Electric Field and Potential Questions and Answers

tallic sphere ctric field at charge on R 2 nnected in tric slab of 3 2 F 23 A solid sphere conducting is surrounded by metallic shell of radius 2r Initial charges on them are 5 C and 3 C respectively If both are connected by thin metallic wire then charge appearing on A and B are 1 4 C each 5 C 2r 3 C A B 2 0 and 8 C 4 2 C and 6uC

In which of the following point P is non zero 1 q 2 3 4 49 4g 9 r 2r r r P P r 9 r P q r option is correct cases electric field a E60 r P q q

plate having negative value Problem 7 Two large parallel metal plates 3 00 mm apart are charged to a potential difference of 12 V a What is the field between them b they are now disconnected from the battery and pulled apart to 5 00 mm What is the new electric field between them and what is now the potential difference Solution VB d Fig 4 27

6 An airplane is flying through a thundercloud at a height of 2000 m This is a very dangerous thing to do because of updrafts turbulence and the possibility of electric dis charge If a charge concentration of 40 0 C is above the plane at a height of 3 000 m within the cloud and a charge concentration of 40 0 C is at height 1 000 m what is the electric field at the aircraft

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

A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure Find the 1 amount of heat produced when switch is closed k 41 0 kq a 2a b 2 kq 3a S a 3a 2a c kq 4a d kq 6a

190 There are four concentric shells A B C and D of radii a 2a 3a and 4a respectively Shells B and D are given charges q and q respectively Shell C is now earthed The potential difference VA Vc is take K 1 4TE 0 a Kq 2a 4a 91 A solid conducting sphere having a cho Kq 3a b Kq c d Kq 6a

Figure shows an arbitrary body through which electric charge is distributed in an arbitrary way The body is divided in two region A and B Using the result The electric force that the charge in region A exerts on the charge in region B is equal to the force that the charge on the entire body exerts on the charge in region B or otherwise solve next two problems Consider a uniformly charged spherical shell of radius R having total charge Q Find electric force exerted on each hemisphere by the charge on the other hemisphere A Q Ane R B B 16xe R Q S8 R 35

Leader lest Series Joint Package Course 20 08 2017 Figure shows a cylindrical conducting rod of diameter d and length d is uniformly charged in vacuum such that electric field near its surface and far from its ends is E Electric field at r on the axis of the cylinder is Then find the value of N 3Eold 2Nr2

A charge of 90 nC is uniformly distributed along a rod of length L The magnitude of the electric field at a point 20 cm from one end of the rod and lies along the axis of the rod is 1 8x10 N C The length in m of the rod is 1 01 55 2 1 80 3 02 05 4 2 30 5 0255

Question 10 10 J In the center of a sphere of radius 0 5 m a charge Q 55 0 nC is placed as shown in the figure Find the flux in N m C through the surface of area 0 785 m and half angle 0 60 0 1 0989 1 2 O1130 4 3 O1271 7 4 O 1413

1S then what is the energy density between the plates 11 64 droplets of mercury each of radius r and carrying charge q coalesce to form a big drop Compare the surface density of charge of each drop with that of the big drop

Passage IV Q No 11 to 14 A thin non conducting ring is placed in XOY plane with its axis along Z axis and centre 0 o is constar origin Ring is charged such that it acquires a charge density of Ao cose and is angle made with positive direction of X axis measured anti clockwise 11 Charge on the ring is a positive everywhere b negative everywhere 3 1 c positive in th part and negative in th part 4 4 d total charge on the ring is zero 12 X component of electric field at centre of the ring is kno 2 k o 20 a c R R 480 R 13 Y component of electric field at the centre of the ring is kno 2k o 20 b c R R 480 R a 4 Electric field at a point distant x from centre of ring will be 20R along X axis R b a c 4 R 480x b along Y axis along X axis 0 23 d along Y axis R 2 m d 20 28 R d 0

k 100 Subjective Questions 1 A 4 00 kg block carrying a charge Q 50 0 C is connected to a spring for which electric field of magnitude E 5 00 x 10 V m directed as shown in figure If the blo The block lies on a frictionless horizontal track and the system is immersed in a uni released from rest when the spring is unstretched at x 0 k m Q E X 0 a By what maximum amount does the spring expand b What is the equilibrium position of the block c Show that the block s motion is simple harmonic and determine its period d Beneat part n if the CC

Two identical charged spheres suspended from a common point by two massless strings of lengths 1 are initially at a distance d d apart because of their mutual repulsion The charges begin to leak from both the spheres at a constant rate As result the spheres approach each other with a velocity v Then v varies as a function of the distance x between the spheres as 1 Ux x 1 2 3 vx x 2 NEET 2016 2 vx x 4

Three charges q q and q are situated in X Y plane at points 0 a 0 0 and 0 a respectively F otential at a distant point r r a in a direction making an angle 0 from the Y axis

Example 8 8 Two charges 5 x 10 8 C and 3 10 8 C are located 16 cm apart At what point s on the line joining the two charges is the electric potential zero Take the potential at infinity to be zero

A point charge q is situated at a distance d from one end of a thin non conducting sheet of constant thickness t and of length L as shown in the figure The width of the sheet varies linearly from 2a to 2b The sheet has a charge Q uniformly distributed Find the q force between the two in Newton Given d 1 cm a 18 m t 0 01 mm L a b 144 m Q 16 104 C q 105 C Do approximation if required d 2a

23 A potentiometer wire of length 4 m and resistance 8 2 is connected in series with a battery of emf 2 V and negligible intemal resistance If the emf of the cell balances against a length of 217 cm of the potentiometer wire find the emf of the cell

Three charged particles having charges q 2q c are placed in a line at points a 0 0 0 a 0 respectively The expression for electric potential a P r 0 for r a is 1 4 1 qa r4 2 1 4ga 2 1 2qa 7 3 1 8qa 41EO

eE eE 62 One half of a semicircular ring of radius R has charge Q while the other half has Q The ring is placed in xy plane where a uniform electric field exists E E y R Find the work required to be done by external agent to rotate the ring about z axis by 90 in clockwise direction

There is a uniformly charged non conducting solid sphere made of material of dielectric constant one If electric potential at infinity be zero then the potential at its surface is V If we take electric potential at its surface to be zero then the potential at the centre will be 1 3V 2 2 V 2

two charges The electric field due to a discrete charge configuration is not defined at the locations of the discrete charges For continuous volume charge distribution it is defined at any point in the distribution For a surface charge distribution electric field is discontinuous across the surface

Example 1 7 Consider the charges q q and q placed at the vertices of an equilateral triangle as shown in Fig 1 10 What is the each charge force on 125 F F 3 F13 A 9 9 1 3 93 q C FS1 F3 C 1 F32 F F B o be repub 2 q 9 nd F21

napart At what point on the line joining the two charges ic potential zero Take the potential at infinity to be zer ion Let us take the origin O at the location of the positive ne joining the two charges is taken to be the x axis the n e is taken to be on the right side of the origin Fig 2 7

Q 11 Shown in the figure is a semicircular metallic strip that has thickness and resistivity p Its inner radius is R and outer radius is R If a voltage Vo is applied between its two ends a current I flows in it In addition it is observed that a transverse voltage AV develops between its inner and outer surfaces due to purely kinetic effects of moving electrons ignore any role of the magnetic field due to the current Then figure is schematic and not drawn to scale A Vot In R p 624 AV V R B the outer surface is at a higher voltage than the inner surface C the outer surface is at a lower voltage than the inner surface D AV x 1

Fare Between Skew Lines Two mutually perpendicular long straight conductos carrying uniformly distributed charges of linear charge densities and 2 are positioned at a distance a from each other Find the interaction force between rods df sid

A non conducting ring of mass m and radius R is charged as shown The linear charge density for corresponding region shown is A It is placed on rough horizontal surface A uniform electric field Eoi is switched on and the ring starts rolling without sliding Angular velocity acquired by the ring when it turns through an angle ofis 16 rad s XEo Value of in SI unit is m GWHI M J AJU R yc Guac dau ch Tafy Gyuz fa fu ga i tuf na da er ua 31 32 g 92 ZW T4 1 Y Aux faya E dau faa fud g fc geal 21 Ga dau ch 7 22 HARIH lal ad such a gwa fchu nu c uftu 16 rad s XEo m PREVIOUS NEXT X

28 9 The Potential of a Charged Conductor 15 A small conducting sphere originally has a charge q The sphere is lowered into a conducting can a Which of the fol lowing quantities are fixed as the sphere is lowered but before it touches the can There may be more than one correct answer A The potential of the can B The potential of the sphere C The charge on the sphere D The net charge on the sphere and can b The ball touches the can Which of the following quanti ties are the same both before and after the ball touches the can There may be more than one correct answer 28

5 12 An alternating voltage is connected in series with a resistance R and an inductance L If the potential drop across the resistance is 200V and across the inductance is 150V then the applied voltage is A 350 V C 500 V B 250 V D 300 V

0 A charge q is lying at mid point of the line joining the two similar charges Q The system will be in if the value of q is b Q 2 d Q 4 equilibrium a Q 2 c Q 4

An electric dipole consists of two point charges 5Q and 5Q separated by a distance 2a as shown in the figure a Find the net electric field at P a distance 2a from the dipole Clearly show your coordinate system b If a point charge of mass M and charge 2Q is placed at P use your result from a to find the force applied by the dipole on this new charge 5Q a a 2a P

uppose that over a certain region of space the electrical potential V is given by the following equation V x y z 3x 4xy xyz a Find the rate of change of the potential at P 5 4 6 in the direction of the vector v i j k b In which direction does V change most rapidly at P c What is the maximum rate of change at P

An infinite number of point charges each carrying 1 C charge are placed along the y axis at y 1 m 2 m 4 m 8 m The total force on a 1 C point charge placed at the origin is x 10 N The value of x to the nearest integer is 1 Take 9x10 Nm C 4 0 ven 9000000

Two charges q1 and q2 are separated by a distance d and exert a force F on each other Analyze Coulomb s Law and identify what new for will exist if q1 is doubled 0 2F O 3 4 F THE

6 A long straight wire carries a current i Let B be the magnetic field at a point P at a distance d from the wire Consider a section of length 1 of this wire such that the point P lies on a perpendicular bisector of the section Let B be the magnetic field at this point due to this section only Find the value of d l so that B differs from B by 1

2 A test charge is moved from lower potential point to a higher potential point The potential energy of test charge will a remain the same c decrease b increase d become zero char C and C

Four charges 2C 3C 4C and 5C respectively are placed at the four corners of a square Which of the following statements is true for the point of intersection of the diagonals 1 E 0 V 0 3 E 0 V 0 2 E 0 V 0 4 E 0 V 0

A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 volts The electric field at the centre of the sphere will be 1 50 volt meter 2 10 volt meter 3 5 volt meter 4 zero

or the system shown in figure find Q for which the resultant force on q is zero

5 33 In the circuit shown in the figure 5 296 the AC source gives a voltage V 20 cos 2000 Neglecting source resistance the voltmeter and ammeter reading will be 652 A OV 0 47A C 0V 1 4 A 5mH ooooooo in H 40 5 F Figure 5 296 B 1 68V 0 47A D 5 6V 1 4 A

65 A charged particle mass m and charge q moves alon X axis with velocity V When it passes through the origin enters a region having uniform electric field E Ej which extends upto x d Equation of path of electron in the region x dis 2 Sept 2020 Morning A y C y 0 qEd d mv 2 x qEd 172 X YA Vo LE d B y D y qEd mv2 x d 9Ed

Three identical charges each of 1 C are kept on the circumference of a circle of radius 1 metre forming equilateral triangle The electric intensity at the center of the circle in N C is 1 9 10 3 27 10 2 13 5 10 4 Zero

15 Find the glanci Hint 20 0 180 Here 52 Find the retarding potential required to stop electron of the de Broglie wavelength 0 5 nm 6 Hint eV hc 2 longths of an x particle and a deutron if they are accelerat

Example 2 3 Figures 2 8 a and b show the field lines of a positive and negative point charge respectively a 0 P O G b B FIGURE 2 8 a Give the signs of the potential difference V V VB VA Give the sign of the potential energy difference of a small negative charge between the points and P A and B c Give the sign of the work done by the field in moving a small positive charge from Q to P d Give the sign of the work done by the external agency in moving a small negative charge from B to A Does the kinetic energy of a small negative charge increase or decrease in going from B to A

9 Two identical charged spheres suspended from a common point by two massless strings of lengths I are initially at a distance d d apart because of their mutual repulsion The charges begin to leak from both the spheres at a constant rate As a result the spheres approach each other with a velocity v Then v varies as a function of the distance x between the spheres as NEET 2016 1 VX 1 1 2 2 Vx X 4 VX 1 2 Eo 13 A charge Q is en surface of radius the outward elec 1 Be double 2 Increase 3 Be redu 4 Remain 14 Two positi separate

If two positive point charges q are placed on the x axis one at x a and the other at x a then the electric field a is maximum at y If charge Q of mass m is kept 2 on y axis at large distance from the centre then it will execute oscillatory and periodic motion but if it is released very close to the origin then it will execute SHM with time period T 2 q O 2 ma oma3 Qg y axis 0 0 q a 0 x axis X R 2 E 41 Emax R 2 X

Both question a and b refer to the system of charges as shown in the figure A spherical shell with an inner radius a and an outer radius b is made of conducting material A point charge Q is placed at the centre of the spherical shell and a total charge q is placed on the shell Charge q is distributed on the surfaces as A Q on the inner surface q on outer surface B Q on the inner surface q Q on the outer surface C Q on the inner surface q Q on the outer surface D The charge q is spread uniformly between the inner and outer surface Assume that the electrostatic potential is zero at an infinite distance from the spherical shell The electrostatic potential at a distance R a R b from the centre of the shell is A 0 B KQ a C KQ q R D K Q 9 b 9 where K a 1 4

Two small spheres each having a mass of 20 g are suspended from a common point by two insulating strings of length 40 cm each The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm Find the charge on each sphere 1 2 4 x 10 C 2 3 6 10 8 C 3 4 17 x 10 8 C 4 6 4 x 10 8 C

In a certain region of space with volume 0 2 m the electric potential is found to be 15 V throughout Wha is the electric field in this region O 30 N C O 7 5 N C O 75 N C Zero