Electric Field and Potential Questions and Answers

Label each of the following statements as true or false If true prove the statement If false provide a counterexample If a proof or counterexample is not provided marked Incomplete may be a If fF dr 0 then F is a gradient field b If F is a gradient field there exists a unique potential function f so that F Vf c Every point in rectangular coordinates can be uniquely described in spherical coordinates d Triple integrals can be used to compute areas volumes and hypervolumes 4D size e Suppose f x y is a joint probability density function The average value of f depends on x and y

4 22 A proton accelerated by a potential difference V gets into the uniform electric field of a parallel plate capacitor whose plates extend over a length in the motion direction The field strength varies with time as E at where a is a constant Assuming the proton to be non relativistic find the angle between the motion directions of the proton before and after its flight through the capacitor the proton gets in the field at the moment t 0 The edge effects are to be neglected al F

Work done by an external agent to move slowly a charge Q from rim of a uniformly charged horizontal disc of radius a and charge per unit area R to center of this disc is B GRQ 2 GRQ 80 1 4 2

A ring of radius R having a uniformly distributed charge Q is fixed in a horizontal plane A bead of mass m and an unknown charge stays in equilibrium at such point on the vertical axis of the ring that if it is displaced slightly up or down it undergoes oscillatory motion Find charge on the bead Intensity of gravitational field is g Bead R

Two concentric rings R and R of same radius R and uniformly charged with charge Qeach are arranged perpendicularly as shown in the figure What is the potential at the centre of the rings 4 Q 2 ER 2 2 ER 20 THEOR R

A test charge qdo is slowly moved from point A to B perpendicula to the uniform electric field as shown in figure The work done b the agent to move the charge from point A to B against the electric field will be B 9 O qoEd O qoEd 9 Ed 2 Zero 9 A E

11 Three charges q q and q are placed as shown in figure The x component of the force on q is proportional to A 1 2 2 sin0 92 93 b 93 C 2 1 2 sine B 9 B 1 2 1 2 cose 93 b a D 1 2 93 cose a 2 FB sino 0 Y 61 9 9

A simple pendulum of length and bob mass m is hanging in front of a large nonconducting sheet of surface charge density o If suddenly a charge q is given to the bob in the position shown in figure Find the maximum angle through which the string is deflected from vertical ww C 2019 2

A short electric dipole of dipole moment P is placed at a radial distance r r a where a is length of dipole from an infinite line of charge having linear charge density X Dipole moment vector is aligned along radial vector 7 The force experienced by the dipole is 4 P 201 P 280 P 48or P

1 An electron travels a distance of 0 10 m perpendicula to an electric field of intensity 3200 V m enterin with a velocity 4 x 107 m s What is the deviation i its path 1 1 1 76 mm 3 176 mm 2 17 6 mm ols 2 4 0 176 mm

44 Consider a non spherical conductor shown in the 4 figure which is given a certain amount of positive charge The charge distributes itself on the surface such that the charge densities are 0 0 and 0 at the regions 1 2 and 3 respectively Then 303 e a 1 0 0 03 1 t Aso 2 t 62 201 t

2 these charges are placed at a distance R There will be maximum repulsion between them when 1 Q Q q Q q 2Q Q 3 3 2 Q 3 Q 3Q 4 Q Q o

1 93 Three charges q q and q are placed as shown in the figure The x component of the force on q is proportional to 93 92 6 93 a 92 93 6 2 sin 0 sin 0 9 b 9 2 93 2 a cose 4 9 2 93 CC cos

A charged shell of radius R carries a total charge Q Given as the flux of electric field through a closed cylindrical surface of height h radius r and with its centre same as that of the shell Here centre of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces Which of the following option s is are correct eo is the permittivity of free space Ifh 2R and r Ifh 2R and r 8R Ifh 8 and r 4R 5 3R 5 3R then o then o E Q 580 Q 580 then 0 Q Ifh 2R and r Rthen EO

A point charge q is kept at a distance of a on the central axis through the figure pa perpendicular to the plane of shaded region Find the electric flux through the shaded region A C 168 B q1 2 2 2 3 D q 24

If the magnetic field in a plane electromagnetic way is given by B 3 10 sin 1 6x10x 48 100t j then what will be expression for electric field 1 E 9sin 1 6 10 x 48 10 01 k V m 2 E 3x10 sin 1 6x10 x 48 10 t i V m 3 E 60sin 1 6 10 x 48 100t k V 4 E 3x10 sin 1 6x10 x 48x10 0 v m

has a tiny hole cut into its surface Show that the electric field 200 vector in the outward normal direction and o is the surface charge density near the hole in the hole is where n is the unit

volume of a solid hemisphere of radius R Then the potential at center O of the hemisphere is Aakash Educational Services Limited Regd Office Aakas 1 4 1 3Q 2R OTP Tev ent to beasla A 2 1 3Q 4 E 4R 0

The figure shows two infinite lines of charge A and B in the plane of paper Both lines are uniformly charged Linear charge density of A is while that of B is A The lines are at a normal separation a with x and y axes as shown and taking z axis to be along the outward normal to the plane of paper electric field strength at any point a 2 0 z can be expressed as 4a2 A 2 e a 42 8a C 4 a 42 2a B 48 a 42 D none of these

A particle of charge Q is executing uniform circular motion about the origin with an angular velocity The particle is at R 0 at t 0 Electric potential at the point P shown in the 1 figure as a function of time is given by k 40 A kQ R 2 cosat B kQ R 2 cosax kQ C R 5 4 cos ax P 28 0 o D R kQ R 5 4 cos ar

Electric field in the given figure is directed along X direction and given by E 5Ax 2B where E is in NC and x is in metre A and B are constants with dimensions Taking A 10 NC 1m 1 and B 5 NC1 calculate i the electric flux through the cube ii net charge enclosed within the cube i Given Ex 5Ax 2B The electric field at face M where Y Ois Z AY M N 10 cm

A charge 10 C placed on the equatorial line of the fixed electric dipole at a distance r that is much larger than the length of dipole It experiences a force 102 N to the right The charge 10 C is now shifted to a point on the axial line of given dipole at the same distance r from the centre It will experience a force A 0 02 N to the right C 0 01 N to the right B 0 02 N to the left D 0 01 N to the left

X and Y are large plates close to each other Each face has an area A X is given a charge Q Y is without any charge Points A B and Care as shown in figure X A B C B A The field at B is The field at B is Y Q 28 A Q A C The fields at A B and C are of the sam magnitude of the sam

Three charges lie on the x axis each at distance a apart from the nearest one The charges are numbered from 1 to 3 moving from left to right A representation of the electric potential V of the three charges at different points is shown above Which one of the following statements is true AN A The electric field is zero at some point between charges 1 and 2 and also at some p between charges 2 and 3 B The electric field is zero at some point between charges 1 and 2 but it is never zero betwe charges 2 and 3 C the electric field is never zero between charges 1 and 2 but it is zero at some point betwe charges 2 and 3 D The electric field is never zero between charges 1 and 2 and it is never zero between char 2 and 3

A point charge placed on the axis of a uniformly charged large non conducting disc experiences a force F due to the disc If the charge density on the disc is a the electric flux through the disc due to the point charge will be 2nF F A B D 0 2no

a A hoop of radius r and mass m is rolling without slipping with velocity v towards a step of height b r on a horizontal surface Assume that the hoop does not rebound and no slipping occurs at the point of contact when the hoop rolls up What is the minimum velocity v needed for the hoop to roll up the step b If the hoop is sliding without rolling towards the step what must be the minimum velocity v for it to roll up the step

1 a Consider a uniformly charged sphere of radius R centred at origin and having a charge density p Let a small spherical region with radius b R is removed with centre at a 0 0 Find out the electrical field in this smaller sphere 5

A positively charged sphere of radius o carries a volume charge density p figure A spherical cavity of radius is then scooped out and left empty is shown Magnitude of the electric field at point B is given by 2 31pro 162 A 51p 162 B 61pro 162 C B D None of these

An oil drop of radius 2 mm with a density 3 g mathonmathongo cm3 is held stationary under a constant electric field 3 55 x 10 V m in the Millikan s oil drop experiment What is the number of excess electrons that the oil drop will possess mathongo consider g 9 81 m s 1 48 8 x 10 1 2 1 73 x 10 0 X 3 17 3 10 0 4 1 73 x 10 2 mathongo mathongo mathongo mathongo mathongo mathongo mathongo

A hollow non conducting shell has a uniform charge density 2x It is found that electrostatic push of one half of shell on the other half is IN If density of charge on the shell is changed such that one half of the shell has a uniform charge density x and the other half a uniform charge density 4x then find the new electrostatic force in N which one half exerts on the other half

A non conducting rod of negligible thickness and length carries a positive charge Q which is uniformly distributed on it A particle carrying a charge Qo is kept at a distance from one end of the rod The potential energy of interaction between the rod and the particle is

NTEGER TYPE QUESTIONS 2 A pyramid with horizontal square base 6 00 m on each side and a height of 4 00 m is placed in a vertical electric field of 52 0 N C The electric flux through the pyramid s through one of in N C m the slanted surface is o then the value of o 231

11 Two point charges 10 C and 10 C are separated by a distance of 40 cm in air Calculate the electrostatic potential energy of the system assuming zero potential energy a CBSE Delhi 2004 infinity evig a

90 J of work is done in moving a charge of 3 C from one terminal of the battery another What is the potential difference of the battery Ans 30 If 4 x 10 J of work is done in moving a particle carrying a charge of 16 x 106 C fr infinity to a point What will be the potential at that point Ans 250

It requires 1 mJ of work of move two identical positive charge q from infinity so that they are separated by distance a How much work is required to move four identical positive charges q from infinity so that they are arranged at the vertices of a tetrahedron with edge length a Options

7 Two small metallic spheres each of mass m are suspended together with strings of length and placed together When a quantum of charge q is transferred to each the strings make an angle of 90 with each other The value of q is A

Two concentric conducting spherical shells of radii R and 2R having charges A and B and potential 2v and 3v respectively Now shell B is earthed by closing switch S Let charges on spherical shells A B become q A q respectively then DA 96 magnitude A B 1 magnitude potential of A after earthing becomes 3v 2 potential difference between A and B VA VB after earthing becomes 2 k

An infinitely long solid cylinder of radius R with uniform volume charge density p has a spherical cavity of radius with its centre on the axis of the cylinder as shown in the figure 2 R Z given by R 2R P Y The magnitude of the electric field at point P which is at a distance 2R from the axis of the cylinder is 23pR The value of Kis

c d 14 2 A 82 A battery an open switch and a resistor are connected in series as shown in figure Consider the following three statements concerning the circuit A voltmeter will read zero if it is connected across points Pand T ii P and Q Which one of the above is are true a only i c only i and iii iii Q and T b only in d i i and iii

72 In the series combination of n cells each cell having emfe and internal resistance r If three cells are wrongly connected then total emf and internal resistance of this combination will be a n nr 3r c HE 4c nr b E 2 nr d m 60 nr

SolveLancer Test At time t 0 a small particle of mass 2 x 10 5 kg comes in the effect of E t Eo sin wt Charge on N particle is 3 0C and Eo 6 and w 1 x 104 rad s Consider only influence of electric field the maximum speed attained by particle is SolveLancer Test a 2 m s b 90 m s c 45 m s d 28 5 m s

4 30 A square in the x y plane in free space has a point charge of Q at corner a 2 a 2 the same at corner a 2 a 2 and a point charge of Q at each of the other two corners a Find the electric potential at any point P along the x axis

A uniformly charged annular disc has inner radius 30 cm outer radius 40 cm and charge density of 10 o in Sl unit Electric potential at a point on the axis at a distance of 30 cm from the centre will be nearly 10 0 V 0 4 V 0 8 V

7 Four point charges are placed at the four corners of a square in the two ways i and ii shown below Will the i electric field ii Electric potential at the centre of the square the same or different in the two configurations and why D A B 0 Q D A Q cl B

Electric Dipole 5 An electric dipole of length 10 cm having charges 6 10 3 C placed at 30 with respect to a uniform electric field experience a torque of magnitude 6 3 Nm Calculate 1 magnitude of CBSE Delhi 2006C electric field and ii potential energy of electric dipole

1 Two identical metallic spheres having unequal opposite charges are placed at a distance of 0 50 m apart in air After bringing them in contact with each other they are again placed at the same distance apart Now the force of repulsion between them is 0 108 N Calculate the CBSE Delhi 2002 final charge on each of them

An infinitely long line of charge has linear density of charge equal to 1 0 nC m Points A and B are at a distance of 2 m and 3 m respectively from the line of charge Potential difference between points A and B VA VB will be equal to 9 V 10 In3 V 18 In 2 V IN

An uniform electric field E is created between two parallel charged plates as shown in figure An elec tron enters the field symmetrically between the plates with a speed v The length of each plate is 1 Find the angle of deviation of the path of the electron as it comes out of the field mass of the electron is m and its charge E To

23 A charged gold leaf electroscope has its leaves apart by certain amount having enclosed air When the electroscope is subjected to X rays then the leaves 1 Further dilate 2 Start oscillating 3 Collapse 4 Remain unaltered

Two spherical conductors of radii 4 m and 5 m are charged to the same potential If o and o be the respective values of the surface density of charge on the two conductors then the ratio the 9 0 is 5 16 25