Electric Field and Potential Questions and Answers

The region between two concentric spheres of radii a and b respectively see figure has volume A charge density p where A is a constant and r is the distance from the centre At the centre of r the spheres is a point charge Q The value of A such that the electric field in the region between the spheres will be constant is JEE Main 2016 2Q Q a 2Q mics Eng 02 JM JA p65

A current I flows through a paraboloidal surface uniformly The magnetic field due to the paraboloidal surface at point P is H4 I K r Then find the value of K

19 as that on the surface of charged solid sphere In the arrangement of concentric shells as shown in the given figure the ratio of electric field at points 1 2 is 1 1 2 3 4 3 2R 3R R Q 2r 2Q 3Q 2 3 4 4 2 3 d charc

A non conducting square plate of side length 2a is uniformly charged with charge Q and a point charge q is placed at perpendicular distance a as shown in figure The electric force on the point charge due to plate is X q X

1 Two charges placed in air at a distance 1 m exert force F on each other If these charges placed inside mica at same distance then the new net force between charges is 1 F 2 F 3 F 4 Depends on area of slab

Example 22 Two identical thin rings each of radius R are coaxially placed a distance R apart If Q and Q are respectively the charges uniformly spread on the two rings the work done in moving a charge q from the centre of one ring to that of the other is JEE 199 a zero c q 2 Q Q 4 R b 9 Q Q 2 1 2 4 E R d q Q Q 2 1 2 4 ER

4 Two concentric conducting thin and 2R carry charges Q 3Q respectively The magnitude of electric field at a distance x outside P and inside Q from the surface of outer sphere is same Then the value of x is R 3 2R 3Q Q P 2 2R 3 O

A cube of edge I is placed in uniform electric field as shown in Fig a if the cube is rotated by angle with vertical as shown in Fig b Calculate the flux of electric field entering the cube

Starting from rest an electron moves through a small distance in an uniform electric field of magnitude 2 104 NC 1 The direction of the field is reversed keeping the magnitude unchanged and a proton moves through the same distance The time of motion will be 1 Same in both cases 2 More in the case of an electron 3 More in the case of proton 4 Independent of charge

Let P r r be the charge density distribution for a TRA solid sphere of radius R and total charge Q For a point p inside the sphere at distance from the centre of the sphere the magnitude of electric field is AIEEE 2009 Q a 0 b 4 r 2 Qr c Q 4 En R d D4

A charge q is placed at each of the points x x0 x 3x0 x 5x0 upto on the x axis and a charge q is placed at each of the points x 2x0 x 4x0 x 6x 8 upto Here xo is a positive constant Take the electric potential at a point due to a charge Q at a distance r from it to be Q 4 or Then the potential at the origin due to the above system of charges is a 0 b c 8 d 9 8 oxo In 2 q ln 2

Position 1 2 3 4 5 6 Battery 900 Voltage V 9 2 3 w 200mA 9V m 20mA Current mA 20 200 140 3V 2V 140mA Resistance Ohm 90

2 Example 1 14 Two identical helium filled balloons A and B fastened to a weight of 5 g by threads floats in equilibrium as shown in figure Calculate the charge on each balloons assuming that they carry equal charges sight u

A block of mass m and charge q is connected to a point O with help of an inextensible string The system is on a horizontal table An electric field is switched on in direction perpendicular to string What will be tension in string when it become parallel to electric field 1 qE 2 l E 2 3qE

H A charged Q is uniformly distributed over a thin rod AB of length L as shown in the figure The electric potential at the point O lying at distance 2L from the end A is 1 0 4 L en 2L 3 2 A 2 L B 3Q 4 L

5 In x y coordinate system a particle P of charge q and mass m enters first quadrant close to x 0 as shown in figure In this region potential varies as V ax Which of the following graphs representing the variation of particle s velocity and acceleration A KKKK B vibrantacademy com 1451

A hemisphere of radius R as shown in figure is uniformly charged with a surface charge density o The electric field at the centre C is 1 3 0 6 0 3 C R 2 4 olo 280 20 E

A metal sphere of mass 20 g carrying a positive charge of 10 C is hung by a thread from a rigid support Teh charged sphere is now immersed in a horizontal electric field of intensity 1000 N C Find the angle made by the thread in the displaced position and the tension in the thread 0 2 N Q 2 54 hung from the same point by two in extensible and

21 The equivalent resistance between points A and B is 1 3 3R 2 2R 3 A R R R ww ww www R R B 2 2R 4 3R

1 Find the value of emf s when Ammeter read 3 A current flowing through it A 1 12 volt 3 12 volt R 3Q2 www 12V E R 692 www R 69 2 6 volt 4 6 volt

When charge of 3 coulomb is placed in Uniform electric field it experiences a force 3000 newton within this field potent difference between two points separated by distance of 1 cm is A 10 Volt C 1000 Volt B 90 Volt D 3000 Volt

Three infinitely long charge sheets are placed as shown in figure The electric field at point P is a 20 O 20 0 b Z 4 O 20 k k P c Z 3a Z a Z a 40 k d 40 k E

37 A thick shell with inner radius R and outer radius 3R has uniform density p c m It has a spherical cavity of radius R as shown in the figure The electric field at the centre 0 of the cavity then the value of a is XXX XX X X 4 XXX XX 0 X R 13R apR is 1280 ostane

1 A total charge Q is broken into two parts Q and Q placed at a distance R The maximum repulsion occurs when 4Q 2 Q Q 200 3 2Q 3Q 3 Q 4 Q 2 2iQ 2 2 2 4 5 Two charges 1 C and 4 C are kept 30 cm apart as shown below Where should another charge 1 Q2 Q 20

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

Dark the circle in Rough work must not be done on the Answer sheet and do Answer sheet Each question carries 4 marks For every wrong response ose the correct answer A spherical conductor of radius R charged with Q units of charge The escape velocity of a particle of charge q and mass m from surface of conductor is Qq 1 4TEOR 3 Qq VeomR Two Qq 2 2mmR MR Qq 4 4x2 mR PHYSIC metal balls with radi and r are at a distance nected to a battery of

An isolated solid metal sphere of is given an electric charge The variation of the intensity of the electric field with the distance r from the centre of the sphere is best shown by E 1 3 0 E R r 2 4 E O E R T

A 6 volt battery of negligible internal resista resistance is connected across a uniform wire AB of length 100cm The positive terminal of another battery of emfAV and internal resistance 1 is joined to the point A as shown in fig Take the potential at B to be zero At which point D of the wire AB from left the potential is equal to the potential at C approximately 6V A 4V www 192 D C N BOTTO 2 2 67 cm meR E 21 X2

3 37 Two identical small conducting spheres A and B have charges 1 mC and 3 mC on them and they attract each other with a force F Two other identical spheres C and D each containing 5 mC are touched separately to A and B respectively and removed The magnitude of force between sphere A and B now is 1 12F 21 2 4F 4 F

e 3x10 Two fixed charges A and B of 5 C each are separated by a distance of 6 m C is the mid point of the line joining A and B A charge Q of 5C is shot perpendicular to the line joining A and B through C with a kinetic energy of 0 06 J The charge Q comes to rest at a point D The distance CD is KCET 2012 a 3m c 3 3m b 3m d 4m

24 A rod is bent into a semi circular arc of radius R The rod has a uniform linear charge distribution 2 The potential at the centre of the arc point P is 1 2 R 2 P 2 R 1 4 0

A fixed ring of radius R is having uniformly distributed charge Q over its circumference A charge q of opposite nature and mass m is kept on its axis at a distance a R from the centre of ring If charge is released from rest then minimum time after which it will pass through centre of the ring will be Effect of gravity is k considered to be negligible K 1 mR 2 kQq 3 2T mR 2 4 1 4 E mR kQq mR AN kOg

In a region of space suppose there exists If a positive uniform electric field E 10i V m charge moves with a velocity 2 potential energy 1 Increases 2 Decreases 3 Does not change Ingroases

Figure shows a hemispherical shell of mass M and radius R and a concentric shell of mass m and radius 3R 4 A the mutual gravitational potential energy of the system will be 4GmM 3R GmM R B the mutual gravitational potential energy of the system will be C the force of attraction between the two masses is 16GMm 9R GMm D the force of attraction between the two masses is R M ARM

PRACTICE PROBLEMS Two identical anions are placed 7 x 10 10 m apart and each o experiences a force of 4 x 10 N Calculate the charge present on each

configuration and a spherical Gaussian surface as shown in the figure while calculating the flux of the electric field over the spherical surface the electric field will be due to a 92 c all the charges c 8 A metallic shell has a point charge q kept inside its cavity Which one of the following diagrams correctly represents the electric lines of forces IIT 2003 a a 9 Three infinitely long charge sheets are placed as shown in the figure 20 O 20 0 40 0 The electric field at point P is 20 b b only the positive charges d 91 and 91 IIT 2004 k Z P 1 1 k 80 40 k z 3a z a X Z A IIT 2005

What is the angle between the electric dipole moment and the electric field due to itself on the equatorial line 1 0 3 180 2 90 4 None of these at the the corner of a cube of side

16 Two charges q1 at the origin and q2 4q1 at x 198 m What is the coordinate of point P meters between the two charges on the x axis where the electric potential is zero

Two identical charged particles each carrying charge q 0 1 mC and of mass m 10 mg are projected along two parallel lines separated by a distance with equal speed Vo 10 m s in opposite directions In the beginning electrostatic interaction between the charges can be ignored due to a large distance between them The minimum distance between the particles is found to be 12 cm The value of Lis equal to A 6 cm C 12 cm B 8 cm D 4 cm

of the electric field strength in the metry plane of this system located between the threads 3 23 An infinitely long cylindrical surface of circular cross section is uniformly charged lengthwise with the surface density 0 cos where o is the polar angle of the cylindrical coordinate system whose z axis coincides with the axis of the given surface Find the magnitude and direction of the electric field strength vector on the z axis 3 24 The electric field strength

Along the x axis three charges x 0 x a and x 2a respectively The resultant electric potential at a point P located at a distance a r from the charge q is E is the permittivity of free space a ga TATE 2 b 9a 3 4Teor 22 9 and 21 12 c 9 2 a ATS 3 are placed at d 9 4Teor

28 Calculate the electrostatic force and gravitational force between the proton and the m The electron in a hydrogen atom They are separated by a distance of 5 3 x 10 magnitude of charges on the electron and proton are 1 6 10 19 C Mass of the electron is 31 27 m 9 1 x 10 kg and mass of proton is m 1 6 10 kg

43 As shown in the figure charges q and q are placed at the vertices B and C of an isosceles triangle The potential at the vertex A is a b c 1 2q 47 a b 1 4TE q a b 1 q A E b d Zero BO q b q

3 An electric dipole of length 2 cm when placed with its axis making an angle of 60 with a uniform electric field experiences a torque of 8 3 N m Calculate the potential energy of the dipole if it has charge of 4 nC Delhi 2014

An observer is at distance r metre from isotropic point light source whose power is H watt The r m s value of electric field at the position of observer is 1 H 1 2r TEC 2 2 H TE C 1 H 3 4r TEC H 1

experien 2 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 3 Two identical small plastic balls are rubbed against a piece of wool such th of them received approximately 2 x 10 2 and 2 5 x 10 2 electrons COF

led with two layers of different materials and B as shown in the figure on the next page The material A has lectric constant k and conductivity o and the material B has Cor 13 A Bs dielectric constant k and conductivity 2 The capacitor is connected across an ideal battery of terminal voltage V Permittivity of free space is to 22 Electric field in the material A is Vo do do a a Vo do do c b 23 What is the total surface charge density on the interface of the two materials EV k k d k d k V ok a k d b Vo do do Vo do d o d V 0 0 do d o v d d

A battery of electro motive force E is connected in series with resistance R and a voltmeter An ammeter is connected in parallel with the battery 1 neither the ammeter nor the voltemter will damaged 2 both ammeter and voltmeter are likely to be damaged 3 only voltmeter is likely to be damaged 4 only ammeter is likely to be damaged

1 0 4 L 2 0 5 L A small sphere with mass 1 2 g hangs by thread between two parallel vertical plates 5 00 c The plates are insulating and have uniform surface charge densities sphere is q 9x10 C What potential difference between the plates will cause the thre assume an angle of 37 with the vertical as shown in Fig and o The cha 37 5 00 cm

33 Force of interaction between two small dipoles at axial positions of each other is directly proportional to rn where r is distance between the center of dipoles Value of n is 1 1 3 3 2 2 4 4