Electric Field and Potential Questions and Answers

Two uniform infinite planes of charge having charge densities o and o intersect at right angle The magnitude of electric field at any position in the space is 1 O 2 3 2 4 O 2E0 2 2 Fo

A point charge q is kept at the centre of curvature of thin semicircular wire of length as shown The wire has uniformly distributed charge q on it The dipole moment of the system is 2ql 1 77 2 TU 2 Fal 9 2 2ql T 4 Zero

4 The figure shows a conducting sphere A of radius a which is surrounded by a neutral conducting spherical shell B of radius b a Initially switches S S and S are open and sphere A carries a charge Q First the switch S is closed to connect the shell B with the ground and then opened Now the switch S is closed so that the sphere A is grounded and then S is opened Finally the switch S is closed to connect the spheres together Find the heat in joule which is produced after closing the switch S Consider b 4 cm a 2 cm and Q 80 C S3 b OPS

Four equal charges l C each are placed at the four corners of a square of each side 3cm Find the force experienced by each charge due to the other three charges

0 Small identical balls with equal charges are fixed at vertices of regular 2008 gon with side a At a certain instant one of the balls is released a sufficiently long time interval later the ball adjacent to the first released ball is freed The kinetic energies of the released balls are found to differ by K at a sufficiently long distance from the polygon Determine the charge q of each ball

4 Three positive charges q 2q 3q are placed at the corners of an equilateral trian If the length of each side of the triangle is d find the direction in degree electric field at the point bisecting the line between q and 2q

Two metallic concentric shells are shown Before closing the switch charge on inner shell is Q and charge on outer shell is 20 Potential at point A is V What will be potential at same point after closing the switch 2a a A

A point source of e m radiation has an average power output of 60 W What is the maximum value of electric field at a distance 3 0 m from the source 1 27 16 V m 3 6 67 V m 2 20 V m 4 80 x 10 7 V m

At a point 20 cm from the centre of a uniformly charged dielectric sphere of radius 10 cm the electric field is 100 V m The electric field at 3 cm from the centre of the sphere will be a 150 V m 120 V m b 125 V m d Zero Fiz kr

Four rigid rods AB BC CD and DA each of linear mass density and length a are connected rigidly to form a square frame This system is placed in an XYZ space as shown in the figure such that it can freely rotate about an axis kk parallel to z axis The plane ABCD is on the y z plane The rods AB and CD are carrying charges of linear charge density p and p respectively An electric field is existing in the space which is E Ej If the wire frame is rotated by a small angle 40 about the kk axis and released Find the time in second required by the frame ABCD to regain its original position for the first time 1 kq m a 2m p 1 3 C m E N C k Z YOU C k

31 An infinite number of charges each of charge 1 C are placed on the x axis with co ordinates x 1 2 4 8 oo If a charge of 1 C is kept at the origin then what is the net force acting on 1C charge DCE 2004 9000 N b 24000 N c 12000 N d 36000 N

A charge Q is given to a conducting sphere radius R Now if a charge Q is placed as shown at a distance r from the centre then magnitude of force of attraction between charges is 1 1 Q 4 r 1 Q Q R 2 Q 1 Q 4 r 0

Four particles having masses m 2m 3m and 4m are placed at the four corners A B C and D of a square ABCD of side a The gravitational force acting on a particle of mass m placed at the centre is a c 4 3Gm a 4 2 Gm b d 3 4Gm a 2 3Gm 2

Linear charge density of arc is and total angle a Derive an expression for potential at centre C 1 Kha 3 Kha 2 K a r 4 Kar

A neutral metal sphere is placed at a large distance from a point charge The magnitude of Coulomb electrostatic interaction force between the charge and sphere is F If the distance between them is doubled the new magnitude of Coulomb electrostatic interaction force between the charge and sphere is 2 F Find the value of n Assuming that the radius of sphere is very small as compared to the distance between them

43 Electric field of a dipole is related to distance r as E x 7 Ex c Exc r Ex a Ex b Exc d Ex 20

17 Two infinite parallel non conducting sheets carry equal positive charge density a One is placed in the yz plane at x 0 and the other at x a Take potential V 0 at x 0 A For 0 x a potential V 0 B For x 2 a potential V x a C For x 2 a potential V o x a 100 of madii R D For x 0 potential V G 0 6m and R 4m are placed in y z plane with their centres at

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

A disc of radius R is kept such that its axis coincide with the x axis and its centre is at d 0 0 The thickness of disc is t and it carries a uniform volume charge density p The external electric field in the space is given by E Kr where K Constant and r is position vector of any point in space with respect to the origin of the coordinate system Find the electric force on the disc

experiences a force of 4 x 10 N Calculate the charge present on Two electrons are placed at a distance d such that electrostatic force between both the electrons is equal to sum of weight of both the electrons Calculate the value of d bhod against a piece of wool such m 11

9 A 2 Eor A 9 B 4 r F Let there be a spherically symmetric charge distribution with charge density varying as 5 p r Pol 4 2 R the origin The electric field at a distance r r R from the origin is given by Por 2 7 4 R 2 J mont upto r R and p r 0 for r R where r is the distance from 4 B 380 5 4por 5 Fre R r

A 10 N Two uniformly charged non conducting hemispherical shells each having uniform charge density o and radius R form a complete sphere not stuck together and surround a concentric spherical conducting shell of radius R 2 If hemispherical parts are in equilibrium then minimum surface charge density of inner conducting shell is A 2 o C 0 D 20 charge 3Q Concentric with this sphere is a conducting spherical she al pholl is h a What is th B 0 2

A E C D 9 In the given figure if Q and Q are positive where could a negative charge be placed so as to have vertically upward net force on it 1 A 3 C 5 F 2 B 4 D

20 C charge is placed inside a closed surface then flux related to surface is If 80 C charge is added inside the surface then change in flux is 1 46 2 50 3 4 80

Consider a conductor with a spherical cavity in it A point charge q is placed at the centre of cavity and a point charge Q is placed outside conductor Statement 1 Total charge induced on cavity wall is equal and opposite to the charge inside Statement 2 If cavity is surrounded by a Gaussian surface where all parts of Gaussian surface are located inside the conductor E d 0 hence induced 40 A Statement 1 is true statement 2 is true and statement 2 is correct explanation for statement 1 B Statement 1 is true statement 2 is true and statement 2 is NOT the correct explanation for statement 1 C Statement 1 is true statement 2 is false D Statement 1 is false statement 2 is true

9 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 3 B 3 a 12 0

electric interaction between these dipoles will be dipoles are placed as shown r is the distance between their centres The energy of C is centre of dipole of moment P2 2k P P cose A B r 3 To C 2k P P cos 0 p3 P2 C P 2k P P sine r D 4k P P cose r3

Two objects placed at some finite distance repel each other then Both must be positively charged Both must be negatively charged Both may be uncharged Both may be negatively charged

20 An electric dipole consists of two opposite charges of magnitude q 3 x 106 C separated by 0 02 m The dipole is placed in an external field of intensity 2 x 105 N C Calculate the dipole moment and the maximum torque on the dipole Ans 0 06 x 10 6 C m 10 12 x 10 Nm Hint P 2a q PE

4 Two point charges 9e and e are kept at a distance a from each other Where should we place a third charge q on the line joining the two charges so that it may be in equilibrium

tration 2 10 2 a particles nuclei of helium fall per second on a neutral sphere calculate the time in which the sph gets charged by 2 C

1 201 301 22 m n potential at origin is zero Find poten

The electric potential in a region is given by V x y z ax ay abz a is a positive constant of appropriate dimensions and b a positive constant such that V is volts when x y z are in m Let b 2 The work done by the electric field when a point charge 4 C moves from the point 0 0 0 1m to the origin is 50 J The radius of the circle of the equipotential curve corresponding to V 6250 volts 2 m is a m Fill a in OMR sheet and z

A small sphere of mass m and having charge q is suspended by a silk thread of length in a uniform horizontal electric field If it stands at a distance x from the vertical line from point of suspension then magnitude of electric field is 1 3 mg q mgx 0 1 8 2 2 4 mg x q 1 mgl 9 x 1

Figure 3 E 12 000N c Vo 40mm B pair of charged conducting plates produces a uniform field of 12 000 N C directed to the right between the plates The paration of the plates is 40 mm 3 In Figure 3 an electron is projected from plate A directly toward plate B with an initial velocity Vo 1 0 x 107 m s The closest approach of the electron to plate B is closest to A 18 mm B 22 mm C 20 mm D 16 mm E 24 mm 3

The equivalent resistance between A and B in the following figure is 30 2 A www 1 120 92 3 30 22 www 30 92 30 92 30 2 ww 2 40 2 4 22 5 9 B

If n cells each of emf and internal resistance rare connected in parallel then the total emf and internal resistances will be a E r n c n r n b nr d In the series combination of n ne nr cells each cell having 11

15 The electric field strength depends only on the x y and z coordinates according to the law a xi yj zk x y 2 in volt between 3 2 6 and 0 3 4 E where a 122 5 SI unit and is a constant Find the potential difference

32 A B C D P and Q are points in a electric field The potentials at these point V A 2 volt V B V P V D 5 volt and V C 8 volt The electric field at P is F 0 2 m B A P K 0 2m 1 10 V m along PQ 2 5 V m along PC 3 15 2 V m along PA C Q D

5 The work done in slowly moving an electron of charge e and mass m from A to B along a semicircular path as shown in the figure in vertical plane in the field of charge Q is 1 2 mgr 3 2mgr 2Qe r 2 Qe r 4 Zero apart How much work is needed to be done to bring

A circuit has a section AB as shown in the figure with E 10 V C 1 0 F C 2 0 F and the potential difference VA VB 5 V The voltage across C is 1 zero 2 5 V 3 10 V 4 15 V A HH C E 11 H 10v C UP B

An infinite number of identically charged bodies are kept along the x axis at points x 0 1m 2m 4m 8m 16m and so on All other charges repel the charge at the origin with a force of 1 2 N Find magnitude of each charge

plane she of electric charge ii Two plane sheets of charge having charge densities o and o are normal to each other What will be the magnitude of electric field at point O 0

42 Find current I 1 MA 2k2 www 146 www IKNIKN www YkN 5 2 MA MA

Three equal charges each of luc are placed at the three corners of an equilateral triangle of sides 3cm each Find the force experienced by each charge due to the other two charges

33 A charge q is placed at 1 2 1 and another charge q is placed at 0 1 0 such that they form an electric dipole There exists a uniform electric field 21 Calculate the torque experienced by the dipole 1 2 29 N m P s afi 2 25X1 5x 3 4 29 N m 4 29 N m 2 x Zilva h 2 29 N m

In the given network if an ideal battery of EMF 48 V is connected between the points A and B the potential difference between the points P and Q will be V 202 252 www 352 Q 352 ww 30 P 40

Problem 10 Figure 1 133 shows three different patterns of electric field lines In each pattern a proton is released from rest at point P and then accelerated towards the point Q by the electric field Rank the patterns according to the linear momentum of the proton when it reaches Q greatest first P P a Q Q

9 Two positive point charges of magnitude q each are fixed at points A and B The origin of coordinate system at the points A and B are situated at distance x on x axis from the origin Which of the following is best represented for force of interaction F versus x graph FA a FA b c FA F4 d L L

Two charged balls are connected by an inextensible thread of length 3 m Masses of balls are 2kg and 1 kg the charges are 20 C and 100 C What minimum constant external force F in N must be applied to the ball of mass 1 kg so that the thread does not slack Neglect gravity and friction Advanced Enthusiast Phy Sheet Electroste