Electric Field and Potential Questions and Answers

Charge Q of mass m revolves around a point charge q due to electrostatic attraction Show that its period of revolution is given by T2 16T EmR Qq

1 Two charges 9e and 3e are placed at a separation The distance of the point where the elect field intensity will be zero is 1 CY 3 4 r 1 3 3r 3 1 r 1 3 3r 1 3 from 9e charge from 9e charge from 3e charge from 3e charge DE Fon

Paragraph for Q no 5 to 8 Consider a system of two equal point charges each Q 8 C which are fixed at points 2m 0 and 2 m 0 Another charge q is held at a point 0 0 0 1m on the y axis Mass of the charge qis 91 mg At t 0 q is released from rest and it is observed to oscillate along y axis in a simple harmonic manner It is also observed that at t 0 the force experienced by it is 9 x 10 N Neglect gravity ange A 2m 0 2m 0 1m Initially 3x102 1Q 2m 2m 0 x B

Column I shows four uniformly charged systems with a cavity Column II and column III list the ratio of potential and field at point A after making the cavity with the values before making the cavity e 1 11 III IV Column 1 S P Solid sphere with spherical cavity R a R 2 R R 29 Cavity 0 origin A P Solid sphere with concentric spherical cavity a 2 A Solid cube with cubical cavity h 4 h Solid cone with conical cavity Column 2 Potential i 7 8 ii 3 4 iii 15 16 iv 5 6 P Q R S Column 3 feild 3 4 1 2 7 8 5 6

A thin spehrical shell of radius R has a charge Q spread uniformly over its surface Which of the following graphs most closely represents the electric field E r produced by the shell in the range 0 r o where r is the distance from the centre of the shell AIEEE 2008 1 0 E r R r 1 2 R E r R 2 r 3 E r n R R 4 Statement 1 is false Statement 2 is true 12 In a uniformly charged sphere of total charge Q and radius R the electric field E is plotted as a function of distance from the centre The graph which would correspond to the above will be AIEEE 2012 3 4 R E r O R 4 R If M mass L Length

8 6 A pendulum bob of mass 80 mg and carrying a charge of 2 x 10 C is at rest in a uniform horizontal electric field of 20 kVm Find the tension in the thread

Two identical copper spheres A and B equally charged repel each other with a force of 4 x 10 N A third similar copper sphere C carrying no charge is now brought into contact with A and placed midway between A and B What force would C experience 4 x 10 5 N

3 4 varied with the applied electric field E as Vd va x E Then V I graph for a wire made of such a material is best given by V 1 2 2 V V

Given Mass of an electron is The charges on three identical ebonite spheres are 2 mC 4 mC and 2 mC respectively Now the first sphere is brought in contact with the second sphere and then moved apart Then the second sphere is brought in contact with the third sphere and moved apart Calculate the charge acquired by each sphere provided each sphere is kept on an insulated stand

65 A charge 10 C is placed at the centre of a hemisphere of radius R 10 cm as shown The electric flux through the hemisphere in MKS units is a 20 105 b 10 105 c 6x 105 d 2 105 R 10 C

Two equal positive charges are kept at points A and B The electric potential at the points between A and B excluding these points is studied while moving from A to B The potential a continuously increases b continuously decreases c increases then decreases d decreases then increases

2 Two fixed equal positive charges each q are located at point A B separated by a distance of 6 m A particle of mass m having equal and opposite charge q moves towards them along the perpendicular bisector line COD where O is the centre of line joining A and B If q charge is released from rest from point C then speed of charge q at O is given by gravity A q 4m X 15 m B q find value of x Neglect

A uniform electric field of 50 2 Vm 1 exists in XY plane making an angle of 45 with positive X axis as shown in below figure The potential difference VA Vg is B 4 m 0 300 v A 0 2 m 45 2 300 V

4 An electric dipole consists of two charges of 0 5 C kept at distance of 1 0 cm Calculate the potential energy required to place the dipole such that it makes an angle of 30 with the external electric field of 0 8 x 10 N C

Half ring of radius a is uniformly charged with charge density Find out electric field inten point O 1 3 i 2 2 a 2 4 4 4 1 2 A neutral water molecule is placed in electr E 1 25 x 10 N C The work done to rota 180 is 2 5 x 10 25 J Find aproximate sepa of center of charges 1 0 625 x 10 m B 0 75 x 10 10 m 2 0 65 x 10 10 4 0 625 x 10

A point charge Q is located at a distance from 2 the centre of an uncharged conducting spherical shell as shown in below figure The electric field at a distance 3R from the point charge is 1 1 4 9R R 2 K 3R 2 1 4TEO 1 5R 2

The electrostatic potential inside a charged spherical ball is given by o ar2 b where r is the distance from the centre and a b are constants Then the charge density inside the ball is a 6a r c 6a b 24 d 24 r

shape of conducting wire PQRS as shown in figure placed in a uniform magnetic field perpendicular to the plane of the paper changes into a circular shape The direction of induced current will be XXXX X X X X X X 1 Clockwise 2 Anti clockwise 3 No current 4 None of these X X X4X X X X X X X X X X X X

The electric field intensity in a region is given by E xi yi V m where x y are in meters Then the pattern of line of forces in x y plane is given by C B D Electric field at origin is zero

The potential on the hollow sphere of radius 1 m is 100 volt The potential at 1 4 m from the centre of sphere is MP PMT 2010 b 500 volt a 1000 volt c 250 volt d 0 volt

10 A short electric dipole is placed along a of a uniformly charged sphere as shown Q 1 1 X 100 R If the force experienced by dipole at r 2R and 4R are F and F respectively then 2 Q 2 4 F is

5 Two point charges q and 2q are placed at the vertices B and C of an equilateral triangle ABC of side a 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 CBSE OD 14C

Question 4 Consider the circuit shown below Find the power dissipated by the resistors Select the correct answer O 29 W O 34 W O 17 W 24 W R 40 V 12 V R 30 12 13 R3 20 R 202 RA 1 5V 115 I

6 Two long parallel wires are at a apart They carry steady equal currents flowing out of the plane of the paper as shown The variation of the magnetic field B along the line XX is given by 1 x 2 X 3 4 x d B B esist B 3 X X X X

2q and 8q are 120 cm apart Where would the location of the neutral point 3T B Calculate the NET Force exerted on the 2uc charge magnitude and 5 A direction Bir 12cm 8 c 20cm 2uc 15cm

A solid sphere of radius R is uniformly charged with charge density p in its volume A spherical R cavity of radius is made in the sphere as 2 shown Then electric potential at the centre of sphere will be 1 3 3pR 880 5pR 12 X O R 2 4 I act as hollow 5pR 680 3pR 480 sphere

28 A thin metallic spherical shell contains a charg Q on it A point charge q is placed at the centre c shell and charge qi is placed outside it as shown in figure The force on the charge a centre due to shell is F 1 Towards left 2 Towards right 3 Upward Q q

5 An electron is released on the axis of a positivel charged ring The motion of electron will be 1 Uniformly accelerated motion 2 Uniform motion 3 Non Oscillatory motion 4 Oscillatory motion

3 a Find the value of two equal charges if they repe one another with a force of 0 1 N when placed 0 5 m apart in air b Determine the magnitude of the charges if they were situated in an insulating liquid whose permittivity was ten times that of vacuum Ans a 1 67 uC b 5 27 C

5 of radius r around the earth of mass M has ing in a circular orbit magnitude of total energy E Then its angular momentum will be 1 2Emr 2 2Emr 4 4Emr 3 Emr The potential energy of interaction between the arc of ring of radius R and mass and the particle of mass m placed at centre of curvature is 1 3 GMmo R 5 GMm 6 R R M 60 mo 2 4 GMm 6R GMm 2R

9 Three concentric conducting spherical shells are arranged as shown in figure The middle and outermost shells are earthed The innermost sphere is given a charge 90 what are the charges in the middle and the outermost sphere respectively a 9o and 90 90 c zero and go b 3a 2d b 90 and zero d q0 and 90 90

67 Two sp i R2 Column I electric field for r R R Letr be the distance of a point from their common centre Then match the following columns and mark the correct choice from the given codes 92 ii electric potential for r R 91 Column II p is constant for 92 and vary for q1 q is zero for 92 and vary for q iii electric potential for R r R r is constant iv electric field for R r R S is zero

63 Two small balls having equal positive charge Q coulomb on each are suspended by two insulated string of equal length L meter from a hook fixed to a stand The whole set up is taken in satellite into space where there is no gravity state of weightlessness Then the IIT 1986 angle between the string and tension in the string is a 180 b 90 1 4T c 180 4780 d 180 1 Q 1 Q 2L 1 Q 21 4 TEO 1 OL 4TE 41 L too to

a E 7kQ r c E 2 k Q r 2 b E kQ r d E 6 kQ r A positively charged insulator is brought near two metallic spheres that are in contact The metallic spheres are then separated The sphere which was at far and from the insulator will have b a negative charge a no net charge c a positive charge d either a negative or a positive charge Two concentric conducting thin shells of radi

Calculate the force between two Protons if they are 4 0 10 15 meters away from each other Where charge of Proton is 1 6 10 19 Coulomb

A small sphere of charge q mass m is at rest on smooth surface Another identical sphere of initial velocity u is projected from infinity towards the first sphere The distance of closest approach between them is 1 4 q T mu K 2 e mu 3 2q 2 TE mu 9 4 mu

A closed solid conductor of irregular shape is given some charge Which of the following statement is correct 1 Potential of conductor will change if its shape is changed 2 Electric field inside it is non zero 3 All points on its surface will have same charge density All of these

A proton of mass m moving with a speed v approaches a stationary proton that is free to move Assume impact parameter to be zero i e head collision How close will the indecent proton go to other proton A C m v e mv B e mvo 0 D None of these

5 Two identical spheres have opposite and unequal charge and are at a distance of 90 cm from each other They are touched together and then are placed at their initial position then they show a repulsive force of 0 025 N The final charge on them will be a 1 5 C b 1 5 C c 3 C d 5 C

12 The potential difference that must be applied to stop the fastest photo electrons emitted by a nickel surface having work function 5 01 eV when ultraviolet light of 200 nm falls on it must be 1 2 V 2 2 4 V 3 1 2 V 4 2 4V

The dipole moment of system is MR3 192 1 7gl 3 5 gl 39 2q X 2 6ql 4 2ql

3 Three point charges are located on a circular arc as shown in the Figure below a What is the total electric field at P the center of the arc 4 A b Find the electric placed at P force that would be exerted on a 25 0 nC point charge 2 A 2 00 nC 3 00 nC 4 00 cm 30 0 30 0 4 00 cm P

9 Two small spheres each having a charge Q are suspended by insulating threads of length L from a hook This arrangement is taken to a space where there is no gravitational effect then the angle between the two threads and the tension in each will be 1 180 3 180 1 4 2L 1 Q 4 21 1 Q 4 L 2 90 4 180 1 Q 4 L

13 Which option is incorrect for electrostatic field 1 It is conservative in nature 2 It may be non conservative 3 It follows inverse square law 4 It produces lengthwise contraction between dissimilar charges 4 Coordinates of a square are given as 1 1 0 m 1 1 0 m 1 1 0 m 1 1 0 m If electric field is 10 V m along z axis electric flux through square

8 A point particle of mass M is attached to one end of a massless rigid non conducting rod of length L Another point particle of the same mass is attached to other end of the rod The two particles carry charges q and q respectively This arrangement is held in a region of a uniform electric field E such that the rod makes a small angle 0 of about 5 say with the field direction as shown in the figure What is the minimum time required for the rod to become parallel to the field after it is set free mL 2pE 3 mL 1 1 2 3 2 A 0 TC mL 22qE q 4 1 1 2mL

A OI liquid in a cylindrical container of diameter D D d as shown in figure If it is burning at the rate of 2 cm hour then the top of the candle will X600 5 Y 200 X 10 106 X0 5x10x 1201 C005 x 2x109 s 402x10 A remain at the same B fall at the rate of height 1 cm hour C fall at the rate of 2 D go up at the rate of 1 an hou

10 An electric dipole with dipole moment 4 x 109 C m is aligned at 30 with the direction of a uniform electric field of magnitude 5 x 104 NC Calculate the magnitude of the torque acting on the dipole

40 The electric field components in the figure below are E 800x N C E E Calculate a The flux through the cube and 8x10 NYC b The charge within the cube 1 01 10 13 C Assume that a 0 1 m y O a D B a C a n X 11

9 91 92 6 5 C 8 0 C 1 5 C Example 5 Two bodies A and B carry charges 3 00 C and 0 44 C How many should be transferred from A to B so that they acquire equal charges

Three concentric spherical shells have radii a b and c a b c and have surface charge densities o 0 and o respectively If VA VB and Vc denote the potentials of the three shells then for c a b we have a Vc V VB c Vc VB VA b Vc VB VA d Vc V VA B