Electric Field and Potential Questions and Answers

0 A plane electromagnetic wave E 100 sin 5 x 108 t 3x V m is propagating through a medium The refractive index of the medium is NCERT Pg 276 1 1 6 3 1 8 2 1 7 4 1 9

Two charged parallel plate capacitors each with separation between plates equal to d are separated by a large distance L d Then the force of interaction between them is proportional to 1 1 d 2 d L4 3 1 d 4 d L

Q 26 A cylinder of radius a 0 1 m is placed as shown below in a uniform electric field of E 50iN C The total electric flux through the cylinderis 24 a 1 5 7N m C b 3 14 Nm C ONm C d 5 0 Nm C

21 If four identical charged particles of charge q are kept at the vertices of regular pentagon then force acting on charge q kept at centre of polygon here r is the distance of vertex from centre of polygon 1 ka 3 6kq p 2 5kq p2 4 Zero and mass m is released

An electric dipole is placed in an uniform electric field with dipole axis making an angle 0 with the direction of electric field For dipole to be in stable equilibrium 80 equals to 1 T 6 3 0 2 4 EM EN 3 2

An electron moving with the speed 5 108 m s is projected parallel to the electric field of intensity 1 10 N C Field is responsible for the retardation of motion of electron Find the distance travelled by the electron before coming to rest for an instant me 9 x 10 31 kg e 1 6 x 10 19 C 1 7 m 2 0 7 mm 3 7 cm 4 0 7 cm

Q 20 An a particle is moved from point A to point B via points C If VA 10 volt VB 35 volt Vc 20 volt then work done is approximately equal to 2 40 10 10J 4 80 10 10J 1 20 x10 10J 3 60 x10 10J

The magnitude of electric field due to an short electric dipole at a distance r from its centre in equatorial position is E If the dipole is rotated through an angle of 90 about its perpendicular axis the magnetude of electric field at the same point wi be 1 E F biuose 2 E 4 4 25

A very thin Metallic spherical shell contain a charge Q over it A point charge q is placed inside the shell at a point T separated from a center by a distance a Another point charge q is placed at a distance b from center of sphere outside the sphere as shown in fig now select the correct statement T R D 91 A Electric field at center due to charge over outer surface of shell is zero LBL Electric field at the centre due to charge over outer surface of shell is 1 C Electric potential at the centre due to all charge in the space is 4 0 1 Electric potential at the center due to all charges in space is 5 2 4 0 La 9 4 b OR OR q Q R 2

Two positive lons each carrying a charge q are separated by a distance d If F is the force of repulsion between the ions then the number of electrons missing from each ion will be e being the charge on an electron 1 4 e Fd e 2 4 Fe d Amc Ed

20 Three concentric spherical shells have radii a b and c a b c and have surface charge densities o o and o respectively If V V and Vc denote the potentials of the three shells then for c a b we have C AIPMT Prelims 2009 1 Vc VB VA 3 Vc VB VA 2 VC Vc VB 4 VC VA V VA VB

Electric charge on sphere A is equal to electric charge of sphere B The spheres are joined by conducting wire Then the wire is removed the common potential on each sphere is found to be v The charge on each sphere before joining is A 1 Question Type Single Correct Type 2 Vr 2K 1 V 2K 1 12 B

Six point charges are placed at the vertex of regular hexagen of side a then what will be potential energy of charge Q centre A B 6KQ a 2KQ a 3KQ a zero Q Q a O O Q

Two charged particles a and b of same mass are accelerated through the same potential difference On entering a region of uniform magnetic field they describe circular paths of radii R and Ra respectively The ratio of charges of a and b is 1 R R R U 1 2 4 R R

Two point charges exert a force 20 N when placed in a free space When this system is placed in dielectric constant 5 then net force on each charge is B 20 5 N 4 N 20 3 N 5N medium hav

21 An infinitely long cylindrical wire of radius R carries a current whose density varies as j br where b is a constant and r is the distance from axis of the wire Choose the correct option regarding magnetic field of induction as function of radial distance from axis of cylinder fr is less than R B Hobr 4 C if r is greater than R B HobR4 2r J B ifr is less than R B Hobr 2 D if r is greater than R B HobR4 2

4 Two metallic spheres of radii 1 cm and 3 cm are given charges of 1 x 10 2 C and 5 10 C respectively If these are connected by a conducting wire the final charge on the bigger sphere is AIPMT Mains 2012 1 2 10 C 2 3 10 C 3 4 x 10 2 C

Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart The spheres are brought into contact and then taken to their original positions Now the two spheres repel each other with a force whose magnitude is equal to that of the initial attractive force The ratio between initial charges on the spheres is Kerala PET 2008 a 3 8 only b 3 8 only c 3 8 or 3 8 d 3

54 6 The electric potential in a certain region is expressed by V 6x 8xy 8y 6yz 4z volts The magnitude of the force acting on a charge of 2 C situated at the origin will be 1 2 N 2 6 N 3 8 N 4 20 N 55 Which statement is true

39 I Charges q and 29 in FIGURE P23 39 are located at x a Determine the electric field at points 1 to 4 Write each field in component form 5 0 nC 2 0 cm 4 0 cm FIGURE P23 36 10 nC 10 nC FIGURE P23 39 20 2a 29 a a 2a 9 2a

A sheet of charge ps 2nC m is present at the plane x 3 in free space and a line charge P 20nC m is located at x 1 z 4 Then the magnitude of electric field intensity in V m at the origin is

There is a cube of side a whose face ABCD is in in X Y pl ane and the positions of the vertices A B C D are A 0 0 0 B 0 a 0 C a a 0 and D a 0 0 There is a charge q which is at a point 1 5a 0 5a 0 5a that is line joining the p osition of q and center of the cube is perpendicular to t he 2 faces adjacent to ABCD What is the flux of q throug h ABCD Answer is not 0 please tell how to construct sy mmetrical surface here and whether answer can be calcul ated or not

10 Two point charges q and q are separated by a distance 27 Find the flux of electric field strength vector across the circle of radius R placed with its centre coinciding with the midpoint of line joining the two charges in the perpendicular plane

A 100 W bulb B two 60 W bulbs B and B are connected to a 250 V source as shown If W W and W are powers of the bulbs then a W W W3 C 250 V b W W W

Two point charges 7 C and 2 C a placed at position 9 cm 0 and 9 cm respectively How much work is required separate two charges infinitely away fr each other INCERT Pg 1 0 2 J 3 0 6 J 2 0 5 J 4 0 7 J

The electric field is uniform in a region of space as shown in the figure A B and C are points in space We take a positive point charge 9 charge 1 from A to C and another positive point charge particle q charge 2 from C to B Which one is true for the work of electric field done on the particles respecting the sign of work O W W OD W W OC W W 0 4 W W

18 Figure shows track of three positive charged particles through uniform electric field E All charges are equal in value Which charge particle has more initial kinetic energy on entering horizontally between the plate INCERT Pg 47 tie 1 20 3 1 Particle 1 2 Particle 2 Plate Plate

5 A simple pendulum is oscillating with time period T Now charge q is given to the bob and similar charge is kept at the point of suspension as shown in figure then 9 q 1 The time period will increase 2 The time period will decrease 3 There is no change in the time period

Two point charges q and q2 occupy fixed positions in free space If at every point on a curved surface surrounding the charges as shown in the figure net electrostatic potentia V created by these charges is 900V what should be the separation between the charges in cm given q 4 0nC q2 1 0nC 1 4TE 9 10 Nm C q1 92

The conducting shells A and Bare arranged as shown below If charge on the shell Bis q then electric flux linked with the spherical Gaussian surface Sis Only one correct answer A B C D 4 E0 I Dz 1 9 200 4 q 200

of electric field lines In ach pattern a proton is released from rest at point P and then accelerated wards the point Q by the electric field Rank the patterns according to the linear omentum of the proton when it reaches Q greatest first

1 The electrostatic force between two small charged spheres having charges of 2 x 10 6 C and 3 x 106 C placed 30 cm apart in air is NCERT Pg 46 1 0 9 N 3 1 2 N 2 0 6 N 4 1 8 N

find charge of 3 00 nC is placed at the origin of an xy coordinate system and a charge of 2 00 nC is placed on ne y axis at y 4 00 cm a If a third charge of 5 00 nC is now placed at the point x 3 00 cm y 4 00 cm ne x and y components of the total force exerted on this charge by the other two charges b Find the magnitude and direction of this force Draw a diagram to show the direction

Neutral metal sphere of radius Ris connected to earth through a switch S which is initially open Two charges 3Q and 2Q are kept at 9R and 3R distances from the centre of the sphere as shown When switch is closed the charge flown from the sphere to the earth is Only one correct answer A Q B Q 3R c Q 9R 2Q 3Q

it such that the upper hemisphere has a uniform surface charge density to while the lower hemisphere has a uniform surface charge density o as shown in the figure Their interface lies in x y plane Which of the following statement s is are correct o Space for rough work X Page 7 A The field at all points of x y plane within the sphere points in the ve z direction B All points of the x y plane within the sphere are equipotential

1 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 r dielectric medium has carved out from it an ellipse governed by the equation x2 x 9 4 y y2 1 The equivalent force between kq 9 2 x 10 2N the charges in air is given by 1 4 where k 0 distances are in meter n What is the value of n if

The mean free path of electrons in a metal is 4x108 m The electric field which can give on an average 2eV energy to an electron in the metal will be in units of V m 1 5 x 107 2 8 x 107 3 5x10 11 4 8x10 11

A non uniform electric field in x direction is increasing uniformly from 2N C at x 1m to 8 N C at x 7m The center of cube is at x 2m If the charge enclosed inside a small cube of side length 10cm is 8 85 x 10 C The value of n will be

1 A conducting sphere having a charge 2 C is surrounded conducting by an uncharged concentric spherical shell The potential difference between the surface of solid sphere and the shell is 5 V If the shell is given a charge 4 C then the new potential difference between the same surfaces will be 1 5 V 3 20 V 2 10 V 4 10 V

D The electric potential at a point x y z is given by V xy volt The electrostatic force acting on 1C charge at a point 1 2 4 m will be 1 2 N 2 2 N 3 2 4 N 4 2 4K N

5 The charge is distributed uniformly in the volum of a sphere of radius 20 cm such that the potential of its surface is 50 V The potential a the centre of the sphere will be 1 75 V 2 25 V 3 50 V 4 Zero

5 Two charged conducting spheres of radii 10 cm and 25 cm are connected to each other by a conducting wire The ratio of electric field at the surfaces of the two spheres will be 1 2 3 N W 2 4 5 2 25 4

An electrified pith ball is brought into contact with an exactly similar unelectri pith ball On being separated and kept 3 cm away from each other in air they r each other with a force of 2 5 x 10 N Find the original charge on the electr pith ball

Test Series 2021 10 Let there are two concentric shells of charge q and q having radii a and b and outer shell is earthed at point A Find net charge on inner surface of ourter layer after earthing 1 2 3 4 9 91 9 92 zero 92 91 b

Questions 20 and 21 are based on the following write up A conducting balloon of radius a is charged to a potential Vo and held at a large height above the earth surface The large height of the balloon from the earth ensures that charge distribution on the surface of the balloon remains unaffected by the presence of the earth It is earthed through a resistance R and a valve is opened The gas inside the balloon escapes through the valve and the size of the balloon decreases The rate of decrease in radius of the balloon is controlled in such a manner that potential of the balloon remains constant Assume electric permittivity of the surrounding air equal to that of free space and charge does not leak to the surrounding air 20 Time rate at which radius r of the balloon changes is best represented by the expression a c 1 4 R r 4 R b a 0 5 av c 2 V d 1 4 R T 4 R 1 How much heat is dissipated in the resistance R until radius of the balloon becomes half b V d 4 V

When a point source of light is at a distance of 50 cm from a photoelectric cell the cut off voltage is found to be V If the same source is placed at a distance Im from the cell the cut off voltage will be A V 4 D 2V0 E 3V B V 2 C Vo 0

1 69 The electric field strength depends only on the x and y a x yj 2 x y coordinates according to the law E 9 where a is a constant and are unit vectors of the x and y axes Find the potential difference between x 1 and x 5 Ans a In 5

The magnitude of electric potential on equatorial line due to an electric dipole is and the magnitude of the electric potential on axial line is E2 The value of E E is equal to O2E2 E O E

There are two spheres of radii R and 2R having charges Q and respectively These two spheres are connected with a cell of emf V as shown through the switch S Neglecting the interaction between the spheres the charge supplied by battery to the sphere A is QbE VAR a 3 then A D 2R B IR Amy 3 4

A particle of mass M and charge q is released 18 from rest in a region of uniform electric field of magnitude E After a time t the distance travelled by the charge is S and the kinetic energy attained by the particle is T Then the ratio T S 1 remains constant with time t 2 varies linearly with the mass M of the particle 3 is independent of the charge q 4 is independent of the magnitude of the FRIEN VISI MISI and has an 1 Fra real 2 fafala 3 4 9