Electric Field and Potential Questions and Answers

dq ds Surface charge density is defined as the charge per unit surface area i e o Two large thin metal plates are parallel and close to each other On their inner faces the plates have surface charge densities of opposite signs having magnitude of 17 0 x 10 22C m as shown below The intensity of electric field at a point is E 0 where Eo permittivity of free space 0 region 1 0 region 3 region 2

Two point charges 6 C and 16 C repel each other with a force of 120 N If a charge o 8 C is added to each of them then force between them will becomes 40 N 30 N 20 N hr mi 60 N

The figure shows a conducting spherical shell of inner radius a and outer radius b has a total charge of Q is concentric Sally with other conducting spherical shell of inner radius c and outer radius d and a total charge of 20 answer the following three questions The electric field in region I r a is 20 2k 2 0 mv

Suppose in Example 21 11 in the textbook that x 0 280 m Q 5 75 C and that the uniformly charged wire is only 6 80 m long and extends along the y axis from y 4 00m to y 2 80m y 0 Part A Part B Ez Ey r x y X Calculate E and E at point P Enter your answers numerically separated by a comma AEO P dE dEx dE N C Determine what the error would be if you simply used the result of Example 21 11 in the textbook E 2 Express this error as E E E and E E Express your answers using two significant figures Enter your answers numerically separated by a comma

Three charges are placed at the vertices of an equilateral triangle of side 10 cm Assume q 1 C 92 2 C and q3 4 C Work done in separating the charges to infinity is a 4 5 J c 45 J b 4 5 J d None of these

7 Consider a charged hemispherical shell shown in figure Indicate the directions not magnitude of the electric field at the central point P and an off center point P on the drum head of the shell 1 K 3 1 1 uniformly uniformly 2 1 P P

b Two forces equal to F and 2F respectively act on a particle when the first force is increased by 100 N and second force is doubled the direction of the resultant remains the same Determine the value of force F

2 20 Two charges 2 C and 2 C are placed at 10cm 0 0 and 20cm 0 0 respectively in the presence of a uniform external electric field of 2 10 4V m directed towards positive x axis Total electrostatic energy of the configuration will be Final Results 0 356 J 0 360 J 0 360 mJ 100 356 mJ

A point charge q is placed at a distance r from the centre of conducting sphere of radius R r R When the switch S is closed which of the following is correct 9 R 1 The potential at O is zero 1 q 4 r 3 The charge on sphere is zero 4 Both 2 3 are correct 2 The potential at O is S

Two pith balls having charge 39 and 2q are placed at distance of a from each other For what value of charge transferred from 1st ball to 2nd ball force between balls becomes maximum 1 2 5q 2 3 7q 4 g 2

Sir see the formulae where I circle h ere I can t understand how they com e and by which concept Please please please simple way mail bta dijiye sir And tell me in question how can I de termine that the question is of chargi ng or discharging Board Competitive Exams Level 30 Current Electricity When the resistance R is infinite or P and N are in open circuit there is no current through the electrolyt 1 2 0 Potential difference between P and N V Vp VA VA VB VB VN V 0 V V V E A cell can be represented as PN emfe of a cell is defined as the potential difference between the positive and negative electrodes in an ope circuit When R is finite 0 Cell is discharging Potential difference between P and N is V Vp VA VA VB VB VN V Ir V V V Ir e Ir V t Ir We can represent it as P Internal resistance of the cells in the circuit may be neglected when the current is such that Ir Internal resistances of dry cells is much higher than common electrolytic cells Note In case of storage cells discharged cells can by charged by a driver cell E by supplying a steady current I through the cell from P to N as shown in figure In this case potential difference between P and N is V V V VA VB VB VN A V Ir V V V Ir Ir V 8 Ir P It can be represented as P P www N Potential difference between terminals of cell may be equal to greater than or less than the emf of cell V E 1 a If current shown from cell is zero i 0 b Cell is ideal r 0 Potential difference between P and N can be written as V IR Equation 29 can be written as IR E Ir So V E R r E ER R r 3 29 P A E N B 30 Board Exam Solu ZEM P Ex S

An infinite long wire having linear charge density o Z 0 Ao Z 0 is placed along the z axis Four points P Q R and S having co ordinates are shown in figure R 1 1 S 4 3 P 3 4 List I P Electric field at point P1 C Q 8 6 Q Electric field at point Q2 C X C 5 List II C 2 0 k R Electric field at point R3 1080 S Electric field at point S4 400 2 260 20 k 1080 2 0 k 20 k 1 0 k 20E0 C

Three charges q q and q are placed on the circumference of a circle of radius r The force on charge 0 placed at the centre of the circle as shown in the figure will be where K q Q q KQq 1 ATEO q 2KQq KQqj 2KQq KQq Kateg 1 X

Two charges 6 C and 4 C are placed 15 cm apart as shown At what distance from A to its right on the line joining point A and B the electrostatic potential is zero distance in cm A 6 10 C X 4 9 60 15 cm 9 45 infinity 20 45 infinity 9 15 45 B 4 10 C

A particle of charge 2 C and mass 1 6 g is moving with a velocity 4 i ms At t 0 the particle enters in a region having an electric field E in NC 1 80 60 3 Find the velocity of the particle at t 5 s

Three identical electric dipoles are arranged parallel to each other at equal s as shown The separation between the charges of a dipole is negligible as compared to the separation between the dipoles In the given configuration total electrostatic interaction energy of three dipoles is U and P P P P P P P 18U 17 A The dipole P is gradually reversed work done by electrostatic forces is 70 B The dipole P is gradually reversed work done by electrostatic forces is 15 C The dipole P and P are fixed and dipole P is set free to rotate the dipole P is in unstable equilibrium D The dipoles P and P are fixed and dipole P is set free to rotate the dipole P is in

Charge Q 2Q and Q are given to three concentric conducting spherical shells P Q and R respectively as show in figure The ratio of magnitude of charges on the inner and outer surface of shell Ris R P 3 3 2 3 3 2

A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm A charge q 20 C is given to the inner sphere The heat generated in the process when the inner sphere is connected to the shell by a conducting wire 12 J 9 J 24 J Zero

48 Three charges q q and q are placed on the circumference of a circle of radius r The force on charge Q placed at the centre of the circle as shown in the figure will be where K 9 KQc 9 KQc

The electric field in a certain region is given by 51 31 kV m The potential difference between points A and B VB VA having coordinates 4 0 3 m and 10 3 0 m respectively is 21 kV 21 KV 39 kV 39 KV

Three charges q q and q are circumference of a circle of radius r The force on charge Qplaced at the centre of the circle as shown in the figure 1 41E0 will be where K q O Q q KQq 2KQ9i kQqj 2KQq r 9 KQqj

Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding The charges on the two rings are q and q The potential difference between the centres of the two rings is X Zero 9 1 1 4 R R d qR 4x d 2 9 1 R 1 R d

If on line OP electrostatic potential charges uniformly potential at O is 30V and potential at P is 15V Electric field at Q along line of motion Given OP 10m O Q A B C D P 1 5 V m in direction Q to O 4 5 V m in direction Q to O 1 5 V m in direction O to Q 4 5 V m in direction Q to P

The electric field in a region is given by Ax B where E is of in NC and x is in meters The values of constants are A 20 SI unit and B 10 SI unit If the potential at x 1 is V and that at x 5 is V2 then V V2 A 48 V B 520 V C 180 V D 320 V

Four electric charges q q q and q are placed at the corners of a square of side 2L as shown in figure The electric potential at point A midway between the two charges qis q A q X Zero 1 2q 4 L 9 2q 1 24 1 5 L 1 2q q 1 5 5

Figure shows three points A B and C in a region of uniform electric field The line AB is perpendicular and BC is parallel to the field lines Then which of the following holds good Where VA VB and Vc represents the electric potential at points A B and C respectively B A XV V Vc V V Vc V V Vc C

A negative charge is moved by an external agent in the direction of electric field Then E Positive work is done by the electric field Potential energy of the charge increases Potential energy of the charge decreases XBoth 1 and 2

Consider a metal sphere of radius R that is cut in two along a plane whose minimum distance from the sphere s centre is h Sphere is uniformly charged by a total electric charge Q The force necessary to hold the two parts of the sphere together is A F B 4 EQE4 F 0 470R C F R h 0 32mEO R D F 32mEOR R h R h

27 identical drops of mercury are charged simultaneously with same potential of 10 volt Assuming the drop to be spherical if all the charged drops are made to combine to form one large drop then its potential will be in volts 90 40 X 160

of Radii R1 and R2 by a wire the energy of the system Quiz R 41 Remains unchanged 8 Will increase 18 Will always decrease X 32 Will always decrease except Q1 R1 Q2 R2 1 None

Two particles carrying charges 1 C and 2 separated by a distance d apply force F on ea other If charges of particles are doubled th force of repulsion between them is 2 2F 4Y4F 1 F 3 3F

11 Two identical non conducting solid spheres of same mass and charge are suspended in air from common point by two non conducting massless strings of same length At equilibrium the ang between the strings is a The spheres are now immersed in a dielectric liquid of density 800 kg m and dielectric constant 21 If the angle between the strings remains the same after the immersio then A electric force between the spheres remains unchanged B electric force between the spheres reduces ma mass density of the spheres is 840 kg m 3 D the tension in the strings holding the spheres remains unchanged

10 The charges on three identical ebonite spheres are 2mC 4mC and 2 mC respectively Now first sphere is bought in contract with 2nd sphere and move apart Then second sphere is bought in contact with third spher and moved apart Calculate the final charge acquired by each sphere provided each is kept on insulating stand

Two short dipoles having dipole moment P and P2 are placed such that their axis are parallel to each other as shown in figure If sepration between them is r then the magnitude of force experienced by P due to P is K 4180 P 6KPP 3KP P KP P r P

Let P Q R be three substances Following observations wer made on rubbing these substances with each other Substances rubbed Substance acquiring ve charge P Substance acquiring ve charge 1 P and Q ii P and R R P What will happen when object made of substance Q is rubbed against an object made of substance R Q becomes positively charged R becomes positively charged X Q becomes positively charged R becomes negatively charged Q becomes negatively charged R becomes positively charged Q becomes negatively charged R becomes negatively charged

A mass m is placed at point P lies on the axis of a ring of mass M and radius R at a distance R from its centre The gravitational force on mass m is Question Type Single Correct Type 1 2 GMm 2R GMm 2R

An electric dipole of moment is at the origin 0 0 0 The electric field due to this dipole at F 1 33 5k note that F p 0 is parallel to ngo A 33 2k B 3 3 2k C 3 3 2k D a mathongo mathango mathango mathange ma

An electric dipole is placed perpendicular to an infinite line of charge at some distance as shown in figure Identify the correct statement P The dipole is attracted towards the line charge The dipole is repelled away from the line charge The dipole does not experience a force X The dipole experience a force as well as a torque

a chan 14 A spherical shell of radius 10 cm is carrying 9 If the electric potential at distances 5 cm 10 cm and 15 cm from the centre of the spherical shell is KCET 20 V V and V3 respectively then a V V V3 c V V V3 b V V V3 d V V V3 ME

Q 14 A small spherical ball having charge q and mass m is tied to a thin massless non conducting string of length I The other end of the string is fixed to an infinitely extended thin non conducting sheet with uniform surface charge density o Under equilibrium the string makes an angle 45 with the sheet as shown in the figure Then o is given by g is the acceleration due to gravity and s is the permittivity of free space A mg 9 B 2m85 9 dankomataraj 45 m C 2ge q D mg 5 9 2

Two charges exert a force of 10 N on each other when separated by a distance 0 2 m in air When they are placed in another medium of dielectric constant K 4 and separated by distance R they exert same force The distance Requals to 2 m 1 m X 0 2 m 0 1 m

A positive point charge Q is brought near an isolated metallic cube of side 10 cm then The interior of the cube becomes negatively charged and surface becomes positively charged The interior of the cube becomes positively charged and surface becomes negatively charged The interior remains charge free and the surface gets non uniform charge distribution The interior remains charge free and the surface gets uniform charge distribution

If a charged body is brought near a charged electroscope then The leaves will further diverge if the charge on the body is opposite to that on the electroscope The leaves will converge if the charge on the body is opposite to that on the electroscope The leaves will further diverge if the charge on the body is similar to that on the electroscope Both 2 and 3

A cyclotron is operated at an oscillator 80 frequency of MHz and has a Dee of radius R 60 cm The magnitude of magnetic field X B in Tesla to accelerate deuteron is Tesla 10 Find x charge on deuteron e 1 6 10 mass of deuteron 3 24 x 10 27 Kg

Figure below shows regular hexagons with charges at the vertices In which of the following cases the electric field at the centre is non zero 20 294 34 29 34 39 2q N 2q 29 29 39 10 0 34

9 In Column l different charge configurations are given and in Column ll the number of neutral points in the region are given Neutral point is the point where electric field is zero Column l Column Il A B 960 Charges placed at vertex C D q q 60 q 60 q 29 q q Charges placed at vertex of the square 2q q P 5 Q 2 R 4 S 1 T 7

Three charges each q are placed at the corners of an isosceles triangle ABC of sides BC and AC 2a D and E are the mid points of BC and CA The work done in taking a charge Q from D to E is AIPMT Mains 2011 1 Zero 3 3qQ 8 B A D E 2 4 C 3qQ 4 A qQ

Two copper pieces each of mass 0 0635 kg are placed at a distance of 0 1 m from each other One electron from each atom of piece 1 is transferred to piece 2 of copper Charges on piece 1 and piece 2 after transfer of electrons will be Atomic weight of copper is 63 5 g mole Avogadro s number 6 x 1023 gram mole 91 1 6 10 C q 1 6 10 1 C 91 9 6 104 C 9 9 6 104 C 91 1 6 10 19 C q 1 6 x 10 1 C 9 9 6 104 C 92 9 6 104 C

Two identical infinite positive line charges are placed along the lines X ta in the x y plane A positive point charge placed at origin is restricted to move along x axis Its equilibrium is Unstable Stable Neutral ob a

The work which is required to be done to make an arrangement of four particles each having a charge q such that the particles lie at the four corners of a square of side a is 1 4 2 2 2 3 kq a kq 2 4 kq a 2 kq 4 2