Cathode Ray Tube A student conducts three experiments with this cathode ray tube using a constant accelerating voltage of 3 8 kV a Show that the electrons leave the hole in the anode at a speed of around 4 x 10 m s and calculate the time taken for these electrons to travel across the length of the deflecting plates 4

The electric field in a certain region of space obeys Ey 0 Ex Ez 0 and JE ax 0 0 E Oy 0 E Oz 0 Then net torque on an electric dipole parallel to the x ax this field is Option A B C directed along the x axis directed along the y axis directed along the z axis Rate this que

The bob of a pendulum has mass m 1kg and charge q 40 C Length of pendulum i 1 0 9 m The point of suspension also has th same charge 40 C What the minimum speed should be imparted to the bob so that it ca complete vertical circle 1 6 ms 1 q pq m u 2 2 ms 2 1

A conducting sphere of radius R and change Q is placed near a uniformly charged non conducting infinitely large thin plate having surface charge density o The find the potential at point A on the surface of sphere due to charge on sphere K b 4R 1 47 2 00 5 4 E0 3 Q

39 The magnitude of the each of two opposite charges that form an electric dipole is increased by a factor of while the separation between the charges is tripled What is the change in magnitude of the torque on t dipole in a uniform field

Following figure shows S S and S i ii iii Q S iv S Now match the following columns and mark the correct code given below Column I s PS 30 ps sa P q r 20 S S Column II Q 0 0 S Q 0 2Q 0

lg of cork with a charge 1 C floats motionless 1 cm above a large uniformly charged plane near the surface of the earth The surface charge density of the plane assuming it to be an infinite sheet is 1 8 7 x 10 8 C m 2 17 3 x 10 8 C m 3 zero 4 1 uC m2

The electric potential decreases uniformly from 120V to 80V as one moves on the X axis from x 1 cm to x 1 cm The electric field at the origin i must be equal to 20 V cm CET S ii may be equal to 20 V cm iii may be greater than 20 V cm iv may be less than 20 V cm 1 i only 3 ii iii iv 2 ii iii 4 iii iv

A non conducting spherical ball of radius R contains a spherical symmetrical charge with volume charge density p Kr where r is the distance from the centre of the ball n Kare the constants what should be value of n such that the electric field inside the ball is directly proportional square of distance from centre A 1 B 1 C 3 D 2

Question statements is true V 30 V S3 A B C S F C 2pF V 20 V F C 3pF With S closed V 15 V V 20 V With S closed V V 25 V With S and S closed V V 0 With S and S closed V 30V V 20V S

C d 2 2 19 Two charges of 10 C are placed at the corners A and B of an equilateral triangle of side length 0 5 m in air The electric potential at C is a 36 104 V b 5 106 V c 7 10 V d 10 V 20 In the rectangle the two

15 A charged particle of mass m 2 kg and charge 1 C is thrown from a horizontal ground at an angle of 45 with horizontal with a speed of 10 m s In space a horizontal electric field E 2 x 10 N C exists Find the range of the projectile 1 5 m 2 30 m 3 10 m TK 45 E 7 u 10m s X

170 Electrostatic 3 If the electric potential on the surface of innermost sphere is zero then relation between a b and c is o is surface charge density b 1 c a b 2 b ac 3 b c 2a 4 b c a a to 6

B C 2 Ecost Meit sind a 4 A rigid frame in the shape of a right pyramid is made of conducting rods The base ABCD is a square and the apex O is vertically above the centre of the base The frame is electrically neutral When it is placed in uniform electric field of intensity E pointing from the corner A towards the corner D total charges induced on the rods DC and OC are known to be q and q2 respectively Now the frame is rotated to make the electric field pointing from the corner A towards the corner C What are the charges induced on each rod

3 x 3 9 Marks II Each question carries 3 mark 3 Two metal spheres of different sizes are charged such that the electric potential is the same at the surface of each Sphere S has radius five times that of sphere S2 Let QA and QB be the charges on each sphere and E1 and E2 are the electric field magnitudes at the surface of each sphere What is i the ratio Q2 Q1 ii the ratio E2 E1

13 An annular disc of inner radius R and outer radius 2R has uniformly distributed charge Q Electric field strength at point P is 1 Q 3 E R PiT R 2 Q 2 ER 2 1

17 Two equal positive point charges are separated by a distance 2a A point test charge is located in a plane which is normal to the line joining these charges and midway between them a Calculate the radius r of the circle of symmetry in this plane for which the force on the test charge has a maximum value b What is the direction of this force assuming a positive test charge a Two similar halls of

1 Assertion If two concentric conducting sphere are connected by a conducting wire no charge can exist on inner sphere Reason When charge on outer sphere will exist then potential of inner shell and outer shell will be same

A point charge Q is located at the centre of a hollow spherical conductor having inner radius as R and outer radius R The conductor being uncharged initially The potential at the inner surface will be 1 1 1 1 R R R R D none of these A KQ C KQ 1 R R T R2 B KQ

3 Assertion Consider a conducting sphere of radius R Now a charge q is placed in front of a sphere Electric potential at point O is kq r B R O Reason Electric potential at the centre of sphere due to induced charges is zero

A particle of charge q and mass m moves under the action of an electric field E 2x where x is a distance from the point where the particle was initially at rest Find the distance travelled by the particle till it comes to rest again 3 A B C D 3 units 4 units 2 unit 1 units

A small electric dipole of dipole moment P is placed near a point charge Q as shown Then the net force on the dipole is towards Option A B towards L towards U P R Rate this questic

Two parallel nonconducting rings are arranged with their central axes along a common line The whole arrangement is shown in the figure Ring 1 has uniform charge q and radius R ring 2 has uniform charge q2 and the same radius R Rings are separated by a distance 3R The electric fields at point P due to ring 1 on the common line at distance R from the ring 1 is four times the electric field at P due 91 to Ring 2 find the ratio of 92 2R E1 00 P A 1 1 B R D 2 1 C 1 2 R 91 2 3 R

xiv Two identical beads each having a mass m and charge c When placed in a hemispherical bowl of radius R wit frictionless non conducting walls the beads move and a equilibrium they are a distance R apart figure 1 42 Determin the charge on cach bead 4 mgR Fo 1 2 R R Figure 1 42

The charge per unit length of the four quadrant of the ring is 22 2A and respectively The electric field at the centre is A B 2 2 R a 2 R 22 2 R C D None xx 2 78 F 2 X X

6 A conducting spherical shell of inner radius 2R and outer radius 3R has a positive point charge q located at its centre What is the electric potential at point P 6 R from its centre as shown in 7 which is at a distance the figure a b c d 2010 1 q 9 4 3R 1 9 2R 4TEO 1 q 4TE R 1 6q 4TE TR 3R R P 9 2R UP CPMT 20 31

ALLE In figure A and B are two identical blocks made of 2 a conducting material These are placed on a horizontal frictionless table and connected by a light conducting spring of force constant k Unstretched length of the spring is LA total charge Q is now given to the system Consequently the spring stretches to an equilibrium length L Value of Qis 1 4 kl 2 L L A 000000 L 000000 B 40 L L B 97 7 K KQ 4760 K L 10

40 180 Mark for Review Equipotential surfaces associated with an electric field which is along y direction are O Planes parallel to xz plane O Planes parallel to xy plane 02 56 hr min Planes parallel to yz plane Coaxial cylinders of increasing radii along the y axis

A ring of radius R with a uniformly distributed charge q as shown in figure 1 37 A charge qo is now placed at the centre of the ring Find the increment in the tension in ring DA Jo 27 4

8 m At a certain distance from a point charge in C the electric field is 200 V m and the potential is 800 V What is this distance 04m 2 m Mark for Review O 16 m 02 56 hr mir

Two very small spheres having charge Q and Q face each other at a certain distance between them If a dielectric having dielectric constant Kinserted between them then electrostatic force between them O Increase Decrease O Remains same 02 56 hr mi Becomes zero

Three charges 9 and q are placed at the corner of an equilateral triangle of side a as shown in the figure The net electric dipole moment of the system will be 9 q 2 a 3 qa 2 O qa O ga 2 a a ojn hr min q 2

9 kV O 18 KV Four charges 1 C 2 C 3 C and 4 C are placed at 1 m 2 m 3 m and 4 m from origin The net electric potential at the origin will be 36 kV Mark for Review O Zero 02 5 hr mi

34 A small conducting sphere is hanged by an i thread between the plates of a parallel plate capacitor as shown in figure The net force on the sphere is A www 1 Towards plate A B 2 Towards plate B 4 Zero

256 Two equal point charges are fixed at x a and x a on the x axis Another point charge Q is placed at the origin The change in the electrical potential energy of Q when it is displaced by a small distance x along the x axis is approximately proportional to IIT 2002 E A x C x 3 B x D

56 Three particles are projected in a uniform electric field with same velocity perpendicular to the field as shown Which particle has highest charge to mass ratio B A

Two short electric dipoles of moment P and 8P are placed in opposite direction on a line at a distance of 15 cm The electric field will be zero at point between the dipoles whose distance from the dipole of moment Pis O 10 cm 6 cm O 12 cm O 5 cm

Two point charges 6 C and 16 uC repel each othe with a force of 120 N If a charge of 8 C is added to each of them then force between them will becomes 40 N O 30 N O 20 N U2 5 hr mi O 60 N

7 2 J Two positive point charges of 10 u C and 4 C are 10 cm apart The work in bringing them 5 cm closer is O 2 4 J 4 8 J Mark for Review 3 6 J 02 5 hr r