Electric Field and Potential Questions and Answers

Single Correct Option 1 Two very large thin conducting plates having same cross sectio shown in figure They are carrying charges Q and 3Q respectively The variation of electric field as a function at x for x 0 to x 3d will be best represented by 3Q as X

Electrostatic field in a region is given by E yzi zx xyk V m where x y and z are in m If electric potential at origin is zero then potential at 1m 1m 1m is 1 1 V 3 3 V 2 1 V 4 3 V

In a van de Graaff generator the radius of sphere is 2 m The maximum potential of the sphere can be given Em 3 x 106 V m 3 x 106 V 6 x 106 V 8 x 106 V

When a small uncharged conducting ball of radius a 1 cm and mass m 50 gm is dropped from a height h above the centre of another large conducting sphere of radius b 1 m having charge Q 100 C it rises to a height h 2m after the collision Find the value of h in m Assume that during the impact there is no dissipation of energy OE m QB h

a 0 4 Six charges are placed at the vertices of a regular hexagon as shown in the figure The electric field on the line passing through point O and perpendicular to the plane of the figure a function of distance x from is x a Q 2Qa EX Q Q b d Q Qa Ex 3Qa 73

6 There are four concentric shells A B C and D of radii a 2a 3a and 4a respectively Shells Band D are given charges q and q respectively Shell C is now earthed The potential difference V Vc is k 1 k c kq 2a kq b G kq 3a kq 6a fal ding Band

18 Four point charges A B C and D are placed at the four corners of a square of side a The energy required to take the charges C and D to infinity they are also infinitely separated from each other is q B q 20 10 ATEA b 2q c ATS a 2 1 d 9 65 1

The electric field in a region of space is E 1 4 3k kN C The electric flux due to this field over an area i 1 m is 1 2 x 103 N m C 1 3 3 103 N m C 1 the 2 4 103 N m C 1 4 3 10 N m C 1 arrangement of the charges

7 The electric potential in a region is represented as V 2x 3y z Obtain expression for electric field strength A 21 3j k C 2i 3 k B 21 3j k D 21 3j k

27 A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm A charge Q 20 C is given to the inner sphere now inner sphere is connected to the shell by a conducting wire the amount of heat generated in process is 1 6 J 3 12 J 2 9 J 4 14 J

The insulating property of air breaks down at the intensity of electric field 3 x 106 V m The maximum charge that can be given to a sphere of diameter 5 m is about O 2x 10 5C 2x 10 C Read More O 4 x 10 6 C

132 For shown charge system B q a Aq a a C q the electric field is A Non zero everywhere B Zero everywhere C Zero at midpoint of BC D Zero at centre of triangle ABC

The electric field due to an electric dipole at a distance r from its centre in axial position is E If the dipole is rotated through an angle of 90 about its perpendicular axis the magnitude of electric field at the same point will be A E C E 2 B E 4 D 2E

2 Electric field at a point on the axis of an electric dipole is E If strength of dipole moment and distance are doubled then new electric field at new point will be dipole is ideal 1 3 2 E 2 E4

4 Electric potential in a region varies with distance as V 3x2 The electric field strength at a point P 2 4 2 m is V 1 12 along ve Y axis m V 2 12 m V 3 12 along ve X axis V 4 12 along ve Y axis m along ve X axis

The electric potential V in volt in a region of space is given by V ax ay 2az where a is a constant given by a 1 25 x 10 V m What is the radius in m of the circle of the equipotential line corresponding to V 6250 V and z 2m Z

21 Uniform electric field of strength 20 is present in a region as shown in the figure Points A and B are separated by 20 3 cm If potential at point A is 40 volt then potential at B is equal to A B 2013 cm 30 THER V E 20 m

5 If W work is done in rotating a dipole in uniform electric field from its stable equilibrium position to an angle 30 then torque needed to hold this dipole at an angle 60 in the same electric field is 3W 1 2 3 3 3W 2 3 2 4 2 3 W 3 2 3 W 3

The electric field lines in a region is shown in the figure EA EB and Ec are the electric field strength at points A B and Crespectively Then B O EA EB Ec O EC EA EB O EA EC ER

3 Which of the following represents correct variation of electric potential due to an ideal electric dipole at large distance r from it 1 V 2 3 V x 1 r 2 Vor 4 V 1 2

Linear charge density on circumference of half ring is If a particle of mass m and charge is kept at the centre of the ring then acceleration of particle is R radius of half ring Ay 1 3 xxxxx xx 1 noi 2 Rm xxxx 1 290 4 Rm 90 R m 2 a 4 a X 1 290 2 Rm 1 290 4TE Rm

A charge q is kept in a closed surface as shown If flux through each plane surface is o then flux through curved surfaces is 1 3 q 380 9 30 EO q 2 4 9 20 280 q d GO

A conducting sphere of radius 10 cm has an unknown charge The electric field at 30 cm from the surface of shell is 3 6 10 N C and points radially outwards What is total charge on the sphere O 16 nc O 32 nC O 64 NC O 42 nC 5

Two positive charges Q and Q2 are fixed at A and B A unit positive charge is taken from A to B along the line joining AB The force experienced by unit charg O Decreases continuously O Increases continuously Increases first and then decreases Decreases first and then increases

Is this a stable equilibrium position for a charged particle placed at this point Discuss the nature of the equilibrium 19 A semicircular ring of radius R is carrying a charge q uniformly distributed over its length Calculate the magnitude of the electric field at the center of the ring Can you calculate the field without using integration For your sake of information Archimedes could have done so 20 Use problem 15 to generate 10 C charge starting with a shell carrying a charge 1 C

A infinite line charge produces a field of 9 x 104 N C at a perpendicular distance of 2 cm The linear charge density is 107 Cm O 2x 10 6 Cm 1 10 Cm O4x 107 Cm1

Two identical positive charges are fixed on the y axis at equal distances from the origin O A particle with a negative charge starts on the x axis at a large distance from O moves along the x axis passes through O and moves far away from O Its acceleration a is taken as positive along its direction of motion The particle s acceleration a is plotted against its x coordinate Which of the following best represents the plot A C 0 a B a D

An electric dipole charges q q masses m each is placed along x axis with its positive charge at 0 0 and the exists in the region Find the angular acceleration of negative charge at a 0 A variable electric field E Ax the dipole A B E Aaq ma 2 E Aa q GO ma 2E Aa q ma D None of these

The insulation property of air breaks down at E 3 x 105 V m The maximum charge that can be given to a sphere of radius 3 m is 03 10 4 C 09x 10 4C 0 6 10 4 C O 4 x 105 C

A hollow uncharged metallic shell of radius R has a charge q at a distance R 2 from the center Find the charge that will flow into the shell after the shell is earthed A q B 2q C q 2 D zero

A particle of charge q is released from rest from a point A It moves due to a electrostatic field in this region to a point B If VA and VB are the potentials of A and B respectively then neglecting electromagnetic radiation the kinetic energy of the particle at B is A q VA VB B q VB VA C q VA VBI D qVBl JI

A dielectric sphere of radius R carries a uniform charge density Calculate the electric field at a distance R 2 from the center if the field at a distance 2R from the center is E A E B E 2 C 2E D 4E 3

Two particles carrying equal negative charge are kept fixed at x a and x a Another charged particle of mass m and charge of magnitude q is initially at rest at the origin and is constrained to move only along the X axis If the particle is displaced slightly in one direction it performs an SHM with time period T Then A The particle may be positively charged B The particle may be negatively charged C T2 000 m D T200 1 q

A uniform electric and magnetic fields are produced pointing in the same direction If an electron is projected with some velocity pointing in the same direction The electron s velocity will decrease in magnitude The electron s velocity will increase in magnitude Velocity remains constant Velocity first increase then suddenly become zero

Practice problems Electrostatics I Electric field potential Gauss s law Q 1 16 4 1 35 minut A half ring of radius R carries a charge per unit length The potential at the center of the half ring is A 27 THE O B 2 TE 0 C 280 D 2 480

A spherical conducting shell of radius R is placed with its center at the origin Two charges Q and Q are placed at a a and a a respectively where a R The field at the center due to induced charges on the conductor will be A C 4 Q 2 towards ai aj towards ai aj B zero D 2 towards ai aj

The region in space with x y 2 R and z 0 has uniform volume charge density p If electric field at point 0 0 1 is E then the electric field at point 0 0 will be x y z R af far 0 0 2 da a faz 0 0 2 aga sa sim A B C D P PR E k 6 Eo E PR k 6Eo E PR PRK E 6E TR

There are 64 identical drops of a conducting fluid Each drop is charged to potential Vo They are combined to form a bigger drop Potential of bigger drop is nVo Find n Answer 0 8 0 8 1 02 03 4 5 6 9 7 1 2 3 4 5 9 5 6 7

Four identical point charges are placed at vertices of square ABCD of side 10 cm with centre at O A point charge placed on Z axis at point 0 0 d experiences maximum possible electrostatic force Value of d in cm is YA D A Answer 0 8 10 cm 0 8 C X B 1 2 3 4 5 6 7 9 1 2 3 3 4 5 6 7 9

In column l configuration of charge is given whereas column Il gives variation of field E and potential V on a function of r Match the entries Column l Q1 Uniformly charged spherical shell Q2 Uniformly charged solid sphere Q3 Cylindrical charge having uniform volume charge density p Q4 Column II A1 A2 A3 A4 A5 V4 EA V E R

Three large conducting charged sheets are kept parallel to each other as shown in figure Net force experienced by a charge q placed between plates A and Bis A B C q 3C 1C Zero X Towards right Towards left 2C Both 2 3 are possible

The electric potential decreases uniformly from V to V along X axis in a coordinate system as we moves from a point xo 0 to xo 0 then the electric field at the origin A must be equal to Xo C must be greater than V Xo V B may be equal to Xo V D may be less than Xo The anergy of electric le

A charge of Q1 8 0 pC is distributed uniformly on a spherical surface radius R 0 02 m and a second charge of Q2 3 0 PC is distributed uniformly on a concentric spherical surface radius R2 0 04 m Determine the magnitude of the electric field 0 34 m from the center of the two surfaces in N C Write your answer with two digits after decimal Q 8 0 pC R1 R2 Q2 3 0 PC

29 A thin disk of radius R is held closing the opening of a thin hemispherical shell of the same radius Both the bodies are made of insulating materials and have uniform charges of surface charge density geach The plate is released keeping the shell fixed How much maximum kinetic energy will the plate acquire after it is released 6 a R o 800 Ro TR 0 480 d Insufficient information

16 In another world instead of the Coulomb s law electric force F on a point like charge q due to another point like charge Q is found to obey the following law Qa 1 ar 4 r Here a is a positive constant and is the position vector of charge q relative to the charge Q F Q 1 ar 4 over a closed path is also a Electric field due to a point charge Q is E b Line integral of this electric field f d zero as in our world c Gauss law f ds enclosed also holds true for this electric field d All the above statements are true but this electric field is not conservative

24 Three identical electric dipoles are arranged parallel to each other at equal separations as shown in the figure The separation between the charges of a dipole is negligible as compared to the separation between the dipoles In the given configuration total electrostatic interaction energy of these dipoles is Uo Now one of the end dipole is gradually reversed how much work is done by the electric forces 17U b a c 18 18U 17 d 17U 18 18U 17

Two smooth spherical non conducting shells each of radius R having uniformly distributed charge Q Q on their surfaces are released on a smooth sun conducting surface when the distance bet 5R The mass of A is m and that of B is 2m The speed of A just before A and B collide is Neglect gravitational interaction take K 40 0 mA ITTITAITEET 5R B TETT 2m

Figure shows two large cylindrical shells having uniform linear charge densities A and A Radius of inner cylinder is a and that of outer cylinder is b A charge particle of mass m charge lens in a cince of radius r Then its speed v is Neglect gravity and assume that radii of both the cylinders to be very small in comparison to their length

An electric dipole of dipole moment p 6 x 10 C m is placed in a uniform external electric 4 N field of intensity 2x 105 as shown in the figure The angle between net electric field with external electric field E at point A will be k r p 45 37 53 0 r 3m A E

A uniform electric field of strength E exists in a region An electron charge e mass m enters a point A with velocity Vj It moves through the electric field exits at point B Then y 2amv ed E Rate of work done by the electric field at B is Rate of work by the electric field at A is non zero Velocity at B is 4ma v d 2av d 0 0 A a 0 B 2a d X