Electric Field and Potential Questions and Answers

111 A series LCR circuit has resonant tangular frequency oo and a large quality factor Q The approximate form for its impedance at high ble frequencies in terms of R 6 Q and wo here is the angular frequency of of ac source and j 1 and R is not very high 1 Z R 1952 Q Rw 2 Z 3 2 3 Z 4 Z VEGEDT 8 QRwo 5 QRw Est

Test 1 Online 13 It is observed that as one moves along positive x axis the electrostatic potential reduces One may conclude that the direction of electric field 1 Must be along x axis 2 Must be perpendicular to x axis 3 May be perpendicular to x axis 4 May be along x axis 14 A parallel plate capacitor has a uniform electric field E in space between the plates If the distance between the plates is d and area of the plate is A the energy stored in the capacitor is 1 EAd 3 E Ad 4 E 15 A capacitor of capacitance C is charged upto 90 V and then connected to an uncharged capacitor of capacitance 2C The final potential difference across each capacitor will be 1 45 V 3 90 V 16 In a certain region potential is given by V K 2xy The electric field at 1 1 has magnitude 1 2 k 2 2 2 k Medical 3 k 2 1 2 30 V 4 60 V 17 The variation of electrostatic potential as a function of distance from a point charge is best represented by X 12 ITutor All India Aakash Test Series for NEET 2021 18 On an insulated rod of length charge Q is uniformly distributed and a point charge q is placed at a distance d from one of its ends as shown The electric force on q is Q 2 3 K qQ 4d d c 9Q 4 9Q n Foundations 4TE X d Divisions of ash A4 C charge is placed in some gaussian surface such that outward flux is 6 What additional charge is needed to be placed inside the surface such that there is net inward flux of magnitude 66 1 6 C 2 14 C 3 28 C 4 10 C 20 When a polythene is rubbed with wool it develops a charge 3 2 x 10 7 C The number of electrons transferred is 1 2 10 3 10 d X 2 8 x 10 0 4 2 x 10 2

Two large conducting sheets are kept parallel to each other as shown In equilibrium the charge density on facing surfaces is d and o Which of the following may not be electric field at A 1 N A So 0 0 i 5 2 0 1 0 0 i

Point charges 4q q and 4q are kept on the X axis at points x 0 x a and x 2a respectively Then 1988 a b c d only q is in stable equilibrium none of the charges is in equilibrium all the charges are in unstable equilibrium all the charges are in stable equilibrium

23 A solid conducting sphere of radius a has a net positive charge 2Q A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge Q The surface charge density on the inner and outer surfaces of the spherical shell will be a c 0 2Q Q 2 4 b 4 c Q 4TC 2 C b Q Q 2 4 b 4 c 2 d None of these b

5 A beam of cathode rays is subjected to crossed electric E and magnetic fields B The fields are adjusted such that the beam is not deflected The specific charge of the cathode rays is given by CBSE AIPMT 2010 SAMB a 2VE 2 VB E c b 2VE B d E 2VB

In the circuit shown in figure the transistor used ha a current gain 100 What should be the bia resistor Rg so that V 5V necglect VBE CE RB B 1 2 10 a 3 1 x 1006 2 1 kQ C E VCE 10 V 5V 20 2 200 10 4 500 Q LB MORD

A point charge is brought in an electric field The electric field at a nearby point a will increase if the charge is positive b will decrease if the charge is negative c may increase if the charge is positive d may decrease if the charge is negative

the circuit shown below is X wwwwwww 50 2 50 2 1 10 volt JEE FOU akash Edaten wwwwww 30 52 Y 10 52 2 92 80 volt points x and y in VA 2 20 volt 4 40 volt

For the circuit shown in figure the potential difference between points a and b is 2V 1 2 4 V 3 2 V 102 www 192 www www 192 452 T4V b ww 12 2V 2 2 8 V 4 3 2 V

21 The centres of two identical small conducting spheres are 1 m apart They carry charges of opposite kind and attract each other with a force F When they are connected by a conducting thin wire they repel each other with a force F 3 What is the ratio of magnitude of charges carried by the spheres initially a 1 1 b 2 1 d 4 1 c 3 1

A rod lies along the x axis with one end at the origin and the other at x o It carries a uniform charge AC m The electric field at the point x a on the axis will be AMU Med 2012 2 4 a E c 2 4 2 2 b E 2 d E 2

1 Figure shows the electric lines of force emerging from a charged body If the electric field at A and B are E A and EB respectively and if the distance between A and Bis r then A r B C

Two point charges of 0 2 C and 0 2 C are separated by 108 m Determine the electric field a an axial point at a distance of 0 1 m from thei midpoint Use the standard value of Eo

A positive charge is uniformly distributed along a circular ring of radius R A small test charge qis placed at the centre of the ring Then q ON A If q 0 and is displaced away from the centre in the plane of the ring it will be pushed back towards the centre B If q 0 and is displaced away from the centre in the plane of the ring it will never return to the centre and will continue moving till it hits the ring C If q 0 it will perform SHM for small displacement along the axis D q at the centre of the ring is in an unstable equilibrium within the plane of the ring for q 0 E 19 36

The terminal potential difference of a cell is greater than its emf when it is a being discharged b open circuit c being charged d being either charged or discharged

15 Figure shows electric field lines in which an electric dipole p is placed as shown Which of the following statements is correct NCERT Exemplar 9 P q a The dipole will not experience any force b The dipole will experience a force towards right c The dipole will experience a force towards left d The dipole will experience a force upwards

Two identical charges are placed at a separation of 1 0 m What should be the magnitude of each charge so that each one repels the other with a force of 36 kg wt 8 10 mS

4 1 What is the force between two small charged spheres having charges of 2 x 107C and 3 x 107C placed 30 cm apart in air

Two identical positive charges are placed on the y axis at y a and y a The variation of V electric potential along x axis is shown by graph V 1 3 V X 2 4 X

A monochromatic light of frequency v is incident on isolated metallic sphere of radius r The threshold frequency is vo vo v Find the number of photoelectrons emitted before the emission of photoelectrons will stop

Which of the following set up can be used to verify law wwwww www www wwwww wwww A A b A d www www A 2003 2M H

2 28 Two fixed identical conducting plates o and B each of are charged to Q and q respectively where Q q 0 A third identical plate y free to move is located on the other side of the plate with charge q at a distance d figure The third plate is released and collides with the plate B Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst B and y YA a B Y TdA q Q a Find the electric field acting on the plate y before collision b Find the charges on and y after the collision c Find the velocity of the plate y after the collision and at a distance d th

4 A positive point charge is placed inside a spherical metallic shell The electric field lines are represented by 2003 A B C D

1 54 8 Figure 1 54 shows four point charges at the 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 2Q 2 cm Use 2 cm 1 41E0 DE Q 2Q B Q 2 cm 2 cm 9x10 Nm C ISCE 98 Ans 9 2 x 105NC 1 parallel to BA

20 A plane electromagnetic wave Ez 100 cos 6 10 t 4x V m propagates in a medium of dielectric constant 1 1 5 3 2 4 2 2 0 4 4 0

um current from a combination of cells now should the cells be grouped a Series b Parallel c Mixed d Depends upon the relative values of external and internal resistance

2 Two concentric metallic spherical shells are given equal amount of positive charges Then a the outer sphere is always at a higher potential b the inner sphere is always at a higher potential c Both the spheres are at the same potential d no prediction can be made about their potentials unless the actual value of charges and radii are known

An electric dipole has a fixed dipole moment p which makes angle with respect to X axis When subjected to an electric field E E it experiences a torque T tk When subjected to another electric field E 3E j it experiences a torque T T The angle

A thin wire is bent in the form of a semicircle of radius 1 m as shown in the figure If carries a total charge of 16 2 coul uniformly distributed over its entire length P is a point on the axis of the semi semicircular ring at a distance of 1 m from O Find the component of electric field in volt m along z axis at point P y C P X

Electrostatics has Statement 1 and Statement 2 Of the four choices given after the statements choose the one that best describes the two statements An insulating solid sphere of radius R has a uniformaly positive charge density p As a result of this AIEEE 2012 uniform charge distribution there is a finite value of electric potential at the centre of the sphere at the surface of the sphre and also at a point out side the sphere The electric potential at infinity is zero Statement 1 When a charge q is taken from the centre to the surface of the sphere its potential qp energy changes by 3 0 pr 3 0 Statement 2 The electric field at a distance r r R from the centre of the sphere is 1 Statement 1 is true Statement 2 is true and Statement 2 is the correct explanation of Statement 1 2 Statement 1 is true Statement 2 is true and Statement 2 is not the correct explanation of statement 1 3 Statement 1 is true Statement 2 is false 4 Statement 1 is false Statement 2 is true

If a point charge is placed is front of a grounded conducting sphere the induced charges on the surface of the sphere is non uniform To calculate the force on Q due to this sphere or electric field at any point on surface of sphere or outside it an image charge must be kept on the line joining centre of sphere and Q To find this image charge and its position we make the potential due to Q and image charge together on any two points on the surface of sphere equal to ZERO Once these value are obtained force on conductor due to Q will be equal to force between image charge and Q Also field at any point on the sphere or outside will be equal to net field due to Q and image charge Now answer the following questions 9 Force between the sphere and Q is equal to Q Rd 4 Eo d R 2Q Rd A C En 2R d R B P Q Rd 4 Eo 2R d 2 Q Rd 4 R 20 D Image charge d 4

Surface charge density o E I 2 II I Area A Surface charge density o FIGURE 2 25 The parallel plate capacitor 74 the plates is disc the area of each plate and d the separation between them The two plates have charges and 9 Since d is much smaller than the linear dimension of the plates d A we can use the result on electric field by an infinite plane sheet of uniform surface charge density Section 1 15 Plate 1 has surface charge density o 9 A and plate 2 has a surface charge density o Using Eq 1 33 the electric field in different regions is Outer region I region above the plate 1 E O 280 O 280 0 2 39

8 A long cylindrical shell carries positive surface charge o in the upper half and negative surface charge o in the lower half The electric field lines around the cylinder will look like figure given in figures are schematic and not drawn to scale JEE Main 2015 1 3 2 4

Two thin conducting plates very large parallel to each other carrying total charges A and 20 A respectively where A is the area of each plate are placed in a uniform external electric field E as shown Find the surface charge on each surface E

Find the electric field at the origin due to the line charge ABCD of linear charge density 2 a 0 0 B y C 0 a 0 a 0 0

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

A parallel plate capacitor has capacitance C If the charges the plates are Q and 30 find the i charges at the inner surfaces of the plates ii potential difference between the plates iii charge flown if the plates are connected iv energy lost by the capacitor in iii v charge flown if any plate is earthed 2 d

3 Consider the situation of figure 29 Q3 The work done in taking a point charge from P to A is WA from P to B is WB and from P to C is Wc a WA WB Wc c WA WB Wc b WA WB Wc d None of these C 1 I 1 q B A P

a region sible that B region to 10 Let E and B denote electric and magnetic fields in a frame S and E and B in another frame S moving with respect to S at a velocity Two of the following equations are wrong Identify them b E E d E E vB it s a By B VE 2 C c By B vE UB

Two identically charged sphere are suspended by string of equal length The strings make an angle of 30 with each other When suspended in a liquid of density 0 8 g cc the angle remains same What is the dielectric constant of liquid Density of sphere 1 6 g cc 1 1 2 30 15 mg 3 3 F 4 4

5 Two thin concentric hollow conducting spheres of radii R and R bear charges Q and Q respectively If R R then the potential of a point at a distance r from the centre R r R is 1 Q Q r 1 ATEO 4180 1 Q 2 1 2 4E0 4 AC Q Q r R R Q

A current of magnitude 1000 005 mA is entering and simultaneously a current of 1000mA is leaving a metallic sphere of radius 20 cm Find the time at which potential of sphere becomes 1 kV 40 1 ms 2 40 ms 3 9 ms 4 10 ms 9

Q 16 4 1 01 13 A particle is projected in a region where an electric field E E with a velocity from the origin at times t 0 If m is the mass of the particle and q is the charge of the particle then the momentum vector of the article when its x coordinate becomes is neglect gravitational effect

19 Three conducting infinite plates are given having charge density o 20 and 4o respectively Electric field at point p is given by 1 20 Co 2 760 Co 20 40 18 76 3 20 26 46 26 Fe 460 36 46 26 226 4 70 80

Q TUR4 r be the charge density distribution for a solid sphere of radius R and total charge Q For a point P inside the sphere at distance r from the centre of sphere the magnitude of electric field is AIEEE 2009 4 144 Let p r 1 4 2 2 Qr 4 R4 3 Qr 3 R4 4 0

Three charges of respective values 2 C 2 2 C and 2 C are arranged along a straight line as shown in the figure Calculate the total electric field intensity due to all three charges at the point P P 1864 10 2 C 1m 2 2 C 1m 2LLC

Two charges of magnitude 5 nC and 2 nC one placed at points 2 cm 0 0 and x cm 0 0 in a region of space where there is no other external field If the electrostatic potential energy of the system is 0 5 J The value of x is 1 20 cm 2 80 cm 3 1

2 k Electric field in a region is found to be E 3yj The total energy stored in electric field inside the cube shown will be A 9a C a B 3 a D 0 D None of these Z a AY 0 a

A rectangular tank of mass m and charge Q over it is placed on a smooth horizontal floor A horizontal electric field E exists in the region Rain drops are falling vertically in the tank at the constant rate of n drops per second Mass of each drop is m Find velocity of tank as function of time