Electric Field and Potential Questions and Answers

A uniform electric field pointing in positive x direction exists in a region Let A be the origin B be the point on the x axis at x 1 cm and C be the point on the y axis at y 1 cm Then the potentials at the points A B and C satisfy 1 V VB A 3 V V 2 V VB A 4 VA Vc

The distance between the two charges 25 C and 36 C is 11 cm At what point on the line joining the two charges the intensity will be zero at a distance of A 4 cm from 36 C B 4 cm from 25 C C 5 cm from 36 C D 5 cm from 25 C

respectively Initially both the keys are open The connection to earth of sphere A through K is such that the wire is insulated from shells B and C Now a charge Q is given to the shell B and key K is closed so that shell A is earthed without touching the shells B and C C B A A 4a B If U and U represent the electrostatic potential energies of the system before and after closing the switch K then 16 27 27 16 2a 21 3 4d U is

String 1 in the figure has linear density 2 50 g m and string 2 has linear density 3 20 g m A student sends pulses in both directions by quickly pulling up on the knot then releasing it She wants both pulses to reach the ends of the strings simultaneously Figure 1 Figure String 1 4m SE String 2 1 of 1 Y Part A What should the string length L be Express your answer with the appropriate units HA Value Submit m Value Request Answer Part B What should the string length L be Express your answer with the appropriate units COM m

Charge 20 and Q are placed as shown in figure The point at which electric field intensity is zero will be somewhere Q 2Q A Between Q and 20 B On the left of Q C On the right of 20 D On the perpendicular bisector of line joining the charges

A heating element using nichrome connected to a 230 V supply draws an initial current of 3 2 A which settles after a few seconds to a steady value of 2 8 A What is the steady temperature of the heating element if the room temperature is 27 0 C Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1 70 x 10 4 C 1

cm Let Consider a dipole with dipole moment 4 8 x 10 30 c a point P lies 4 1 x 10 m away from centre of dipole Match the values of potentials given in column II with column I and mark the correct choice from the given codes Column I Point is along axis of dipole p nearer to positive charge ii Point is 45 above the axis but q nearer to positive charge i iii Point is 45 above the axis but r nearer to negative charge Codes a i p ii r iii q b i q ii p iii r c i r ii q iii p Column II 1 8 10 V 1 8 10 V 2 6 10 V

At the three corners of an equilateral triangle charges are placed as shown in figure The magnitude of electric field at point O is a c 1 20 4 2 2 1 4 b d 1 Q 4 1 2 3 4

A circuit shown in the figure in which k is closed and k is open Inductor L can b connected in series to capacitor C by dosing switch k and opening k 20 V R 200 www C 2 F C 3 F 6000002 L 2Hk A The switch ky is closed and k is opened for long time The charge on capacitor C will be 24 C B Att 0 when capacitors are fully charged switch k is opened and switch k is closed so that inductor is connected in series with capacitor C The maximum X charge will appear on capacitor C at time t is sec 500 C Att 0 when capacitors are fully charged switch k is opened and switch k is closed so that inductor is connected in series with capacitor C The maximum T charge will appear on capacitor C at time tis sec 1000 D The maximum energy in inductor approximately will be 0 144 mJ

A point charge Q 10 2 C is held fixed at the origin A second point charge q 4 C is released from rest at point A at distance d 3 cm from the origin What is the kinetic energy in unit J Joule of the charge q when it reaches point B at distance D 19 cm from the origin Enter your answer as positive decimal number with 1 digit after the decimal point Don t enter the unit J 8 25 pm

Fig 2 28 shows four point charges at the corners of a square of side 2 cm Find the magnitude and direction of the electric field at the centre O of the square if Q 0 02 C Use 1 4 TEO 9 x 10 N m C 2 Ans 9 2x105 NC parallel to side BA 2 Q 2Q A D Q Fig 2 28 B

We have two electric dipoles Each dipole consists of two equal and opposite point charges at the end of an insulating rod of length c The dipoles are placed along the x axis at a large distance r apart oriented as shown below Mark the correct statement s ao d

viii For a spherically symmetrical charge distribution electric field at a distance r from the centre of sphere is E kr where k is a constant What will be the volume charge density at a distance r from the centre of sphere 9kr6

A small particle of mass m 69 mg has a negative charge of q 5 C This particle is left at rest beneath an insulating charged plane sheet with uniform surface density of charge o What should be the value of o in unit nC m2 nano Coulomb per meter square to held the particle suspended at rest beneath the plane Enter your answer as positive decimal number with 2 digits after the decimal point Don t enter the unit nC m2 Remark the unit of mass in the international

Two concentric spheres of radii 1 m and 2 m have simila charges with equal surface densities o The electric potential at the common center is 0 300 0 2000 b w

A point charge q is located at the centre of the spherical layer of uniform isotropic dielectric with relative permittivity k The inside radius of the layer is equal to a and the outside radius is b Find the electrostatic energy inside the dielectric layer q 8Tk o Eb 6 a do tanquo reit

Two long parallel wires are located in a poorly conducting medium with resistivity p The distance between the axes of the wires is equal to 1 the cross section radius of each wire equals a In the case a I find 1 The current density at the point equally placed from the axes of the wires by a distance r if the potential difference between the wires is equal to V 2 The electric resistance of the medium per unit length of the wires VI 2pr In pin

vi In a system of two concentric spherical conducting shells charge q is given to both inner and outer shells as shown in figure 1 361 Inner shell is connected to earth by a switch Find the amount of heat produced when switch is closed 5Kq 8a 200 9 S Figure 1 361 2a q

ns Two large circular discs separated by a distance of 0 01 m are connected to a battery via a switch as shown in the figure Charged oil drops of density 900 kg m are released through a tiny hole at the center of the top disc Once some oil drops achieve terminal velocity the switch is closed to apply a voltage of 200 V across the discs As a result an oil drop of radius 8 x 10 7 m stops moving vertically and floats between the discs The number of electrons present in this oil drop is neglect the buoyancy force take acceleration due to gravity 10 ms 2 and charge on an electron e 1 6x10 19 C 6 l Resonance qE mg Resonance Eduventures Ltd Reg Office Corp Office CG Tower A 46 52 IPIA Near City Mall Jhalawar Road Kota Raj 324005 Ph No 91 744 2777777 2777700 FAX No 91 022 39167222 o know more sms RESO at 56677 Website www resonance ac in E mail contact resonance ac in CIN U80302RJ2007PLC024029 Toll Free 1800 258 5555 7340010333fb com ocedu twitter com ResonanceEds www youtube com resowatch blog resonance ace This solution was download from Resonance JEE ADVANCED 2020 Solution portal PAGE 2 q mg E 900x Switch 200 V JEE ADVANCED 2020 DATE 27 09 2020 OFFICIAL PAPER 2 PHYSICS 900x4 8 10 7 x10 3 2x104 200 0 01 x512x10 21x10 0 01 m

101 Six charged particles each of magnitude q lie on the circumference of a ring of radius R as shown in the figure Find the magnitude of net electrostatic force 1 acting on the charge particle at P k 4RE0 q q 30 30 P 9 60 9 30 30 9

Charge is distributed throughout spherical region of space in such a manner that its volume charge density is given by relation p br2 0 r R where b is positive constant Total charge enclosed within sphere of radius R is rbR bR5

ELECTROSTATICS 1 Page 2 Ex 31 A thin half ring of radius R 20 cm is uniformly charged with a total charge q 0 70 nC Find magnitude of the electric field strength at the curvature centre of this half ring

56 Four equal positive charges are fixed at the vertices of a square of side L Z axis is perpendicular to the plane of the square The point Z 0 is the point where the diagonals of the square intersect each other The plot of electric field due to the four charges as one moves on the Z axis is ET E a c O ET 2L L N Z N b d Et LY L Z N

69 An electron goes from one equi potential surface to another along one of the four paths shown in the diagram Rank the paths according to the work done by the electrostatic force from the least to the greatest 90V 4 80V a 1 2 3 4 c 1 3 4 and 2 equal 3 70V 60V 50V b b 4 3 2 1 baik d 4 and 2 equal 3 1

An alpha nucleus of energy mu bombards a heavy nuclear target of charge Ze Then the distance of closest approach for the alpha nucleus will be proportional to HRESHOW A 2 B 1 m HE Correct Answer 1 Ze Lerum UPOZ PRVENS

Ex 25 In the given arrangement of a charged square frame find field at centre The linear density is as shown in figure Sol E F due to 1 sin 45 sin 45 sin 45 sin 45 2 2KX l E F due to 2 E F due to 3 2K l E F due to 4 4 2KX l 6 2K2 l 8 2K2 l 2 14 32 3 4 42 221

radius b is centered at the origin in the yz plane The annulus is filled with positive charge of density The electric field along the x axis is where k Z 1 AREZ 0

The coil a dynamo is rotating in a magnetic field The developed induced e m f changes and the number of magnetic lines of force also changes Which of the following condition is correct A Lines of force minimum but induced e m f is zero B Lines of force maximum but induced e m f is zero Lines of force maximum but induced e m f is not zero D Lines of force maximum but induced e m f is also maximum Answer B Solution Lines of force maximum but induced e m f is zero

63 Four charges of 6 C 2 C 12 C and 4 C are placed at the corners of a square of side 1 m The square is in x y plane and its center is at origin Electric potential due to these charges is zero everywhere on the line a x y z 0 c x 0 y b x 0 z d x z y 0

Three infinite line charges of charge per unit length 2 22 and are kept in xy plane parallel to the y axis They pass through x a x a and x 2a respectively Find the electric field at different points on the x axis A At x 2a E C At x 3a 2 E 25k2 i 6a 64k 5a k B At x 0 E a 2ka 3a D At x 0 E 5

TPH Two point charges of 1 C and 1 C are separated by a distance of 100 A point Pis at a distance of 10 cm from the mid point and on the perpendicular bisector of the line joining th two charges The electric field at Pwill be a 9 NC 1 c 90 Vm 1 b 0 9 Vm 1 d 0 09 NC 1 more of a rigid square

A ring carries a linear charge density on one half and the linear charge density of same magnitude but opposite sign on the other half A the component of electric field along the axis of ring at all points on the axis is zero B the component of electric field along the axis of ring at point on the axis is zero only at the centre C the resultant field at the centre is zero D the electric field at all points on the axis of ring is perpendicular to axis

172 Four persons P Q R and S of same mass travel with same speed u along a square of side d such that each one always faces the other After what time will they meet each other 1 u 2d P u S u U R d 2d 2 3u

In a conducting sphere there is a cavity of arbitrary non spherical shape Inside the cavity a charge Q is placed as shown The induced surface charge density on inner surface of cavity and outer surface of conductor respectively will be Q Uniform non uniform Uniform uniform Non uniform uniform Non uniform Non uniform

In the given arrangements the charges given to the metallic plates A B and D are Qo Qo and 2Qo respectively the metal plate C is neutral separation distance between the plates is d d is very small when compared to plate area dimensions Initially all switches are open A 110 S B H111 S 12 d CD S3 120 When all the switches are closed The amount of the charge passing through the

Two extremely large nonconducting horizontal sheets are parallel and separated by distance d 4 3 cm The upper sheet carries uniform surface density of charge o 541 pC m and the lower sheet carries uniform surface density of charge o 122 pC m What is the magnitude E of the electric field in unit N C Newton per Coulomb at a point P outside the two sheets at distance D 7 6 cm above the upper sheet Enter your answer as positive decimal number with 1 digit after the decimal point Don t enter the unit N C Activate Wi Go to Settings

2 5 points Figure below represents electric field lines produced by two point charges q and q2 What are the magnitudes and signs of the two charges in term of a reference positive charge qa O 91 q and q2 2q Oq1 q and q2 29 Oq1 q and q2 q O 91 q and q2 9 Activa Go to S

A dipole of dipole moment p P j is placed at point 1 0 There exists an electric field E 2ax 2by 2cy Then A B C force on dipole is 2p c force on dipole is p 2c 4b1 j Torque on dipole about its centroidal axis is 2p ak

A non conducting infinite rod is placed along the z axis the upper half of the rod lying along z 0 is charged positively with a uniform linear charge density while the lower half z 0 is charged negatively with a uniform linear charge density The origin is located at the junction of the positive and negative halves of the rod A uniformly charged annular disc surface charge density o of inner radius R and outer radius 2R is placed in the x y plane with its centre of the origin The force on the rod due to the disc is 20 R Eo A B GAR 280 C GAR Eo D o R 380

The work done in taking a charge q once round a circle of radius r and having a charge Q at centre is 9 Q 4 26 qQ 4 Tor qQ 4 or O Zero

33 1000 similar electrified rain drops merge together into one drop so that their total charge remains unchanged The electric energy gets increased by b 200 times d 400 times a 100 times c 300 times CURMEDY

Two charges 5 C and 10 C are placed 20 cm apart The potential energy of the system is O 2 25 J 4 5 J O 2 25 J O 4 5 J

An electric field of strength E 1 0 kV cm produces polarization in water equivalent to the correct orientation of only one out of N molecules Find N The electric moment of a water molecule equals p 0 62 10 2 C m

A charge of 2 C is uniformly distributed on a spherical shell of radius 5 m Electric potential at the centre of sphere is O Zero O 4 5 10 V O 7 2 10 V O 3 6 10 V

Three charges Q Q2 and q are located on the same line as shown in the figure If Q 9 00 C Q 8 00 C q 5 00 C a 30 0 cm and b 40 0 cm what is the x component F of electric force on the charge q expressed in Newton N Enter Fx as algebraid number with 2 digits after the decimal point Fx is positive if it is along positive x axis to the right and negative if it is along negative x axis to the left Enter only the numerical value don t enter the unit N Q Q a 9 b Activate V Go to Setting

The X Y Z space has an infinite charged sheet having charge density on the Y Z plane A negative charge particle Q is placed at a 0 0 The variation of net electric field on x axis is shown in the figure Then choose the incorrect option A Q 62ra B Q 64 a 50 C The net electric field at the point a 2 0 0 is 2 50 D At point 5a 2 0 0 the net electric field is 18 a 0 0 2a 0 0

A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength x10 Vm 81 7 When the field is switched off the drop is observed to fall with terminal velocity 2 x 10 ms Given g 9 8 ms 2 viscosity of the air 1 8 x 10 5 Ns m2 and the density of oil 900 kg m 3 the magnitude of q is A 1 6 x 10 19 C B 3 2 x 10 19 C C 4 8 x 10 19 C D 8 0 x 10 19 C

An electric dipole when placed in a uniform electric field has minimum potential energy The angle between dipol moment and electric field is O T 22 O Zero

1 The entire x 0 plane of a cartesian coordinate system is a thin insulating sheet of uniform surface charge density o A thin insulating spherical shell of radius a and uniform surface charge density 20 is centred at the point A 2a 0 0 The electric potential at A is arbitrarily fixed as zero O A The electric field E at the point B 2a a 2 0 is 2 B The electric potential at the point C a 2 0 0 is oa 12 C The electric potential at the point D 2a 0 0 is 3oa 2 a D The electric field E at the point B 2a 0 is 2 0 80 2a 5 5 COM

A point charge q 5 00 C is held fixed in space From a horizontal distance of 4 00 cm a small sphere with mass 4 00 x 10 3 kg and charge q2 2 00 C is fired toward the fixed charge with an initial speed of 42 0 m s Gravity can be neglected Part A What is the acceleration of the sphere at the instant when its speed is 21 0 m s Express your answer with the appropriate units a HA Value Units