Electric Field and Potential Questions and Answers

A cuboid is of dimension a x a b Charge q is placed at the centre of edge having length b If flux through face ABCD is then select the correct statement s H a b GOD B 4 All of these q G E F 3q 32E0 1 Flux through the entire cuboid is 3 Flux through the face BEFD is 2 Flux through the face ABEH is zero q 32E0 4 0

Two equilateral triangular plates are placed parallel to each other The separation between them is much smaller than their linear dimensions and they overlap each other completely One of them carries uniform positive charge and other uniform negative charge Surface charge densities on the plates are equal in modulus B Well inside the region between the plates electric field remains uniform but near the edges it becomes nonuniform If modulus of electric field well inside the plates is E find modulus of electric field at the mid point of line AB What happens if the plates have the shape of a regular pentagon

Two parallel half plane are uniformly charged with surface charge density to and Find the magnitude and direction of the electric field E at the point Plocated at a heigh h above the edge of the positively charged half plane see figure Distance d betwee half planes is much smaller than h

A point charge Q is placed at the centre of an isolated conducting shell of radius R Find the electrostatic potential energy stored outside the spherical shell if the shell also contains charge Q distributed uniformly over it X Q X

Two identical metal spheres carry charges of q and 2q respectively When the spheres are separated by a large distance r the force between them is F Now the spheres are allowed to touch and then moved back arochiasis ballas to the same separation Find the new force of repulsion between them een two positive ions carrying equal charges is 4 x 10 9 N when their

Figure shows three small spheres that have charges of equal magnitudes whose sign are shown and are at rest on a frictionless surface Spheres y and z are fixed in place and are at equal distance from sphere x Which of the four paths shown will x take A A C C B B D D B

A sphere has charge volume p Po 1 where x is distance from the centre and R is its radius The electric field inside the sphere at a distance x fro s equal to the electric field at the surface Find x in cm Take R 12cm

B Consider a point charge q placed at the origin and another point charge 2q placed at a distance of 9 m from the charge q Determine the point between the two charges at which electric potential is zero

Q3 Aswer one only A Three charges are at the corners of an equilateral triangle as shown in Figure below Calculate the 3rd charge and its force 57 q1 3 0 75m q2 5 c 13marks B Consider a point charge q placed at the origin and another point charge 2q placed at a distance of 9 m from the charge q Determine the point between the two charges at which electric potential is zero

Two identical point charges are placed at separation of L P is a point on the line joining the charges at a distance x from the charge which is on left side one The field at P is E E is plotted against for values of x from close to zero to slightly less than Which of the following best represents the resulting curve 3 E E V 3 1 M E 2

Three identical small balls each of mass 0 1 g are suspended at one point on silk thread having a length of 1 20cm What charges should be imparted to the balls for each thread to form an angle of a 30 with the vertical

1 Two identical particles A and B each having charge q when release free space with initial separation ro between them their separa becomes double in time to How long will it take to double the separa if charge of particle A is made aq that of particle B is made bq and are released with initial separation nro ton

In a potentiometer of ten meter length an unknown emf voltage source is balanced at 60cm length of the potentiometer wire while a 3volt battery is balanced at 45cm length then the emf of the voltage source is O 3V O 2 25V O 4V O 4 5V Marks 4 1

Two spherical conducting shells of radii R and 2R is filled with material of resistivity p The strength 3R 2 of electric field at r from centre when a battery is connected as shown is 1 3 16V 3R 8V 9R 2R 2V 2 3R 4 4V 3R

Consider a conductor with a spherical cavity as shown There is a charge Q placed outside and a negative charge q inside the cavity to the left of the centre of cavity Now choose the correct statement s A Force acting on q must be towards left B Force acting on Q will be towards left C Force on Q will change if q is displaced slightly from its position D Force on q will change if Q is displaced slightly from its position

charged particle q is placed at a distance d from the center of neutral conducting sphere of radius R d then in static condition at the center of sphere magnitude of electric field due to induced charge is kq d D D magnitude of electric potential due to induced charge is magnitude of electric field due to induced charge is zero magnitude of electric field due to charge q is kq d2 kq R 1 ATTEO where k

Two identical beads each have a mass m and charge q When placed in a hemispherical bowl of radius R with frictionless non conducting walls the beads move and at equilibrium they are a distance R apart figure Determine the charge on each bead R R

A sphere of radius R has uniformly distributed charge density p There is a spherical cavity as shown in the figure has centre at C It is given that AB d OC l and the angle between OC and AB is 60 The potential difference in volt between A and B is K Volt Find the value of K 2 If numerically pld 54 0

A conducting sphere of radius R and charge Q is placed near a uniformly charged non conducting infinitely large thin plate having surface charge density on front surface only Assume that A B C are just inside the sphere BO 4R L GR A The potential difference across points Band on the sphere is B The potential difference between points B and C is zero C The electric field at O due to charge on sphere is more than electric field at C due to charge on sphere D Electric field at O due to cha

When a charge q is kept at a 0 0 the electric field vector at 0 b 0 is a bj Now another charge 2q is also kept at a 0 0 The net electric field vector at 0 b 0 is A bj B ai 2bj C a 3bj D Zero

An electron is projected into a charged field of strength 2000 N C with initial 10 m sec perpendiculars to the field What is the ratio of the electric force on the electron and its weight Ans 3 6 X 10

26 Two point charges A and B having charges Q and Q respectively are placed at certain distance apart and force acting between them is F If 25 charge of A is transferred to B then force between the charges becomes a F C 16F 9 b d 9F 16 4F 3

Consider a spherical symmetric distribution of charge The centre of symmetry is at O Electric flux linked with a spherical Gaussian surface of radius r and centered at O is given by r Choose the correct option s A Volume charge density at a distance r from O is given by B Volume charge density at a distance r from O is given by 2 0 TU Er TO C Electrostatic potential energy stored in the spherical region of radius r centred at O is given by Er 28T D Electrostatic potential energy stored in the spherical region of radius r centred at O is given by 56 Er 7

Two point charges separated by a distance L 4 00 cm are fixed on the x axis as shown in the figure q1 7 00 nC and q2 2 92 nC At what point on the x axis in cm to the right of the two charges does the electric potential vanish Vnet 0 2 L x V

Two point charges q 92 when kept at a certain distance apart exert force F on each other If q is increased by 50 q is decreased to 20 distance is same Then force between the charge is 1 9F 3 F 10 10 2 3 4 5 F FL

15 Gravitational potential of a ring of radius R mass M on the axis at a distance x from center is given by V x 1 2 3 GM R x Using the above expression find the gravitation potential of the uniform disc of mass M and radi R on the axis at a distance x from the center the disc 4 O X 1 Nm kg 2GM R 2GM R x x R 2GM R x x R R x x 2GM x x R

Sphere is charged miy move from A to B along diameter AB then electri field AX B 1 First increases then decreases 2 First decreases then increases 3 Remains same

3 Charges 2Q and Q are placed as shown in figure The point at which electric field intensity is zero will be NCERT 2Q Q a somewhere b somewhere E between Q and 2Q on the left of Q c somewhere on the right of 2Q d somewhere on the right bisector of

A conductor having uniform linear charge density Is placed in circular form in 3 quadrants with different polarities as shown in the figure Let E be the electric field at O Then the angle made by E with the line along y axis is 0 C can A tan B tan 1 D None R

An electric point charge q 6 C is placed at origin of x y Co ordinate axis Calculate electric potential due to the charge at point P 12m 16m in free space 1 1 2 kV 3 3 7 kV NCERT Pg 54 2 2 3 kV 4 2 7 kV

Two spheres M and N having charge q and q2 are kept q1 at some distance from each other q amount of charge is taken from the sphere M and transferred to the sphere N What is the new charge of the two spheres so that the force acting between them becomes maximum 9 9 each

A leaf electroscope is a simple apparatus to detect any charge on a body It consist of two metal leaves OA and OB free to rotate about O Initially both leaves are very slightly separated When a charged object is touched to the metal knob at the top of the conducting rod charge flows from knob to the leaves through the conducting rod As the leaves are now charged similarly they start repelling each other and get separated deflected by certain angle The angle of deflection in static equilibrium is an indicator of the amount of charge on the charged boy Glass window Metal knob Metal rod Rubber B 2 Gold leaves O O A B A B 2 When a 20C rod is touched to the knob the deflection of leaves was 5 and when an identical rod of 40C is touched the deflection was found to be 9 If an identical rod of 30 C is touched then the deflection may be A 0 C 7 D 11

Two insulated metal spheres of the same size are charged with 15 esu and 25 esu The distance between their centres is 10 cm What is the force acting between the two charges If the two spheres are made to touch each other and then placed in their previous positions what will be 3 75 dyn 0 25 dyn the force acting between them

A B hollow non conducting cylinder of radius R is uniformally charged with surface charge density o A non conducting small circular ring of radius a and mass m having charge q uniformly distributed over its length is placed coaxially inside the hollow cylinder at its centre The arrangement is located in a gravity free space nswer C If the cylinder is rotated with a constant angular velocity w about its axis as shown in the figure R Then the angular velocity acquired by the ring is 4 qowR m 2 qowR m HogowR o m 7 G Rate this question

A conducting sphere of radius R is given a charge q and a point charge Q is placed at a distance d from its centre as shown in figure Electric potential at point P is A B C D Q 1 O 9 R d 4180 b 1 9 4 R 1 29 4 d R 10 4 h q P R

13 Consider two spheres of the same radius R having uniformly distributed volume charge density p of same magnitude and opposite sign e and e The spheres overlap such that vector joining centre of the negative sphere to that of positive sphere is d d R Consider position vector i form the mid point of line joining the centre that makes an angle with d A Electric potential at is pR d cos 0 r o for r R B Magnitude of electric field at F is E C Electric field in the region of overlap is D Electric field in region of overlans is pR d 3 r pr 3 0 3 cos 0 1 for r R 4 8

for r R d Decreases as r increases for r R and for r R 25 Two parallel infinite line charges with linear charge densities C m and C m are placed at a distance of 2R in free space What is the electric field mid way between the two line charges 22 TE R a Zero C 2 TER N C b d N C 2 2 R N C

1 5 A small ball of mass m and charge q tied with a string of length 1 rotating in a vertical circle under gravity and a uniform horizontal electric field E as shown in figure 1 396 The tension in the string will be minimum at an angle Figure 1 396 m

A metal sphere of 4 cm radius is suspended within a hollow sphere of 6 cm radius The inner sphere is charged to a potential of 3 esu when the outer sphere is earthed The charge on the inner sphere is Question Type Single Correct Type 154 esu 2 4 esu 3 30 esu

A positively charged sphere A is brought close without touching to a neutral sphere B The far side of sphere B is touched with a grounded wire What is the charge on sphere B after the wire is removed B A O Positive O Negative It stays neutral

1 6 If uniform electric field E Ei 2Eoj where E is a constant exists in a region of space and at 0 0 the electric potential Vis zero then the potential at x 0 will be A Zero B Eo xo C 2E0 o D 5 Exo

A particle of charge q and mass m is suspended from a point on the wall by a rigid massless rod of length a 3 m as shown Above the point of suspension we have fixed a particle of charge q at a distance a On slight displacement from the mean position the suspended particle executes SHM Find the time kq period of SHM is second Take mg g n 2 a 9 a

The electric field intensity at the centre of a uniformly charged hemispherical shell is E Now two portions of the hemisphere are cut from either side and remaining portion is shown in figure If 3 then electric field intensity at centre due to remaining portion is A 3 B 3E 2 O Eo 2 D Eo 3 1

negligible mass with two small balls each of mass mand electric charge Q attached to its ends The rod can rotate in the horizontal plane about L a fixed vertical axis crossing it a distance from one of its ends A uniform horizontal electric field E along x axis is established At first the rod is in unstable equilibrium If it is disturbed slightly from this position the maximum velocity attained by the ball which is closer to the axis in subsequent motion is 1 3 2QEL m QEL 5m 1 2 3 24 In what position the rod must be set so that if displaced a little from that position it begins simple harmonic oscillations about the axis Consider the situation of previous problem 1 2 8QE 5mL 2QEL 5m 25 What would be the angular frequency of SHM in the above question i e Q 24 4QEL m 2 5mL V QE OF

Consider a system of n charges 9 92 with position vectors 7 72 73 relative some origin O Deduce the expression for th net electric field E at a point P with positio

at B What is its direction q 100 Two positively charged particles each of mass 1 7 x 10 27 kg and carrying a charge of 1 6x10 19 Care placed distance d apart If each experiences a repulsive force equal to its weight find the value of d ABC is a right angled triangle Calculate the magnitude of force on charge Q

Charge respectively which are at a distance 2L apart C is the mid point between A and B The work done in moving a charge Q along the sernicircle CRD as shown in figure is of 9 A qQ 1 2 EOL qQ 3 C 2L 2 R 9 B LA qQ 6 EL qQ D

5 The given diagram shows two semi infinite line of charges having equal in magnitude linear charge density but with opposite sign The electric field at any point on x axis for x 0 is along the unit vector A cose sinej B D sine sinej

Four equal charges q are placed at centre of a conducting hollow sphere If they are displaced 1 5 cr from centre the change in flux will be Radius of sphere 1 5 cm 2 tripled 2004 RPMT doubled 3 constant none of these

Note that the electric field E due to Q though defined operationally in terms of some test charge q is independent of q This is because F is proportional to q so the ratio F q does not depend on q The force F on the charge q due to the charge Q depends on the particular location of charge q which may take any value in the space around the charge Q Thus the electric field E due to Q is also dependent on the space coordinate r For different positions of the charge q all over the space we get different values of electric field E The field exists at every point in three dimensional space