Electric Field and Potential Questions and Answers

2 An electric dipole of moment p is placed in an electric field of intensity E The dipole acquires a position such that the axis of the dipole makes an angle 0 with the direction of the field Assuming that the potential energy of the dipole to be zero when 0 90 the torque and the potential energy of the dipole will respectively be a pEsine pEcose b pEsin0 2pEcose c pEsine 2pEcose d pEcos0 pEsine

Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately NCERT Exemplar a spheres b planes c paraboloids d ellipsoids

Two charged spherical conductors of radii R and R are connected by a wire Then the ratio of surface charge densities of the spheres o 0 is Kerala PET 2010 b a c e R B2 R R2 R22 d R2 R

Q Charges Q 20 and 4Q are uniformly distributed in three dielectric solid spheres 1 2 and 3 of radii R 2 R and 2R respectively as shown in figure If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1 2 and 3 are E E and E3 respectively then JEE Advance Single Correct Choice AR R 2 Sphere 1 2Q 1 E E E3 F R Sphere 2 2 4 4Q CR E3 E E E E E 2R Sphere 3

Given an equilateral triangle with side Find E at the centroid The linear charge density is as shown in figure B 1 A c 1 1 C

The electric field at 40 cm from centre of a charged conducting sphere of radius 20 cm is E Then electric field at 10 cm from the centre is W F ge E 16 3 16 E 1 2 E 2 4 Zero Te

the dipole at a distance of 10 cm from the center of the dipole 10 An electric dipole consists of two charges 108 C lying 10 cm apart Calculate the electric field at a point P situated 10 cm fro each charge and on an axis which is perpendicular to the axis of the dipole 11 An electric dipole consists of charges 2e and 2e separated by 0 78 nm The dipole lies in an electric field of strength 3 4 x 10 N

For the system shown in figure Find Q for which resultant force n q is zero Q 0 a a 9 0 0 O a a 9 FA

A positive point charge q is projected along x aixs Electric field is directed along y axis E fo 1 Find the trajectory of charge after x d A y qEod d mv 2 qEnd d 2mv 2 C y B y qfE d d mv 2 x qEnd d 2mv 2 D y x

A charged particle with charge q and mass m starts with an initial kinetic energy K at the middle of a uniformly charged spherical region of total charge Q and radius R q and Q have opposite signs The spherically charged region is not free to move The value of K is such that the particle will just reach the boundary of the spherically charged region How much time does it take for the particle to reach the boundary of the region 4T E MR 2 V qQ 2 mR 1 t 2 t mR qQ 2 Eo TC 2 4T E MR

11 An electric dipole consists of charges 2e and 2e separated by 0 78 nm The dipole lies in an electric field of strength 3 4 x 10 N C Calculate the magnitude of the torque on the dipole when the dipole moment is a parallel to b perpendicular to and c antiparallel to the electric field

16 A dipole of dipole moment 10 7 Cm in the negative z direction is placed in an electric field along positive z direction The magnitude of electric field increases uniformly along the positive z directi at the rate of 10 NC per meter The force experienced by the dipole is 10 3N

A bullet of mass 2 g is having a charge of 2 C Through what potential difference must it be accelerated starting from rest to acquire a speed of 10 m s a 5 kV c 5 V b 50 kV d 50 V 2004

33 A point charge q is placed at a distance d from an isolated conducting plane The field at a point P on the other side of the plane is NCERT Exemplar a directed perpendicular to the plane and away from the plane b directed perpendicular to the plane but towards the plane c directed radially away from the point charge d directed radially towards the point charge

The mean free path of conduction electrons in copper is about 4x108 m For a copper block find the electric field which can give on an average 1 eV energy to a conduction electron

If VAB is 4 V in the given figure then resistance X will be 5 V a 50 102 wwwww 2 V b 10Q X ww ww c 15Q B d 2002

15 5 x 10 N C directed towards 10 C Two charges 8 C and 2 C are placed 10cm apart The intensity of the electric field is zero at point 1 10cm from the first charge on the other side 2 40cm from the first charge on the other side 3 20 3cm from the second charge on the other side 4 40cm from the second charge on the other s

On the circuit shown what is the current measured by the ammeter Each resistor is 50 ohms and the battery is 50 volts 1 Point 0 15 A 0 27 A 0 21 A 0 36 A 111 TIMOT 50 V A II TIMOT All resistors 50 ohms

A hollow charged metal sphere has radius r If the potential difference between its surface and a point at a distance 3r from the centre is V then the electric field intensity at distance 3r from the centre is 1 3 V 3r V 6r 2 4 V 4r V 2r Vzoka kg

Between two infinitely long wires having linear charge densities and there are two points A and B as shown in the figure The amount of work done by the electric field in moving a point charge qo from A to B is equal to B A C 7 90 270 In 2 22 90 In 2 TEO D 2290 In 2 TEO 290 In 2 TEO 2 a A a BO 2 a

A hollow charged conductor has a tiny hole cut into its su Show that the electric field in the hole is o 2e n where is the unit vector in the outward normal direction and o is the surface charge density near the hole for the electric field due to a long thin wire of Hint

3 4j 5k 5 2 the X axis The intensity of the electric field at origin is n chares Q 4Q 9Q 16Q are placed at distances of 1 2 3 nQ nQ 4T EO 1 nQ 2 Eo 8 metres from the origin on nQ

3 The force experienced by a charge in an electric field of intensity 200Vm is 1 milli newton The 4 F E q charge is Suc 2 5C The electric field intensity in air 3 10 C 4 20 C

1 Find the electric intensity at a distance of 1m from a charge of InC InC 10 C 9N C 2 18N C 3 12N C 4 24N C 2 The force F experienced by a charge q placed in a electric field

2 Electric field at centre O of semicircle of radius a having linear charge density given as a 22 Ea 2 c 2 b d Ea 0 a 2 2000

PRACTICE PROBLEMS 2016021 8 9 An electric dipole consists of two charges 10 C lying 10 cm apart Calculate the electric field at a point P situated on the axis the dipole at a distance of 10 cm from the center of the dipole

2 The electrostatic force on a small sphere of charge 0 4 C due to another small sphere of charge 0 8 C in air is 0 2 N a What is the distance between the two spheres b What is the force on the second sphere due to the first

A metal sphere is charged What is meant by the quantisation of charge f fundamental charge 2 T

20 For the given figure if F is force on q due to q and F F is force on q due to q then find F 9 30 9 30 9 20 35 3

sphere An infinite line charge produces a field of 9 104 N C at a distance of 2 cm Calculate the linear charge density

A proton and an electron are placed 1 6 cr in free space Find the magnitude of elect force between them What is the nature force

Figure shows a shell of radius R having charge q uniformly distributed over it A point charge q is placed at the centre of shell Find work required to increase radius of shell from R to R as shown in fiugre b R a

value of the point charge 1 A conducting sphere of radius 10 cm has an unknown charge the electric field 20 cm from the centre of the sphere is 1 5 x 10 N and points radially inward what is the net charge on the sphere A uniformly charged conducting sphere of 2 4 m diameter has d the charge on t

An electric dipole consists of two equal and opposite point charges and 9 separated by a distance 2 P is a point collinear with the charges such that its distance from the positive charge is half of its distance from the negative charge The electric intensity at P is 1 30 Ans 4 16 densities

capacitar 30 Eight identical spherical drops each carrying a charge 1 nC are at a potential of 900 V each All these drops combine together to form a single large drop Calculate the potential of this large drop Assume no wastage of any kind and take the capacitance of a sphere of radius r as proportional to r 3600 V hotton of volts The charge stored in it is 360 uC When potentia

01 Two infinitely large sheets having charge densities and 2 respectively 01 02 are placed near each other separated by distance d A charge q is placed in between two plates such that there is no effect on charge distribution on plates Now this charge is moved at an angle of 45 with the horizontal towards plate having charge density 2 by distance a a d Find the work done by electric field in the process 02 B a A45 2005 2004

point charge q is placed at distance R 2 from its centre C Also there is a charge 2q 1 K 4ca E placed outside the shell at a distance of 2R as shown Then K R 2 9 3q C 2R 2q 48 A the magnitude of electric field at the centre C due to charges on the outer surface of Ka shell is before closing the switch S 2R B the electric potential at the centre C due to charges on the outer surface of shell is Kq before closing the switch S R C the electric potential at the centre C due to charges on the outer surface of shell is Kq after closing the switch S R

100 mm The en charged particles are kept fixed on the X axis at point x 10 mm 20 mm 30 mm st particle has a charge 10 C the second 8 x 10 C the third 27 x 10 C and so on The tenth particle as a charge 1000 x 10 C Find the magnitude of electric force acting on a 1 C charge placed at the origin 1C 91 92 93 94 C

Statement I Two concentric charged shell are given The potential difference between the shells depends on charge of inner shell BA Statement II Potential due to charge of outer shell remains same at every point inside the sphere

Q 29 1 0 30 1 Questions Q 29 Q 30 Each of these questions contains two statements Statement I and Statement II Each of these has four alternatives choices You have to select the correct choice 1 If both Statement I and Statement II are true and Statement II is the correct explanation of Statement I 2 If both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I 3 If Statement I is true but Statement II is false 4 If Statement I is false but Statement II is true Statement I In a free fall weight of a body becomes effectively zero Statement II Acceleration due to gravity acting on a body having free fall is zero Statement I Two concentric charged shell are given The potential difference between the shells depends on charge of inner shell BA Statement II Potential due to charge of outer shell remains same at every point inside the sphere

a Very Short Answer Questions REFLECTION OF LIGHT 2 1 What is meant by a self luminous source What is a transparent medium How do you define a beam 3 4 Draw the diagram of a convergent beam How do you define the angle of incidence How do you define angle of reflection How are angles of incidence and angle of reflection related to each other 5 6 7 8 Mention one characteristic of image produced by a plane mirror 9 What is the magnification of image produced by a plane mirror 10 A boy is running a way from a plane mirror with a speed of 10 ms What is his relative speed with respect to his image 11 A clock showing time as 11 45 is placed in front of a plane mirror What time will be observed through the mirror 12 What is the distance between centre of curvature and pole of a concave mirror in terms of its focal length What do you mean by principle axis of a spherical mirror 13 14 An object is placed at the centre of curvature of a concave mirror Where will its image be obtained 15 For what purpose do we use a parabolic mirror

A hollow spherical shell of radius r has a uniform charge density o It is kept in a cube of edge 3r such that the center of the cube coincides with the center of the shell Calculate the electric flux that comes out of a face ot not 2r 0 of the cube Ans

3 The total energy of electron in the ground state of hydrogen atom is 13 6 eV The kinetic energy of an electron in the first excited state is AIPMT Prelims 2007 1 1 7 eV 2 3 4 eV 3 6 8 eV

1 Charge q2 of mass m revolves around a stationary charge q in a circular orbit of radius r The orbital periodic time of 92 would be 1 3 4 mr kq 92 4x mr kq 92 71 2 71 2 2 4 49192 4x mr 71 2 4 mr kq192 11 2

Glass ball is rubbed with ebonite ball and kept at a separation of 1cm If the force of attraction between them is 10N find charge on each ball

3 A uniformly charged rod of length 4 cm and linear charge density 30 C m is placed as shown in figure Calculate the x component of electric field at point P 3yd novieP aubst to sisrices ni How b3cm 4cm 1 36 x 105 N C 2 9 x 105 N C 3 1 8 x 10 N C tristog

13 Two equally charged small balls A and B placed at a fixed distance experience a force F similar uncharged ball C after touching one of them is placed at the midpoint of the balls T force experienced by the ball A is b 3F 2 a F 2 F 4 c 2F d 4F

You are part of a design team assigned the task of making an electronic oscillator that will be the timing mechanism of a micro machine You start by trying to understand a simple model which is an electron moving along an axis through the center and perpendicular to the plane of a thin positively charged ring You need to determine how the oscillation frequency of the electron depends on the size and charge of the ring for displacements of the electron from the center of the ring which are small compared to the size of the ring A team member suggests that you first determine the acceleration of he electron along the axis as a function of the size and charge of the ring and then use that expression o determine the oscillation frequency of the electron for small oscillations

Three charges are arranged on the vertices of an equilateral triangle as shown in the figure Find the dipole moment of the 3 combination Find the electric field due to this distribution at a distance r from B along BC where r d B 20 d

A cow and a man are standing in a mead road when lightning strikes the ground nearby Who is more likely to be killed and Why Cow because man is wearing shoes 2 Cow because its legs are far apart 3 Man because cow is poor conductor of electricity 4 Both are equally likely to be killed