Electric Field and Potential Questions and Answers

0 A spherical shell of radius R is given charge 3q on its surface and a point charge q is placed at distance R 2 from its centre C Also there is a charge 2q placed outside the shell at a distance of 2R as shown Then SK 3q R 2 q C R 2R 2q A The magnitude of electric field at the centre C due to charges on the outer surface of shell is before closing the switch S Kq 2R B The electric potential at the centre C due to charges on the outer surface of shell is closing the switch S C The electric potential at the centre C due to charges on the outer surface of shell is closing the switch S D Charge flown through the switch into earth after closing the switch S is 5q Kq R Kq R before after

Seawater at a frequency f 9 x 102 Hz has permittivity 80 and resistivity p 0 25 m Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V t V sin 2 ft Then the conduction current density becomes 10 times the displacement current density after time 1 800 s The value of x is I Given 9 10 Nm C 4

The electrons in a particle beam kinetic energy of 1 6 10 17J What are the magnitude and direction of the electric field that stops these electrons in a distance of 10 0cm 1 103 v m in the direction of velocity of electrons 2 10 v m positive direction of velocity of electrons 3 103 v m perpendicular to velocity of electrons 4 106 x m perpendicular to velocity of electrons 36

electron at the moment reaches the opposite prato A proton accelerated by a potential difference V gets into the uniform electric field of a parallel plate capacitor whose plates extend over a length in the motion direction The field strength varies with time as be E at where a is a constant Assuming the proton to non relativistic find the angle between the motion directions of the proton before and after its flight through the capacitor the proton gets in the field at the moment t 0 The edge effects are to be neglected A particle with specific charge q m moves rectilinearly due to an

Q 10 Two balls carrying charges 8 C and 5 C are placed at certain distance apart The net electric field along the line joining the charges will be zero at a point Choose only 1 answer A B between the charged balls D beyond the ball with 8 C charge C beyond the ball with 5 C charge field cannot be zero

released from rest at point P and then accelerated towards the point Q by the electric field Rank the patterns according to the linear momentum of the proton when it reaches Q greates first P P a Q Q

2 A point charge is placed at the centre of a hollow conducting sphere of internal radius r and outer radius 2r The ratio of the surface charge density of the inner surface to that of the outer surface will be Whoi qab lo

A system of two charges 7 C and 2 C at 9 0 0 cm and 9 0 0 cm respectively are placed in an external field E 9x105 V m Total electrostatic energy of the configuration is 49 3 J 59 3 J 69 3 J

Q 48 There is an infinite non conducting sheet of charge having uniform charge density o The electric field at a point P at a distance x from the sheet is Eo Point O is the foot of the perpendicular drawn from point P on the sheet A circu lar portion of radius r x centered at O is removed from the sheet Now the field at point P becomes E AE Find AE r X P

Q 46 Consider a uniformly charged hemispherical shell What can you say about the direction of electric field at points on the equatorial plane e g point P X X P X Equatorial plane

Q 45 A uniformly charged semicircular ring ABCD produces an electric field Eo at the centre O AB BC and CD are three equal arcs on the ring Portion AB and CD ar cut from either side and removed Find the field at O du to remaining part BC A X B I I 1 1 1 C X D

Two uniformly charged nonconducting spheres each of radius R are fixed in a gravity free space as shown in the figure If an electron is released at rest from the point A then its speed just before striking the other sphere is mass of electron me Q A CC 10R Q C

Q 62 A pyramid has four faces all of them being equilateral triangle of side a A charge Q is placed at the centre of one of the faces What is the flux of electric field emerging from any one of the other three faces of the pyramid

A solid non conducting sphere of radius R having variable volume charge density p where Ar R is the distance from centre If electric field R distance from the centre of charged sphere 2 E 2R 0 1 2 3 6 N C Value of A 16 will be 2 4 4 8

39 In a region the intensity of an electric field is given by E 81 8j k in NC 1 The electric flux through a surface S 101 m in the region is a 10 Nm C c 8 Nm C 1 b 80 Nm C d None 3 I 4

13 Two point charges of 30 C and 40 C are 20 cm apart from each other Where will be the electric field zero on the line joining the charges from 30 C charge 20 3 2 1 a cm 20 3 5 14 In which of al C cm b 20 3 3 2 d 5 cm cm 17 13

A uniform electric field Eof 300 NC is directed along negative X axis A B and C are three points in the field having x and y coordinates in metres as shown in fig Find the potential differences A VAR AVCR and AVCA C 14 YA

In certain region of space there exists a uniform electric field of 2 10 kv m A rectangular coil of dimensions 10 cm 20 cm is placed in x y plane The electric flux through the coil is zero 30 Vm 40 Vm 50 Vm

8 An insulating hollow cube of side 1 carries uniform charge on all of its surfaces The surface charge density is o Determine the force acting on 6212 a face due all the other faces ZEO va F

For the electric circuit shown here write the Kirchhoff s circuital law equations the solutions of which will given currents in the three resistors Do not solve the equations AIPMT Mains 2006 202 www 10V 452 www 12V 80 www DE OF

Charge q 6 0nC is on Y axis at y 3cm and charge q2 6 0nC is on Y axis at y 3cm then M force experienced by test charge q 2nC on x 4 cm will be 51 8 N If both 9 and 9 are positive and same magnitude and q 2nC then it will do SHM about origin If la Hq 1 but q ve q ve and q 2 nC then q will do SHM about origin If 19 Hq 6 nC q ve q ve force experienced by q 2 nC placed on x 4 cm will be 51 8 j N

The law governing the force between electric charges is know as O Faraday s law Ohm s law O Ampere s law 02 59 hr min Coulomb s law

Three charges Q 2q q are placed at the vertices o an equilateral triangle of side a as shown in the figur If the net electrostatic energy of the system is zero then Q is equal to Q q 0 9 0 9 10 O 0 29 O 0 9 6 29

marks 11 Figure shown below three different patterns of electric field lineIn cach pattern a proton is released From re at point P and then accelerated towards the point Q by the electric field Rank the pattern according to the linea momentum of the proton when it reaches Q greatest first

A ball with charge 20e is placed at the centre of a hollow spherical shell which has net charge of 40e The charge of the shell s outer surface 20e 40e 60e hr min 80e

Two charges 9 and 92 are located at 9 0 and 9 0 in the x y plane in a medium of dielectric constant 4 The dielectric medium has carved out from it an ellipse r x2 y governed by the equation 1 The 4 9 equivalent force between the charges in air is 1 kq 92 ARE O n What is the value of n if distances are in meter given by x 10 2N where

For a dipole having magnitude of charge q 4 x 10 6 C and distance between the charges d 0 02 m If this dipole is placed in a electric field E 2 105 N C Then maximum torque on the dipole will be 1 6 10 2 Nm 3 2 x 10 Nm 2 4 x 10 Nm 4 8 x 10 2 Nm

Two identical beads each of mass m and charge q can slide on two long parallel insulating frictionless rigid rods that are a distance d apart Initially the beads are so far from each other that no electrostatic interaction exists between them With what speed must one of the beads be projected so that it passes over the other bead Assume radii of the beads negligibly small as compared to the distance between the rods Neglect effects of gravity Dm Flighalt cotof vo

A B E HOM D In the given figure if Q and Q are positive where could a negative charge be placed so as to have vertically upward net force on it 2 B 4 D C 5 E In the given figure if the vertical distance from point E to B is the same as the horizontal distance from E to either charge and the electric field at B due to either charge has magnitude 1 0 106 what is the magnitude of the net electric field 1 Zero 3 1 0 108 5 2 0 108 2 7 1 x 105 4 1 414 106

Point charges 9 4 C and 9 2 C are kept at point 0 and x 4 respectively electrical potential will be zero at points where x is in cm 8 x 3 cm and x 8 cm x cm and x 6 cm x 2 cm and x 6 cm hr min x 1 cm and x 5 cm

In an electric field shown in figure three equipotential surfaces are shown If function of electric field is E 2x V m and given that V V V V3 then we have y Z 1 X X 2 X X 3 X X 4 data insufficient X TX 1 2 3 X

Three point charges of strengths q 4 0 x 10 C 92 1 0 x 10 C and Q 10 6 C are fixed in a right triangle as shown above The distance between q and Q is d 4 0 cm and the distance between q and Q is de 3 0 cm What is the approximate electric field strength at location of charge O due to the

67 If electric potential of the inner sphere is 10 volt and that of the outer shell is 50 volt ther potential at common centre is 1 10 V 2 18 V 3 15 V 4 Zero a b

A particle of mass m and charge q is placed at rest in a uniform electric field E and then released The KE attained by the particle after moving a distance y is 1 qEy 2 qEy 3 qEy 4 q Ey

A solid insulating sphere of radius a 2 cm has a uniform charge density p A conducting spherical shell of inner radius b 4 cm and outer radius c 5 cm is concentric with the solid sphere and has a charge 1 C If the electric field at r 0 9 cm from the center of this charge configuration is 97x 10 N C find the charge density on the outer surface of the conducting shell Your result must be in multiples of 104 C m That means if you get a result of just typ 9 22 in the answer box Maximum of 5 of error is accepted in your answer Take k 9x10 Nm C Insulator 4 Conductor

The width of deplection region in P N junction diode is 500 nm and an internal electric field is 6 105 V m What is the kinetic energy which a conduction electron must have in order to diffuse from the N side to P side Question Type Single Correct Type 1 0 03 eV 2 0 3 eV 3 0 45 eV

5 Three concentric spherical shells A B and C of radii a b and c a b c have surface charge densities o o and o respectively If V V and Vdenote the potentials of the three shells then for c a b we have A 1 Vc VB VA 3 Vc V VA B AIPMT Mains 2009 2 Vc V VB A 4 Vc VB VA C

Three balls with charges of q 2q and 3q are placed at the corners of a square measuring L on each side as shown in Figure 16 6 Assume this set of three balls is not interacting with anything else in the universe and assume that gravitational interactions are negligible What is the magnitude and direction of the net electrostatic force on the ball of charge q q L

Assertion A The net force on a dipole in a uniform electric dipole is zero Reason R Electric dipole moment is a vector directed from q to q A A B B C

A semicircular ring of radius 0 5 m is uniformly charged with a total charge of 1 4 x 10 9 C The electric field intensity at the centre of this ring is 1 zero LOL II 2 320 V m 4 32 V m 81

Consider a metallic ring of radius 1 m mass 1 kg and carrying a current of 1A in a gravity free space in the x y plane with its centre O at the origin as shown in the figure If a uniform magnetic field 31 43 T is applied then the instantaneous acceleration of the point P which is on the y axis at the moment will be CX 7 m s Find the value of C X

2012 1 Two ideal diodes are connected to a battery as shown in the circuit The current supplied by the battery is Dit A C D 14 ESV a 0 75 A c 0 25 A 1002 www 200 www B D F b zero d 0 5A 95 Th A for cir A

Figure shows a very long smooth non conducting rod of radius r charged with uniform charge density fixed horizontally A neutral and smooth ring B of mass M can slide freely on the rod which happens to just fit in it A is a nonconducting particle having mass m and charge q attached to the ring by means of a non conducting and inextensible string of length R If P is released from the position shown in figure then answer the following questions The loss in electrostatic potential energy when string becomes vertical is R A q2 n 41 q 27 R q n 1 B C n 1 2r in 1 D

Q 64 Point charge q is placed at a point on the axis of a square non conducting surface The axis is perpendicular to the square surface and is passing through its centre Flux of Electric field through the square caused due to charge q is o If the square is given a surface charge of uniform density o find the force on the square surface due to point charge q

22 An oil drop having a mass of 4 8 x 10 10g and charge of 30 x10 8C stands still between two charged horizontal plates separated by a distance of 1cm If now polarity of the plates is changed instantaneous acceleration of the

dius carries uniform surface charge density of o per unit is made of two hemispherical shells held together by pressing them with force F see figure F is proportional to O 1 8 20

A hollow metallic sphere is charged Inside the sphere A The potential is zero but the electric field is finite B The electric field is zero but the potential is finite C Both the electric field and the potential are finite D Both the electric field and the potential are zero

15 Two charge q and 3q are placed fixed on x axis separated by a distance d Where should a third charge 2q be placed such that it will not experience any force 1 3 to the left of q 1 3 to the right of q C c 1 5 to the left of q d 1 5 to the right of q a b

Point charges 9 4 C and 9 2 C are kept at point x 0 and x 4 respectively electrical potential will be zero at points where x is in cm 8 O x cm and x 8 cm Ox 1 12 cm and x 6 cm O x 2 cm and x 6 cm O x 1 cm and x 5 cm

36 A circular disc of radius r is placed along the plane of paper A uniform electric field E is also present in the plane of paper What amount of electric flux is associated with it a r b Zero 2 r r q d E