Electric Field and Potential Questions and Answers

Q 19 75 Consider a hemispherical surface with its centre at the origin and its circular base entirely in the X Y plane A uniform electric field exists Then the net electric flux through the hemispherical surface depends on only the X and Y components of only the Z component of E the X Y and Z components of only the magnitude of E and is independent of its individual components

5 Two charges 1 C and 4 uC are separa 12m Where should a unit charge be placed along the line joining the two changes so that the resultant force on it is zero 1 4m from 4 C 3 4m from 1 C 2 8m from 1 C 4 3m from 1 C charges in air E L

field E a particle carrying charge 0 002 C is taken from the origin O to the point 10 along a straight line path Then the particle is taken from A to the point B 1 1 also along a straight line path The coordinates are in metres If the work done on the charge by the electric field in the journeys 0 A and A B is respectively 4 J and 3 J the electric field E is 2500 2500 41 3 5 i 3j 5 Vm V m 500 1 3J VIB V m 500 1 3j 1

5 Let E 2xyi xj be the electric field distribution in the space All are in SI units Then which of the following options is are correct k constant A Electric field is zero on y axis B Electric field will make an angle of 60 with ve x axis at point 2 1 C Volume charge density pv 2 oy D Volume charge density pv oy

Three concentric metal shells of radius a 2a and 3a are given charges Q Q and Q respectively If total electrostatic poten KQ energy of this charge distribution is 2a 3a Q Q Q a 48 then the find value of K

Q 18 75 Two thin conducting spherical shells of radius Rand 2R are fixed concentrically and given total charge Q and respectively Let r denote the distance from their common centre Consider the following statements 1 shells depends on the potential difference between the Q but not on Q the electric field in the region 11 r 2R is proportional to 2 2 Which of these options is correct Both 1 and II are correct 1 is correct and II is incorrect II is correct and 1 is incorrect Both I and II are incorrect

2 26 Define the term electric dipole moment and derive the expression for electric field intensity due to dipole on its equatorial position 3 OR

An electron is fired parallel to uniform electric and uniform magnetic field acting simultaneously and in the same direction The electron 1 Moves along a circular path 2 Moves along a parabolic path 3 Loses K E 4 Gains KF

Q11 75 A small electric dipole with dipole moment p is fixed at the origin with its dipole moment vector pointing in the X direction The electric field due to the dipole at the point a a is KUP 5 16 P TE a 5 P 16 Te a 10 EY FY 3j 10 2 P 16 2 me a Y i 2

Q 6 75 Two infinitely long wires are fixed in the X Y plane along the lines x a and X a The wires are charged uniformly with charge per unit length and respectively The electric field at the point 290 is 2 6 TEA 2 3 E a 2 1

Q8 75 A very long insulating cylinder of radius R is charged uniformly with charge per unit volume P Let E T denote the magnitude of electric field at any point that lies at a distance r from the axis of the cylinder If for some a R and some b R E a E b then ab R a b R ab R

15 The electric potential in a certain region of space along X axis varies as Vx 3x 5 where x is in meter and V in volts The electric field at point 4 0 is a 24V b 12 V c 12V d 24V

Two point charges q and 2q are placed at a certain distance apart Where should a third point charge be placed so that it is in equilibrium 1 on the line joining the two charges on the right of 2q 2 on the line joining the two charges on the left of q 3 between q and 2q 4 at any point on the right bisector of the line joining q and 2a

X PHYSICS 12 Two identical metal spheres possess 60C and 20C of charges They are brought in contact and then separated by 10 cm The force between them is 1 36 10 N 3 36 10 2 N 2 36 10 N 4 3 6 10 N livided into two parts 9 and 42 force of

In finding the electric field using Gauss Law the formula T Al is applicable In the formula is permittivity of free space A is the area of Gaussian surface and qenc is charge enclosed by the Gaussian surface The equation can be used in which of the following situation 1 Only when the Gaussian surface is an equipotential surface 2 Only when E constant on the surface 3 For any choice of Gaussian surface 4 Only when the Gaussian surface is an equipotential surface and IEI is constant on the surface

If the magnitude of intensity of electric field at a distance x on axial line and at a distance y on equatorial line a given dipole are equal then x y is Question Type Single Correct Type 11 1 2 1 2 3 1 2

A point charge Q of negligible dimension is kept near not touching any face the corner A of a cube having faces of negligible thickness as shown in the figure Under the appropriate assumption considering the size of the charge Answer the following questions A 1 a a The flux crossing three faces close to the charge if charge is just inside the cube will be 9 880 9 80 7q 880 9 680

Q18 The electric field in a certain region of space is 5 4 4k 10 N C Calculate the electric flux due to this field over an area of 2 x 10 2m a 6 x 10 Nm C 1 c 10 x 105 N m C 1 b 8 x 10 Nm C 1 d none of the above

9 An electric dipole having point charges qand separated by a fixed distance d is kept under the in of a uniform electric field E such that the axis of the dipole is making an angle 45 with the direction shown in the figure If the electric dipole is allowed to rotate in the ry plane with its center being stationary the magnitude of the set torque acting on the electric dipole B 2gdE C 2 E qdE 2

R AI DUAL CAMERA Eo Uncharged e A iii Two concentric conducting shells a Inner sphere is given charge Q and outer is uncharged 1 of p K d Su when Kis closed 12 R 29 Net charge on outer sphere is zero Net charge on outer sphere is q akash Educational Services Limited Regd Office Aakash Tower 8 Pusa Road New Delhi 110005 Ph 011 4 OL

Q1 Two identical conducting spheres A and B carry equal charge They are separated by a distance much larger than their diameter and the force between them is F A third identical conducting sphere C is uncharged Sphere C is first touched to A then to B and then removed As a result the force between A and B would be equal to Online April 16 2018 a b 3F 4 2 c F d 3F 8

Answer A B C Your Attempt Correct answer the magnetic field at a point on axis is zero the electric field on axis of cylinder is zero The magnetic field outside the conductor is zero Rate this

Q13 The given graph shows variation with distance r from centre of 11 Jan 2019 To To a Electric field of a uniformly charged sphere b Potential of a uniformly charged spherical shell c Potential of a uniformly charged sphere d Electric field of a uniformly charged spherical shell Q14 Three charger r

10 Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges Alternate charges 1 3 5 7 9 have charge q each while 2 4 6 8 10 have charge q each The potential V and the electric field E at the centre of the circle are respectively Take V 0 at infinity Sep 05 2020 1 a V 10q 4 R b V 0 E d 1 c V 0 E 0 10q E 0 10q 4 E R 10g

Q7 For a uniformly charged ring of radius R the electric field on its axis has the largest magnitude at a distance h from its centre Then value of h is 9 Jan 2019 1 R 5 a S R b Z2Z c R d B 2

Which one of the following grap variation of electric field with distance r from centre of a charged spherical conductor of r R 1 E 2 E M 3 E r R 4 1 A sowied

The flux linked with a circuit is given by 31 7 The graph between time x axis and induced emf y axis will be A straight line O Circle O Parabola O None of these

Two identical metal balls are in a weakly conducting medium of conductivity o at large separation We connect a battery between the two objects to charge them upto potential difference V If we disconnect the battery the charge will leak Now potential difference between balls at any time is given by V V e t t where t is equal to 7 to O 2 EO 3 2 4 4 o O TEO

WH in figure in which two Consider situation isolated conducting spheres are connected Initial K is open and K is closed Charge on sphere of radius a is Q Now K is opened and K is closed Now charge on sphere of radius b is q 1 H I K 1 a KQ a Choose the correct answer 1 Terminal potential of battery is equal to www 2 K Kq b 16

A neutral conductor kept in uniform external electric field E and a point charge q is placed inside the conductor not at centre If net force on q is F then force on q due to charge on outer surface of conductor is

charges 20 10 cm apart If N is number of electric field line leaving 20 C charge and N is number of electric field line entering 15 C charge then N N A placed 3 34

Consider the point charges 5 nC and 3 nC are located at 4 0 2 and 5 0 3 respectively The net electric field intensity at point 7 3 1 will be 1 4ax 1 284ay 1 004az 1 4ax 1 284ay 1 004az None of these 1 28ax 1 11ay 1 235az

An extremely long wire is uniformly charged An electron is revolving about the wire in circle of radius The speed of electron is proportional tor Here n DA1 OB 2 c3 2

Two point charges 2 C and 2 uC are being located at points 0 0 1 and 0 0 1 respectively The net electric potential at point P 3 0 4 due to the two charges will be 1733 5 577 8 288 9

Let E1 r and E2 r be the respective electric fields at a distance r from a point charge and an infinite plane with uniform surface charge density o If E ro E2 ro at a given distance ro then A Q 20TT B Q 40KT Oc Q onr OD Q 80TT

A circular disk of radius 7m has surface charge density ps 0 75p where 0 p 7 is the distance of any point on the disk from its centre The total charge stored on the disk is 171 5T 256TT 108TT 62 5

your answer in response area For CORRECT answer you will be awarded 4 Marks and for WRONG answer there is a negatives marking of 1 Mark No marks will be awarded if you leave question unattempted Three point charges each having charge q are kept at the comers of cube as shown find electric field at origin due to this combination side of cube is a I 94 Kq A Ka i j k 2a B Kq i j k D 2 2a kq C kg i j k kq i j k

Write two uses 22 Two charges of magnitudes 2Q and Q are located at points a 0 and 4a 0 respectively What is the electric flux due to these charges through a sphere of radius 3a with its center at the origin After come time the battery is

d becomes zero A system consists of two charges 4 C and 3 C with no external field placed at 5 cm 0 0 and 5 cm 0 0 respectively The amount of work required to separate the two charges infinitely away from each other is a 1 1 J c 2 51 Two charges of magnitude 5 nC and b 21 d 31 38 re th

Four equal positive charges each of value Q are arranged at the four corners of a square of side a each A body of mass m and having a unit positive charge is in equilibrium at a heighth above the centre of the square Find Q

2 0 50 A 3 0 75 A 4 1 0 A 7 The electric field intensity due to a dipole of length 2 cm 7 and having a charge of 80 C at a point on the axis at distance 20 cm from centre of dipole in air is 1 18 x 10 N C 2 36 x 10 N C 3 18 x 10 N C 4 36 x 10 N C 2 0 50 A 3 0 75 A 4 1 0 A farge faya 20 cm 1 18 x 10 N C 2 36 x 10 N C 3 18 x 10 N C 4 36 x 10 N C 80 C effung 2cm fanga faya

SolveLancer Test Q R R R K N R Figure shows a metal sphere of radius R It has 2 cavities of radius as shown and the charges Q and Q placed in them Which of the following statement is correct 1 Electric field outside sphere is zero every where 11 Electric field inside the cavities is zero III The potential outside the sphere is same at every point IV surface charge density of the outer surface doubles if Q is replaced Q SolveLancer Test a II IV b III IV c I II III d I III

Polar molecules are the molecules 1 having zero dipole moment 2 acquire a dipole moment only in the presence of electric field due to displacement of charges 3 acquire a dipole moment only when magnetic field is absent

60 Two equal positive charges q are placed at the vertices B and C of an isosceles triangle of bas a and height h 3 3a 2 as shown in the adjacent figure When a charge of is placed at A it found that at a point inside the triangle the net electric field due to the three charges vanishes this point is at a height h 3 then what is q A h B a A d 3 3q B d 3 3q C d 3q D q 3q h 3

A uniform but time varying magnetic field B t exists in a circular region of radius a and is directed into the plane of the paper as shown The magnitude of the induced electric field at point p at a distance r from the centre of the circular region and emm too on a Is zono B t X X X X X X X XX X X X X X X X X X X X X X X X X X X a eser P X X X X X X b Doorenses s as 1 r

A rod AB of length a and mass m is positively charged with charge Q It is pivoted at end and is hanging freely in uniformly charged p charge per unit volume spherical region Centre of spherically charged region is O which is at a distance a from point of suspension of rod Find the initial torque on the rod about O A B 1 Q 6

d An acce ting Two identical charged spheres suspended from a common point by two massless strings of lengths are mutually at a distance d d 1 apart because of their mutual repulsion The charges begin to leak from both the spheres at a constant rate As a result the spheres approach each other with a velocity v Then v varies as a function of the distance x between the spheres as a vox b vox d 2

Example 53 A ball of mass m 1 g is suspended from a thread in a capacitor In the absence of any charges the period of oscillation of the ball is T 0 628 s After the capacitor and the ball are charged time period becomes T 0 314 s What force by the electric field is exerted on the ball What is the length of the thread Find the period of oscillation if the sign of the charge on the ball is reversed

A point electric dipole is at the origin of coordinates with its dipole moment along the positive Z axis Consider a circular disc of radius R with its centre at z L and its plane perpendicular to the Z axis The modulus of the electric flux due to the dipole through the disc is maximum when R is equal to 3 A infinity D L 2 B 2 L C L

The insulation property of air breaks down at E 3 105 V m The maximum charge that can be given to a sphere of radius 3 m is 3 x 10 4 C 9 10 4 C 6 x 10 4 C 4 x 105 C