Electric Field and Potential Questions and Answers

21 A rod of length L has a total charge Q distribut uniformly along its length It is bent in the shape of a semicircle The electric field at the centre of avisa curvature of semicircle is 2Q 1 SOL 3 Q 2 2 of 2 EL Q 2 2 L I ko R2

The adjacent figure shows charged spherical shells A B and C having charge densities o o o and radii a b c respectively If VA Vc then b equals to A a c C ac B a c D none of these O a C B O 6

19 In a uniformly charged sphere of total charge Q and radius R the electric field E is plotted as function of distance from the centre The graph which would correspond to the above will be a EA b EAL

Determine the potential difference between the points C and D in the given figure a 3 6 V c 12 V www D 12V 3UF 643 www 10 b 7 2 V d 10 8 V C P M T

An electric dipole is placed at origin O such that equator is y axis At a point P far away from dipo the net electric field is in direction along y axis OP makes an angle a with the x axis then 1 tan a 3 2 tan a 2 3 tan a 1 4 tan q

10 0 cm on an x axis 12 In the figure particle 1 of charge 1 0 C and particle 2 of charge 3 0 C are held at separation L If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero what must be the a x and b y coordinates of particle 3 y 201 X

7 Two identical particles each of mass m and charges q and q are revolving around their common centre of mass in a circle of radius r under the influence of electrostatic attraction The kinetic energy of each particle is a c 9 4 4r 2 1 q 4 8r b d 1 q 4 2r 2 1 q 4TE r

ing spheres are of radii r and r The outer sphere is given a charge q The charge q on the inner sphere will be inner sphere is grounded 1 q 2 q 3 q r2 10 9 oll q wkow corto 1444 r2

Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively and having an equal charge 10 C are connected by a copper wire and then they are separated Then a both spheres will have equal charges b surface charge density on the 20 cm sphere will be greater than that on the 15 cm sphere c surface charge density on the 15 cm sphere will greater than that on the 20 cm sphere d surface charge density on the two spheres wil

A solid insulating sphere of radius R is given a charge Q which is uniformly distribute over the volume If at a point inside the sphere the potential is 1 5 times the potential the surface this point will be A at a distance of 2R 3 from the centre C at a distance of 2R 3 from the surface B at the centre D data insufficient

Three charges 91 92 and q3 are located at the vertices of an equilateral triangle of a Find the electric potential energy of the system are brought one by one

55 If a charge q is placed at the a hemispherical body as shown below then the flux linked with the curved surface is 9 1 EO 9 2 200 3 2q E 4 q 2 E

After one bee left a flower with a positive charge that bee flew away and another bee with the same amount of positive charge flew close to the plant Draw a diagram that best represents the electric field lines between the bee and the flower Defend your illustration

24 If the attractive force between a 5 C charged particle and an 8 C charged particle is 10 5 N what is the distance between the two particles 124x1 1645 877210 5910

Positive charges of 9 nC and 4 nC are placed at the points A and C respectively of a right angled triangle ABC in which ZB 90 AB 3 cm and BC 2cm Find the electric intensity at B 12 73 x 10 N C making a 45 with E and E ilotoral triangle ABC

Statement 1 A point charge q is placed inside a cavity of conductor as shown Another point charge Q is placed outside the conductor as shown Now as the point charge Q is pushed away from conductor the potential difference V V between two points A and B within the cavity of sphere remains constant Statement 2 The electric field due to charges on outer surface of conductor and outside the conductor is zero at all points inside the conductor q B 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

25 As a result of change in the magnetic flux linked to the closed loop as shown in the figure an e m f V volt is induced in the loop The work done in joule in taking a charge Q coulomb once along the loop is 1 QV QK 2 2QV

Q 17 The force of attraction between two charges 70 C and 80 C separated by a distance of 0 25 mis 201 6N What is the dielectric constant of the medium separating the charges 4 O 105N

A spherical cavity is created in a neutral solid conducting sphere Inside the cavity a dipole is placed as shown in the figure Electrostatic potential at point P only due to charge induced on the inner surface of the cavity is assume that d A C q sine 4mo d q sine B D q sine 4 mod q sine 4tFod Bie

4 3 4 As one moves radially from infinity towards the centre of uniformly charged sphere electric field intensity will V 1 Increase continuously 2 Decrease continuously 3 First decrease then increase

BASED ON GAUSS LAW Figure shows a charge Q placed at the centre of open face of a cylinder as shown in figure A second charge q is placed at one of the positions A B C and D out of which positions A and D are lying on a straight line parallel to open face of cylinder In which position s of this second charge the flux of the electric field through the cylinder remains unchanged LAJA C C B B LIBID De

The electric field components of the field shown in figure are E ax 2 E E 0 in which a 5 N C m2 Calculate a the flux de through the cube and b the charge within the cube Assume a 1m AIPMT Mains 2008 1 AR

A parallel plate capacitor has a capacitance C and charge Q Another plate is inserted in between the plates of the capacitor at the center and is connected by a long wire to another far off spherical conductor of radius R What is the potential difference between the edge of the sphere and one of the outer plates A C 0 0 2 2C B D Q 4C 20 C

16 Two pith balls carrying equal charges are suspended from a common point by strings of equal length the equilibrium separation between them is r Now the strings are rigidly clamped at half the height The equilibrium separation between the balls NEET 2013 now becomes a c 2 2r 3 3 b d 1 2r 3 y 2 placed

2 A bar magnet of length 3 cm has points A and B along its axis at distances of 24 cm and 48 cm o opposite sides Ratio of magnetic fields at these points will be A 1 8 3 3 K24 cm 2 48 cm 1 2 2 4 4 B

Find the net potential energy of the system of charges shown in the adjacent figure a q q a

An electric dipole is kept at origin as shown in the diagram The point A B C are on a circular arc with centre of curvature at origin If the electric fields at A B and C respectively are E E E3 then which of the following is incorrect d 1 B A 1 E E 3 E E 14 C X d 2 E 2E 4 E3 2E

26 The electric field required to keep a water drop of mass m just to remain suspended when charged with one electron is DPMT 1999 2001 mg a mg b e em g c emg d

1 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 a directed perpendicular to the plane but towards the plane b directed perpendicular to the plane and away from the plane c directed radially away from the point charge d directed radially towards the point charge

field is more at P than at P In fact the electric field s proportional to the lines per unit area if the lines riginate isotropically from the charge P P

2 A charged particle having charge q and mass m accelerated by a potential difference Vo enters inside a parallel plate capacitor parallel to length of plates at midpoint of its separation between plates at t 0 Potential difference across capacitor varies with time t as V a dt where a is constant and d is separation between plates Angle of deviation as it comes out of plates is T 4 ma214 2qV3 Value of 1 16 2 32 3 8 4 4 will be

IX 9 Three charges q q and q are placed at the corners of an equilateral Physics Vol 3 triangle of side a Find the resultant electric force on a charge q placed at the centroid O of the triangle 1 2 2 3q 2 a Four equal 6q 5 2 a 6q a 3 5 EO MK 2q a 4 5 EO

38 A positively charged ring is in y z plane with its centre at origin A positive test charge q held at Porigin is released along x axis then its speed 1 Increases continuously car 2 Decreases continuously 3 First increases then decreases 4 First decreases then increases hey

The electric potential at a point x y in the xy plane is given by V Kxy The electric field intensity at a distance r from the origin varies as a b r d 2 c 2r

assiq Bad isola asa o ela al elisa A B C q 2 0 9 2 0 3 1 D 1 0 0 faydo doll 6 C B q A

3 9 The X Y Z space has an infinite charged sheet having charge density o on the Y Z plane A negative charge particle Q is placed at a 0 0 The variation of net electric field on x axis is shown in the figure Then choose the correct option s A Q 2 2 B Q 4 a C The net electric field at the point a 2 0 0 is 50 20 D At point 5a 2 0 0 the net electric field is 50 1880 E a 0 0 2a 0 0

Four identical charges 50 C each are placed one at each corner of a square of side 2 m How much external energy is required to bring another charge of 50 C from infinity to the centre of the square a 64 J c 16 J b 41 J d 10 J

Determine the equivalent resistance between point A and B in 2 considering that connecting wires have no resistance www 802 12 2 202 50 602 222 www 50 522 www 5222 www 502 www 3602 692 W 802 202 wwww 602 122

If the distance of separation between two charges is increased the electrical potential energy of the system a May increases or decreases b Decreases c Increase d Remain the same

Inside a uniformly charged ball at r r the electric m field is maximum Then Given P Po R 1 1 volume charge density R 3 1 m 3 r 2R 3 m 2 m 3R 2 rm 4 rm 4R 3

41 Eight charges having the valves as shown are arranged symmetrically on a circle of radius 0 4m in air Potential at centre O will be 13 a 63 10 0 volt b 63 104 volt c 63 106 volt d Zero 7 C a 15 C O 7 C 5 C 5 C B 11 C 4 7 C 12 0 5 C 12

unstable Example 15 Two point charges of charge values Q and q are placed at distances x and x 2 respectively from a third charge of charge value 4q all charges being in the same straight line Calculate the magnitude and nature of charge Q such that the net force experienced by the charge q is zero CBSE D 98 Solution Suppose the three charges are placed as

8 A system of three charges are placed as shown in the figure q c q Kd If D d the potential energy of the system is best given by JEE Main 2019 9 April Shift 1 1 1 a 4 o 4 TEO 1 4 TEO q 2qQd d D D q qQd d 2D b d Q 1 4 q butqQd d D q d qQd D

net It is important to note here that the force which the charges exert on each other is not changed by the presenc a third charge d Enhancer 2 Two equal charges q are separated b distance d Third similar charge is placed on a perpendicular bisector at a distance The force 2 experienced by the third charge when whole set up i placed in vacuum and a medium of dielectric consta is Fo and Fm respectively If Fm 0 then 2 a Fo 72 10 q K 2

apart 3 Two point charges 3 C and 3 C are kept 20 cm apart in air Find the electric field midway between the charges on the line joining them What will be the force experienced by a charge 1 5 x 10 C placed at this point 5 4 x 106 N C 8 1 x 10 N 4 N Wh

A negatively charged rod is moved near conducting sphere as shown What will be the movements of the electrons and protons in the conducting sphere Negatively charged rod Electrons move to left A B move to right C does not move D move to right O Conducting sphere Protons move to right move to left move to left does not move

8 Two identical pith balls each weighing 25 mg are hung from the same point by two in extensible and non conducting threads of equal length Equal amounts of identical charge given in the pith balls keeps them in equilibrium when the distance of their separation is 10 cm with the threads making an angle of 40 find the charge on each pith ball 0 01 x 10 C X respectively from a positive charge 4q

24 A large non conducting sheet S is given a uniform charge density Two uncharged small metal rods A and B are placed near the sheet as shown in the following diagram Then the incorrect option is 8 S 1 S attracts A A B 2 S attracts B

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

existing in space is 0 The electric potential V x y z A xy yz zx a Write the dimensional formula of A b Find the expression for the electric field c If A is 10 SI units find the magnitude of the electric field at 1 m 1 m 1 m