Electric Field and Potential Questions and Answers

that of larger sphel b the charge density of smaller sphere is more than that of larger sphere c both spheres may have same charge density d none of these 43 Two metal spheres one of radius R and the other of radius 2R both have same surface charge density o If they are brought in contact and separated then the new surface charge densities on each of the sphere are respectively 52 36 0 10 3 546 c 0 a b 0 0 6 d 3 6 2

A ring carrying current lies in x z plane as shown A short magnetic dipole with dipole moment directed along x axis is fixed at origin If the ring is free to move anywhere then it will AY M Quibeo only X Z 1 Rotate clockwise about z axis 2 Rotate anticlockwise about z axis 3 Move along z axis 4 Move along v axis

strong The cheat along aving ect to que of dipole c d 30 0 44 Two charged conducting spheres of radia and are connected to each other by a wire The ration electric fields at the surfaces of two spheres is b a a 3 5 c 6 615 b d

b a 13 For a system of two dipoles P and P2 as shown in the figure both are at origin and perpendicular to each other along x and y axes respectively A Work done in taking electron from P to R on QPR 0 P P B tan a 2 P P P P C tan a 2 P P D 7 YA P P E dr 4 2neor P 10 SAIP 45 fa P P UR to dimensions of dipole

An electric dipole consists of two opposite charges each of magnitude 0 1 C separated by 40 mm The dipole is aligned at 30 with the direction of uniform electric field of magnitude 106 NC 1 The magnitude of the torque acting on the dipole is A zero B 8 x 10 3 Nm C 4 x 10 Nm D 2 x 10 3 Nm

ut the h the the 31 The work done in carrying a charge q once round circle of radius a with a charge Q at its centre is b a c 9Q 4Tea 9 4Tea 9Q 47 a d zero POTENTIAL ENERGY OF A SYSTEM OF CHAR

Consider four point charges placed on the vertices of a square of side x as shown Electric dipole moment of the system is Q X 2Q X Q xx X 2 2 Q 1 2 1 Qx i 1 2 2 1 Qx 1 i 3 2 1 Qx i 1 4 2 1 Qx 1 1

An oil drop carrying charge Q is held in equilibrium by a potential difference of 600V between the horizonta plates In order to hold another drop of twice the radius in equilibrium a potential drop of 1600V had to be maintained The charge on the second drop is 1 2 20 2 2Q 3 30 12 3Q 4 3Q

Two small objects each having a charge of Q are located on the y axis a distance a and a from the origin Another small object having a charge q starts at rest on the x axis very far away i e at x The two objects on the y axis are fixed in place The object of charge q is released from rest is attracted to the other two objects and travels along the x axis What is its speed as it passes through the origin

When identical point charges are placed at the vertices of a cube of edge length a each of them experiences a net force of magnitude F Now these charges are placed on the vertices of another cube of edge length b What will magnitude of the net force on any of the charges be These cubes are simply geometrical constructs and not made of any matter a c aF b a F 6 b d bF a 62 F a

The short dipoles each of dipole moment p are placed at origin The dipole moment of one dipole is along x axis while that of other is along y axis The electric field at a point a 0 is given by A 1 2p 2 20 a B 1760 P a 3 1 5p

7 Derive an expression to determine torque for an electric dipole with its sp cases 8 Two point charges q and 2q are placed at the vertices B and C of an equilateral triangle ABC of side as given in the figure Obtain the expression for i the magnitude and ii the direction of the resultant electric field at the vertex A due to these two charges

A non conducting semicircular disc as shown in figure has a uniform surface charge density o The ratio of electric field to electric potential at the centre of the disc will be A 1 lnb a b a B 2 C 1 n b a b a b a D 2 n b a

QTwo point charges q and q are held fixed at d 0 and d 0 respectively of a x y coordinate system Then A B C the electric field E at all points on the axis has the same direction work has to be done in bringing a test charge from co to the origin electric field at all points on y axis is along x axis D the dipole moment is 2qd along the x axis

20 Four equal charges q each are placed at four corners of a square of side a each Work done in carrying a charge q from its centre to infinity is 29 a zero b TOE c 2q Tega d Tea

a Er b E c Exr d Exp 100 An early model for an atom considered it to have a positively charged point nucleus of charge Ze surrounded by a uniform density of negative charge upto a radius R The atom as a whole is neutral The electric field at a distance r from the nucleus is r R Ze 1 r Ze 1 a b 4TE L R c Ze 47E0 d ATEL Ze 4TE 3 A very lolly of fixed negat by a uniform c coaxial with p of the cylia electric field the required p a 6 A system com of radius R an charge with t a positive cor centre of the for which the sphere is inder

Best The electric potential at a point in free space due to a charge Q coulomb is Qx 10 V The electric fiel at that point is a 12mQx 10 Vm b 4RE Qx 10 V c 12TE Qx 100 V m d 4meQ x 10 is co 2 b c d

entre pole pole P A cube of a metal is given a positive charge Q For the above system which of the following statements is true 1 Electric potential at the surface of the cube is zero 2 Electric potential within the cube is zero 3 Electric field is normal to the surface of the cube 4 Electric field varies within the cube 12

AME Q x 10 V m 8 Two points A and B are located in diametrically opposite directions of a point charge of 2 Ca distances 2 m and 1 m respectively from it The potential difference between A and B is a 3 x 10 V b 6 x 10 V c 9 x 10 V d 3 x 10 v A charge a is placed at the 9 16 13 W 2 E

6 The electric field intensity at a point P due to point charge q kept at point Q is 24 NC and the electric potential at point P due to same charge is 12 JC The order of magnitude of charge q is a 10 C c 10 10 C b 10 C d 10 C

4 The potential at a point due to a charge of 5 x 107 C located 10 cm away is a 3 5 10 V c 4 5 x 10 V 5 b 3 5 x 10 V d 4 5 x 105 V 1

Given the potential V r sin 0 cos 1 Find the electric flux density D at 2 7 3 7 3 2 Find the charge within the sphere r 2 3 Calculate the work done in moving a 1 C charge from point A 1 30 120 to B 4 30 60 4 Calculate the total work done in moving a 2 C charge from point A to C and from C to B A 1 30 120 C 4 30 120 and B 4 30 60

PART B 3 x 4 12 Marks a List the properties of Electric lines of forces and state why two lines of forces never intersect b Draw the figure depicting lines of force for two positive charges placed near

We want to design a spherical vacuum capacitor with a given radius a for outer sphere which will be able to store the greatest amount of electrical energy subject to the constraint that the electric field strength at the surface of xa Find x inner sphere may not exceed Eo The radius b choosen for the inner sphere conductor is given by 4

coulomb s law 89 A point charge 20 C is at a distance 6 cm directly above the centre of a square of side 12 cm as shown is figure The magnitude of electric flux through the square is 6 cm 12 cm a 2 5 x 10 N m C b 3 8 x 10 Nm C c 4 2 x 105 Nm C 1 d 2 9 x 10 N m C 12 cm

12 93 Two infinite plane parallel sheets separated by a distance d have equal and opposite uniform charge densities o Electric field at a point between the sheets is 0 a 200 b Eo c zero d depends on the location of the point

95 Two large thin metal plates are parallel and close to each other On their inner faces the plates have surface charge densities of opposite signs and magnitude 27 x 10 22C m The electric field Ein region II in between the plates is to 11 III a 4 25 x 10 NC c 3 05 x 10 10 NC 6 A charged ball B hangs from a silk b 6 28 x 10 10 NC 1 d 5 03 x 10 10 NC 1 F

a 7 3 x 10 C c 7 3 x 10 6 C b 3 7 x 10 6C d 3 7 x 10 C 78 A metallic spherical shell has an inner radius R and outer radius R A charge is placed at the centre of the spherical cavity The surface charge density on the inner surface is a 9 4x R b 4nR c 4t R d 4x R

c zero d depends on the location of the point 94 Two large thin metal plates are parallel and close to each other On their inner faces the plates have surface charge densities of opposite signs and of magnitude 16 x 10 22 C m2 The electric field between the plates is a 1 8 x 10 10 NC 1 b 1 9 x 10 10 NC 1 c 1 6 x 10 10 NC 1 d 1 5 x 10 10 NC 1 thin metal plates are parallel and close

An electric dipole consists of charges 2 0 x 10 C separated by a distance of 2 0 x 10 m It is placed 2 0 cm near a long line charge of linear charge density 4 0 x 10 Cm as shown in the figure such that the negative charge is at a distance of 2 0 cm from the line charge The force acting on the dipole will be a 7 2 N towards the line charge b 6 6 N away from the line charge c 0 6 N away from the line charge d 0 6 N towards the line charge

c 6 7 x 10 6 7 x 91 Two parallel infinite line charges and are placed with a separation distance R in free space The net electric field exactly mid way between the two line charges is a zero b 2 TER c 2 TER d A 2MER

ous nts P c A B p C q d A r B q C p B LC P 77 A uniformly charged conducting sphere of 4 4 m diameter has a surface charge density of 60 C m The charge on the sphere is a 7 3 x 10 C b 3 7 x 10 6 C d 3 7 x 10 C c 7 3 x 10 6 C

MEG Objective NCERT P 74 In a certain region of space electric field is the 2 direction throughout The magnitude electric field is however not constant but incre uniformly along the positive 2 direction at the the system having a total dipole moment equal rate of 10 N Cm The force experienced b 10 C m in the negative z direction is a 10 N b 102N c 10 N d

A spherical metallic conductor has a spherical cavity A positive charge is placed inside the cavity at its centre Another positive charge is placed outside it The conductor is initially electrically neutral Column I Cause Column II Effect If outside charge is shifted to other position p A B C D If inside charge is shifted to other position within cavity If magnitude of charge inside cavity is increased If conductor is earthed q r s Distribution of charge on inner surface of cavity changes Distribution of charge on outer surface of conductor changes Electric potential at the centre of conductor changes due to charges present on outer surface of conductor Force on the charge placed inside cavity changes

A charge is kept fixed at point A as shown in the figure in a gravity free space A semicircular ring of linear charge density 2 mass m radius R is released from rest Initially centre of semicircular ring coincides with the fixed charge The initial acceleration of the semicircular ring is A C 2K Q mR K Q mR B K Q 2mR D 0 A fix

SolveLancer Test There are two points X and Y around a point charge It is given that Ex 3 V m Vx 7V and Ey 3 V m If the charge becomes 3 times then Ey 3 V m then Vy is approximately SolveLancer Test a 12V b 4V c 36V d Insufficient data

a A b B 49 A particle of mass m and charge g enters the region between the two charged plates initially moving along x axis with speed v as shown in figure The length of plate is L and a uniform electric field E is maintained between the plates The vertical deflection of the particle at the far edge of the plate is 3 a GEL qEL b 2mv 2mvx c 2mv GEL d 2mv qE L charged he figure c 55 Figure show point charge charges are

A parallel plate capacitor have unequal charges 20 and Q as shown in the figure If capacitance of the capacitor is C and P is a point outside of the capacitor Then A a point charge at point P will not experience any electric force due to capacitor plates B the potential difference between the plates will be 3Q 2C C the energy stored in the electric field in the region between the plates is 90 8C D the force on one plate due to the other plate is Q 27Eod

27 The electrostatic potential difference between points A and B VA Vg which are distances 2 0 m and rB 1 0 m from an infinitely long thin wire 1 0 C m is 1 12 47 10 V 2 12 47 10 V X 3 18 10 V 4 18 10 V 28 In the above situation i e Q 27 if an electron is released from rest at point A it s speed at point B will be 1 6 6 107 m s 2 3 3 x 107 m s 3 1 1 x 107 m s 4 2 2 107 m s

0 Two charges 20 C and 20 C are placed 10 mm apart The electric field at point P on the axis of the dipole 10 cm away from its centre O on the side of the positive charge is A 0 B 20 C 20 C a 8 6 x 10 NC c 3 6 x 10 NC P b 4 1 x 106 NC d 4 6 x 10 NC

48 The tracks of three charged particles in a uniform electrostatic field as shown in the figure Which particle has the highest charge to mass ratio a A b B C c C d A and B charme a enters the region B c 54 Which correc the ele charge

c d zero 46 In question number 45 what will be the electric field 51 at centre O if the charge from one of the corners say A is removed along OA b e c 4TEOF 4 TEF along OC d 24 TEOF 29 along OB along OA 4Teor 4TE In question number 45 what will be the electric field 52

Two parallel equilateral triangular plates are placed overlapping each other very close to each other The plates carry uniformly distributed unlike charges of equal moduli Deep inside the region between the plates electric field is uniform but near the edges it becomes nonuniform If modulus of electric field deep inside the plates is Eo find modulus of electric field at the midpoint of line AB What happens if the plates have the shape of a regular pentagon

B c unchanged d thrice 39 A force of 2 25 N acts on a charge of 15 x 10 C The intensity of electric field at that point is a 150 NC 1 b 15 NC 1 c 1500 NC d 1 5 NC

Consider an atom with atomic number Z as consisting of a positive point charge at the centre and surrounded by a distribution of negative electricity uniformly distributed within a sphere of radius R The electric field at a point inside the atom at a distance r from the centre is 1 Ze 1 2 4TEO r R 2 Ze 1 1 4 TEO 2 R

Consider a system of two uniform thin concentric non conducting shells of charge with respective charges q and 2q and radii R and 3R A point charge 4Q is placed at a distance 5R from the common centre of the shells Net force experienced by the outer shell is 2Q 5 E R 2Q 25 E R 2Q 9TE R2 zero

The electric flux passing through wire frame ABCD of length and breadth b whose centre is d distance away from an infinite line charge of linear density is consider plane of frame is perpendicular to line OP 22 0 b al 2b A tan tan 2d d C TEO al TEO tan b 2d B D TEO ne TEO tan d b

Question No 21 Three large plates A B and C are placed parallel to each other and charges are shown in the figure The charge that appears on left surface of plate B is 3C 4C A B 5C C

In the figure two points A and B are located within a region that contains an electric field A negative char is placed at A and then moved to B Does the potential energy of the system increase decrease or rema same A B

Displacement current is same as A B C D conduction current due to flow of free electron conduction current due to flow of positive ions conduction current due to flow of both positive and negative free charge carriers is not a conduction current but is caused by time varying electric field