Electric Field and Potential Questions and Answers

A short electric dipole has a dipole moment of 16 10 C m The electric potential due to the dipole at a point at a distance of 0 6m from the centre of the dipole situated on a line making an angle of 60 with the dipole axis is

moments d 4qai and dB 2gai placed on the x axis with a separation R as shown in the figure The distance from A at which both of them produce the same potential is R X

In the figure a hemispherical bowl of radius R is shown Electric field of intensity E is preser perpendicular to the circular cross section of the hemisphere The electric flux through th hemisphere is A 0 B ETR2 C E2TR2 D E3TR2

d Let V 2xy z and 0 Given point P 1 2 1 find i V at P ii E at P iii pv at P iv the equation of the equipotential surface passing through P v Does V satisfy Laplace s equation

34 180 An incorrect statement regarding a Gaussian surface selected should be that it Can pass through any material medium whether conducting or non conducting May pass through continuous charge distribution May pass through a region where no material medium is present May pass through any discrete point charge

neet prep Mini Test 21 Different Types of AC Circuit Contact Number 9667591930 852 nusoidal voltage source Then Both circuit should have the same value of capacitance inductor n both circuits the ratio of L and C will be the same

In the circuit diagram a capacitor which is initially uncharged is connected to an ideal cell of emf through a resistor R A leaky dielectric fills the space between the plates of dielectric The capacitance of the capacitor with dielectric is C Resistance of the dielectric is R R R WW A Charge on the capacitor as function of time t is B Maximum charge on the capacitor is ECOP 2 K 21 0 21 RC C C When charge on the capacitor is maximum then current in the circuit is 2R D Maximum voltage across resistor R is s

Three large identical conducting plates of area A are closely placed parallel to each other as shown the area A is perpendicular to plane of diagram The net charge on left middle and right plates are Q QM and QR respectively Three infinitely large parallel surfaces SS and S are drawn passing through middle of each plate such that surfaces are perpendicular to plane of diagram as shown Then pick up the correct option s left right Q S Sy S The net charge on left side of surface S is equal to net charge on right side of surface SR The net charge on left side of surface S is equal to net charge on right side of surface S the net charge on left side of surface S is equal to net charge on right side of surface S net charge on right side of surface S is equal to net charge on left side of surface Sp COY The

Four charges are placed on corners of a square as shown in figure having side of 5 cm If Q is one microcoulomb then electric field intensity at centre will be Q 20 a 1 02 10 N C upwards b 2 04 10 N C downwards c 2 04 10 N C upwards d 1 02 10 N C downwards

A dipole with electric dipole moment P is at distance r from a long thread charged uniformly with linear charge density r a The electric force on dipole due to charged thread is 284 pi 4or 2mo 2px 9 attractive attractive repulsive

An incorrect statement regarding a Gaussian surface selected should be that it Can pass through any material medium whether conducting or non conducting May pass through continuous charge distribution May pass through a region where no material medium is present May pass through any discrete point charge

In a uniform magnetic field a ring is rotating about its axis which is parallel to the magnetic field and the magnetic field is perpendicular to the plane of the ring The induced electric field in the ring 1 is zero 2 depends on the radius of the ring 3 depends on the nature of the material of the ring 4 depends on the product of the magnetic field and speed 1

Two concentric shells have radii R and 2R charges qA and qB potentials 2V and 3V respectively Now shell B is earthed If final charges on them become q and q Then Question Type Single Correct Type 1 qA qB B 2 9 29 3 Potential difference between A and B after earthing becomes V 2

According to Coulomb s law if the charge on each one of a pair of charged particles is quadrupled increased by a factor of 4 the electric force between them will be a 1 2 its original value b 1 4 its original value c 1 8 its original value d 1 16 its original value none of these 16 times its original value e

A point charge Q is kept at a distance 3a from the centre of a spherical conducting shell of charge 30 1 mark the CORRECT statement s and radius a Assuming K 3Q a K DIGITAL A Before closing switch the electric field at C due to the spherical shell is s B Before closing switch the potential of the shell is y fxx X 8kQ 3a C After closing the key the charge on the shell is 3 D After closing the key the charge of the shell is zero KQ 9a

Two small spherical balls each carrying a charge Q 10 C 10 micro coulomb are suspended by two insulating threads of equal lengths 3m each from a point fixed in the ceiling It is found that in equilibrium threads are separated by an angle 120 between them as shown in the figure What is the tension in the threads Given 1 9x109 Nm C 4 EO 120 A Question Type Single Correct Type 1 N 2 1 8 N 0 2 3 N

The variation of electric field between two charges Q and 2 aloll 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 Q b a Q and Q are both positive and Q Q11 Q and Q are both positive and Q Q Q is positive and Q2 is negative and Q2 Q11 Q1 Q2 are both negative and Q Q

List I shows different configurations of charge distribution List II gives the corresponding total electrostatics energy of the configuration or the corresponding work done List I P Q R S q A q Four point charges are kept at the vertices of a regular tetrahedron of side R The total electrostatic energy of the configuration is 9 q Thin spherical shell 2R Codes P A 1 B 4 C 3 4R Two thin spherical uniformly charged shells having uniform charge q are separated by distance 4R The total electrostatic energy of the configuration is q 2R B 9 4R A solid non conducting sphere of radius R having uniform charge q is kept inside a thin spherical non conducting shell of radius 2R having uniform charge q The total electrostatic energy of the configuration is Magnitude of work done in expanding the sphere having uniform charge q from radius R to 4R is Q 3 2 2 Thin spherical shell R 4 3 1 S 2 1 4 List II 1 2 3 4 6kq R 6kq 9 R 40 6kq 6R 0 6kq 40R

76 In a regular polygon of n sides each corner is at a distance r from the centre Identical charges are placed at n 1 corners At the centre the intensity is and the potential is V The ratio V E has magnitude a rn c n 1 r b r n 1 d r n 1 n

D OR An electric dipole is kept first to the left and then to the right of a negatively charged infinite plane sheet having a uniform surface charge density The arrows p and p2 show the directions of its electric dipole moments in the two cases Da Identify for each case whether the dipol is in stable equiblirium or unstable equilibrium Justify your answer Next the dipole is kept in a similar way as shown near an infinitely long straight wire having uniform negative linear charge density Pr P Will the dipole be in equilibrium at these two positions Justify your

A uniform electric field is present in X Y plane Due to electrostatic field electric potentials of point A 2 m 2 m B 2 m 2 m and C 2 m 6 m are 4 V 10 V and 16 V respectively The electric field is V m 31 21 3i 6j 2 4i 6j 51 6j 2

from a long thread charged uniformly with linear charge density A r a The electric force on dipole due to charged thread is 2a p 4 teor p 22 2pi Teor2 pi q 2 attractive attractive repulsive repulsive

A bob of mass m 100 gm having charge q 50 C connected with a non conducting string of length Im is whirled in vertical plane with minimum speed such that it can complete a circular path in space where electric field of strength E 2 10 N C apar from gravity is switched on as shown in figure The velocity of bob at the point where tension in string become zero is take g 10m s v 5i 3j 1m m B 10 a 30 L E 11 X C F 5 37 D F 3i j

The electric potential varies in space according to the relation V 3x 4y 5 volts where x and y are in meters A particle of mass 10 g starts from point 2m 3 2 m 0 under the influence of this field The charge on the particle is 10 C The magnitude of electric field in X direction is O 3Vm O4Vm OSVm 1 O 7Vm

68 There are four concentric shells A B C and D of radii a 2a 3a and 4a respectively Shells Band Dare given charges q and q respectively Shell C is now earthed The potential difference VA VC is Kq a c 2a Kq 4a b d Kq 3a Kq 6a

An electric dipole of dipole moment 10 C m is released from rest in uniform electric field 10 V m at angle 60 Maximum rotational kinetic energy of the dipole is say K and maximum torque during the motion is t then A K 5 0 x 105 J B K 2 0 x 10 J C T 5 0 x 10 N m D t 8 7 x 10 N m

conducting 90 A non conducting A uniformly distributed charge of linear charge density and a non conducting ring of uniformly distributed charge Q are placed as shown in the figure Point A is the centre of ring and line AB is the axis of the ring perpendicular to plane of ring The electrostatic interaction energy between ring and rod is R rod rod AB a In 2 3 QN 410 c In 2 3 AB of length 3k has 3R QN b In 2 3 210 QN In 2 3 d B 2TE

A particle having charge q 2 00 uC and mass m 0 0100 kg is connected to a string having length L 1 50 m and is tied to the pivot point P in the figure The particle string and pivot point all lie on a frictionless horizontal table The particle is released from rest when the string makes an angle 0 60 with a uniform electric field of magnitude E 300 V m The speed in m s of the particle when the string is parallel to the electric field shown in figure is x then 10x is MERI O F

Figure shows three metallic plates with charges Q 3Q and Q respectively Electric charges on faces of second plate after final distribution is 1 2 31 7Q Q 2 2 50 2 2Q Q 3Q 3Q 3Q

A charge Q is distributed non uniformly whose exact nature of distribution is unknown on a ring of radius R For this situation mark the correct statement s A the electric potential at centre of ring is 4 R B electric potential as well as electric field intensity at centre of ring can t be determined C electric potential can be determined but electric field intensity can t be determined at centre or at any known given point on axis D electric field intensity at centre of ring may be zero

Two charged small balls each of charge q and mass m when suspended from a common point by strings of length in air then these strings form an angle of 120 with each other When the system is immersed in a liquid of dielectric constant 1 1 k relative density of liquid w r t ball s material is 3 then the angle between the strings remain same electrostatic force between charged particle in medium is given by K times of force in vaccuum If the system without liquid is placed in a gravitational free space then angle between the strings will be O O O 0 90 180 remain unchanged

98 The potential due to point a charge at a point A is 7V and the electric field there is 3 V m There is another point B such that electric field at this point has smaller magnitude as compared to that at point A However if magnitude of the charge is tripled the electric field at B becomes 3 V m The potential at B now is closest to a 7 3 V b 7 V c 12 V d 21 V

A conductor of non uniform curvature kept in uniform external electric field the charge A has the greatest concentration on the part of greatest radius of curvature B has the greatest concentration on the parts of least radius of curvature C is distributed uniformly on the whole surface D none of these

A positively charged particle with mass 3 4 g and charge 12 C is initially moving with velocity 5 8 m s enters in an electric field of strength 150 N C which is directed towards right of the page Calculate the horizontal distance travelled by the charged particle within the field in 2 0 s nswer a 13 m b 11 m c 31 m d 20 m O A B C D

97 A conducting spherical shell is carrying a charge Q on its outer surface Its inner surface is connected to the ground by means of a wire of resistance R and a switch k as shown in the figure When the switch k is closed the quantity of charge flowing to the ground equals a Q c zero O R 77777777 b Q b Q 2

Two charges separated by 60cm are moved farther apart until the fore between them has decreased by a factor of 4 How far apart are the charges then

Two tram cars are kept at 4 km and 9 km radially from a distribution substation of 700 volt The first car is returning 30 A and the second car returning 40 A through rails If the resistance of the trolley wire is 0 3 0 km and of track is 0 06 0 km then the voltage across the first car is 700 V Substation Dail 4 km 9 km CAR 1 te bo CAR 2 Trolley Wire

Two point charges each of charge q are fixed at a 0 and a 0 Another positive point charge q placed at the origin is free to move along x axis The charge q at the origin in equilibrium will have A maximum force and minimum potential energy B minimum force and maximum potential energy C maximum force and maximum potential energy D minimum force and minimum potential energy 6 a 0 al q a 0

An a particle passes rapidly through the exact centre of a hydrogen molecule moving on a line perpendicular to the internuclear axis The distance between the nuclei is b Where on its path does the x particle experience the maximum force b a 3 2 A B b 2 3 C 2 2 D b 2 2

33 A large sheet carries uniform surface charge density o A rod of length 21 has a linear charge density on one half and on the second half The rod is hinged at mid point O and makes an angle 0 with the normal to the sheet The maximum torque experienced by the rod is if 0 is variable a c ON 280 02 EO 2 he 10 b d ON 80

non conducting solid sphere of radius 30 cm and relative permittivity 1 has the volume charge density p e space from the centre of the sphere Then choose the correct statement s 1 2 3 27 7 C m 1 where r in cm is the radial distance of any point in 4 30cm Density of electric field lines is maximum at r 25 cm Density of electric field lines is maximum at r 20 cm 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 charge density in the same space r 30 cm to r Variation of magnitude of electric field due to the sphere with respect to radial distance r is rectangular hyperbola in the region r 30 tor

86 In the figure A B C and D are four concentric spheres of radius a 2a 3a and 4a They contain charges 3q 6q 9q and 12q respectively In the beginning switches S and S are open If sphere C is only earthed Aq amount of charge flows from the sphere C to the earth If the sphere B is only earthed then Aq2 amount of charge flows from the sphere B Aqil to the earth the value of 4921 is equal to a 1 c 2 3 K 3a O 2a a V B O 4a b 3 5 d 1 2 D

an mistake a voltmeter is connected in series and ammeter in parallel When the circuit is switched on a Both ammeter and voltmeter will be damaged b Neither the ammeter nor the voltmeter will be damaged c Only the ammeter will be damaged d Only the voltmeter will be damaged If T

A particle of mass m and charge q is located midway between two fixed charged particles each having a charge q and a distance 2 apart If it is displaced along the line connecting them and released Also find its time period for SHM a 4 c 2 mat to q ma Eo 2 q b d mat Eo 2q 2m Eo 2 q

Seawater at a frequency f 9 10 Hz has permittivity 800 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 27ft Then the conduction current density becomes 10 times the displacement current density after time t s The value of x is 800 1 Given 9 x 10 Nm C

4 A small electric dipole of dipole moment p is placed perpendicular to an infinitely long wire of linear charge density The centre of dipole is at a distance r from the wire as shown The electric force on the dipole is ap 1 Gr or n ap 2 A teor 2 an

The figure shows the equipotential contours due to three point charges The labels on the contours are in Volts 3 y axis m O 15 312 1 476 5 828 0 221 71 118 1 828 0 663 6 87 3 20 L 15 10 5 0 x axis m a 357 9 83 0 0 0 53 7 5 15 3 38 9 10 15 The electric field at e is directed normal to the 221 7 V contour and away from the 3121 V contour A charge released from rest on one of these contours will not move along the contour Two of charges are positive and one is negative 118 1 J of work is done to move a charge of 1 Coulomb from d to c along the contour

4 Given a uniform electric field E 5x10 i NC find the flux of this field through a square of 10 cm on a side whose plane is parallel to the Y Z plane What would be the flux through the same square if the plane makes a 30 angle with the X axis

A dipole with charges of magnitude 2nC is placed inside a cavit of a solid conductor The solid conductor has a net charge of 5nC What is the total charge at the outer surface of the conductor Choices a 2nC b 3nC 4nC d 5nC 3

A pendulum bob of mass m carrying a charge q is at rest with its string making an angle 8 with the vertical in a uniform horizontal field E The tension in the string is mg sin e mg cose qE sin 8 min se qE cose