Electric Field and Potential Questions and Answers

A charge Q is uniformly distributed over a large plastic plate The electric field at a point p close to the centre of plate is 10vm If the plate is replaced by a copper plate of the some geometrical dimensions and carrying the same charge Q The field at the point P will become A zero B 5V m C 20V m D 10V m

A charge Q is uniformly distributed over arod of length 7 consider a hypothetica cube is edge T with the centre of cube at one end of the rod The minimum possibl flux of electric field through the entire surface of the cube is

3 32N Two particles each of mass m and carrying charge Q are seperated by same distance If they are in equilibrium under mutual gravitational and electro static forces then Q m in c Kg is of the order of 1 10 5 3 10 15 2 10 0 4 10 20 and Bare suspended

2 2 charges are separated by distance d F is the force between them The value of Q is halved To have the same force between the charges the distance of separation should be d 1 d 2 d s c 3 4 2d

suspended from a common point on the ceiling by insulating mass less strings of equal lengths They come to equilibrium with each string making angle 0 from the vertical If the mass of each charge is m then the electrostatic potential at the centre of line joining them will Online April 22 2013 1 4T EO a 2 k mg tan 0 c 4 kmg tan 0 be k b k mg tan 0 d kmg tan A

Three conducting concentric spherical shells A B and C having radii a 2a and 3a respectively are placed as shown Initially A and C carry some positive charge where as shell B is uncharged Now switch S is closed The potential difference VA V between shells A and B will A 2a B S 3a 1 Increase 2 Decrease 3 Remain unchanged 4 Increase or decrease depending upon actual

9 Two concentric uniformly charged spherical shells of radius 10cm and 20cm having charges 10C and 20C on them are arranged as shown in figure The magnitude of potential difference between the two shells is 1 4 5 x 1011V 3 0 10C 10cm 20cm 20C 2 2 7 1011 V 4 None of these

Consider two concentric non conducting uniformly charged spherical shells of radius 3m and 6m having charges 10 C and 200 C respectively Find the interaction potential energy between two spheres in joules

8 Two infinitely large planes A and B intersect each other at right angles and carry uniform surface charge densities to and o Which of the following figures best represents electric field lines a c A A B B b A d A B B

A copper rod moves with a constant angular velocity w about a long straight wire carrying a current I If the ends of the rod from the wire are at distances a and b then the e m f induced in the rod is

A dipole of dipole moment P 21 3j 4k is placed at point A 2 3 1 The electric potential due this dipole at the point B 4 1 0 is b 10 volt All the parameters specified here are in S I units what is the magnitude of b 2

44 A cloud is at potential of 8x10 V re ground A charge of 40C is transferred in a lighting stroke between the cloud and the earth The energy released is 1 3 2 10 J 3 2 108 J 2 5x10 J 4 32 10 2 J

52 A B C are three points on a circle of radius 1 These points form the corners of an equilateral triangle A charge 2C is placed at the centre of the circle The work done in carrying a charge of 0 1 C from A to B is 1 Zero 2 18x10 J 3 1 8x10 J 4 54x10 J cm

A hollow metal sphere of radius Sem is charged such that the potential on its surface is 10V The potential at the centre of the sphere is 1 0 V 2 10 V 3 Same as at point Sem away from the surface

3 An infinite number of charges each equal to q are placed along the X axis at x 1 x 2 x 4 x 8 The potential at the point x 0 due to this set of charges is e 4t E 1 2 20 4T E

5 Some equipotential surfaces are shown in the figure The magnitude and direction of the electric field is 0 10 20 V 20 30 V 30 40 V 0 30 cm 1 100 V m making angle 120 with the x axis 2 100 V m making angle 60 with the x axis 3 200 V m making angle 120 with the x axis 4 None of these

3 10 V m 42 The p d between two plates separated by a distance of 1 mm is 100 V The force on an electron placed in between the plates is 1 10 N 2 1 6 10 24 N 3 1 6 10 14 N 4 1 6 10 19 N 5 100J of work is done when 2 uC charge is moved 4

Charge 6 12 and 24 nano coulomb are placed on the corners of a square of side 10 2 cm The charge that must be placed at the fourth corner so that the potential at the centre of the square may be zero is 1 42 nC 3 42 nC 2 36 nC 4 30 nC

Two concentric shells have radii R and 2R charges q4 and q and potentials 2V and 3 2 V respectively if potential at infinity is zero Now shell B is earthed and let charges on them become q and q B Then A 94 9B 1 2 d A 9 B 1 B C potential of A after earthing becomes 3 2 V DY potential difference between A and B after earthing becomes V 2

37 Two like charges in the ratio 1 4 are 30cm apart The resultant field strength vanishes at distance from the smaller charge 1 20cm 3 5cm 8 If an electron experion no 2 10cm 4 25cm

When the rms voltages VL Vc and VR are measured respectively across the inductor L the capacitor C and the resistor R in a series LCR circuit connected to an AC source it is found that the ratio V VC V 1 2 3 If the rms voltage of the AC source is 100 V the VR is O 50 V 30 10V O 90 V 100 V

3 4 5 1023 V 4 45 1 16 A spark is produced between two insulated surfaces maintained at a potential difference of 5x10 volt If the energy output is 10 J the charge transferred during the spark is 2 5 10 C 4 2 10 C 1 5 10 C 3 2 10 2 C

an oscillating LC circuit the maximum charge on the capacitor is Q The charge on the capacitor when the energy is stored equally between the electric and magnetic id is N D 2

50 The potential difference between two parallel plates is 10 volt If the plates are separated by 0 5 cm the force on an electron between the plates is 1 2 10 N 3 20 N 2 3 2x10 13 N 4 32 10 2 N

In potentiometer a balance point is obtained when 1 The e m f of the battery becomes equal to the e m f of the experimental cell 2 The p d of the wire between the ve end to jockey becomes equal to the e m f of the experimental cell 3 The p d of the wire between ve point and jockey becomes equal to the e m f of the battery 4 The p d across the potentiometer wire becomes equal to the e m f of the battery

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 v q X 157 o m find value of x Neglect gravity A q q 0 D 4m

A test charge q is moved without acceleration from A to C along the path from A to B and then from B to C in electric field E as shown in the figure 2 3 B 2 0 6 0 A 317 E i Calculate the potential difference between A and C ii At which point of the two is the electric potential more and why

An electric dipole is held in a uniform electric field i Using suitable diagram show that it does not undergo any translatory acceleration and ii Derive an expression for torque acting on it

A galvanometer 1 0 1 A R 60 is converted to an ammeter of range 10 1 A by the help of shunt S Same galvanometer is converted in to a voltmeter of range 100 6 volt by the help of a resistance R Value of Rand Sare R 1000 Q R 2000 Q S 0 120 S 0 06 Q

3 40 Hz 4 50 Hz 41 Electric potential in a region is given by V 6x 8xy 8y 6yz 4z The magnitude of electric force acting on a 2C charge placed at origin is where x y and z are in meter and V is in volt 1 2 N 2 20 N 3 6 N 4 8 N 3 40 Hz 4 50 Hz 41 umfaga faV 6x 8xy 8y 6yz 42 fe 20 g x y 1 2 N 2 20 N 3 6 N 4 8 N

0 Q Work done by external agent in carrying an electron from point O to O is 5 2 2 2 5 2 2 1 3 4ekQ a re placed at the corners of a square of side a 4ekQ 5 2 2 4 4ekQ a 4ekQ a 1 1 5

Som 24 An inclined plane makes an angle of 30 with the horizontal electric field E of 100 V m A particle of mass 1 kg and charge 0 01 C slides down from a height of 1 m If the coefficient of friction is 0 2 the time taken for the particle to reach the bottom is sec A 8 0 to E 100 V m 30 1 m nads lovni

The electric potential at a point due to electric dipole will be max and minimum when angles between the axis of dipole and line joining the point to the dipole axis are respectively 90 and 45 O 0 and 90 O 0 and 45 O 0 and 180

Three point charges of 1 C 2 C and 3 C are placed at the corners of an equilaterals triangle of side 1 m What is work required to move these charges to the corners of smaller equilateral triangle of side 0 5 m O 99 10 J O 66 10 J 22 108 J 11 108 J

An assembly of charges q 9 9 9 m 8 m respectively from origin The electric potential due to these charges at origin is 60 60 40 www q 2780

An oil drop carrying charge of 2 electrons has mass 3 2 x 10 17 kg It falls freely in air with terminal velocity The electric field required to make drop move upwards with same speed is 0 4 x 10 V m 0 3 x 10 V m 02 x 10 V m 8 x 10 V m

9 Which of the following statements is incorrect regarding the electric 1 There is tension in every line and it tries to pull its ends together There is attraction between lines 3 The field direction at any point is along the tangent to the line of force passing through that point and alor the direction of line of force 4 The field intensity is proportional to the number of lines passing through unit area held normal to the lo fold direction

In the figure shown A and C are concentric conducting spherical shells of radius a and c respectively A is surrounded by a concentric dielectric medium of inner radius a outer radius b and dielectric constant k If sphere A is given a charges Q the potential at the outer surface of the dielectric is fra A baik fara 1 a c A 3 Qf at Q 4 E0 kb Ca A a AWI fe Q 4 en b B Q b 42 4 E0 a 1 k b a d None of these

18 An electric dipole of length 1 cm is placed with the axis making an angle of 30 to an electric field of strength 10 NC If it experiences a torque of 10 2 Nm the potential energy of the dipole is a 0 245 J c 0 0245 J b 2 45 104 J d 245 0 J

3 Three identical charge Q are fixed at each corner of a equilateral triangle What should be the minimum velocity given to charged particle q placed at the centre of the triangle to escape from the electric field of identical charges m mass of charge particle at centre 1 3 201 Q 7 2 Qq 3 4TE Im S 2 2 3Qq 3 Q 9 1 2 4 RUA Q Qq 3 7 2 bal 2 e Im S 1 3Q9 37 2 2

Q80 In the study of transistor as amplifier if a and where I I and I are the collector IE IB base and emitter currents then 2000 a b B c B COR 1 a a 1 a 88 1 a

Q 13 75 A small dipole is placed on the axis of a circular ring with its dipole moment vector pointing along the axis away from the centre of the ring The ring is charged uniformly over its length The dipole is rotated by 180 such that now its dipole moment vector points directly towards the centre of the ring Let the work done in the process be denoted by W Which of these options is correct W 0 if the ring is positively charged and W 0 if the ring is negatively charged W 0 if the ring is positively charged and W 0 if the ring is negatively charged W 0

PART E V Answer ANY TWO of the following questions 2x5 10 k Two point charges 2 nC and 3 nC are placed at two corners of an equilateral triangle of side 20 cm in free space Calculate the magnitude of resultant electric field at the third corner of the triangle If an alpha particle is placed at the third corner what is the force acting on it Charge on alpha particle is 3 2 x 10 9 C

s The acceleration of an electron due to the mutu between the electron and a proton when they are l IS m 9x 10 kg e 1 6 10 C 1 Take 9x10 Nm C 41 a 10 m s b 1022 m s 2020 Covid Be c 10 m s d 10

Q 14 75 A massless non conducting rod of length L lies along the X axis with its centre at the origin The two ends of the rod carry point charges Q and Q as shown A uniform electric field of magnitude E exists in the X direction The work done in slowly rotating the rod about the origin counter clockwise by 60 is Q E y E 0

Q 5 75 A non conducting sphere of radius R is charged such that the region R 2 r denotes the distance from the centre of the sphere has uniform charge density 2p and the region R STER 2 has uniform charge density P The electric potential at the surface of the sphere is 5pR 8 80 3 pR 880

Q7 A uniformly charged conducting sphere of 2 4 m diameter has surface charge density of 80 C m 1 Find the charge on the sphere 2 What is the total flux leaving the surface 3 Calculate the electric field at a point on the surface of sphere 5

Q 23 75 Two particles carrying charge Q each are fixed at the points 4 0 and 40 A third particle of mass m and carrying charge Q is released from rest from the point 0 3a If in its subsequent motion the maximum velocity attained by this particle is 12 1 0 Nne am

The work done in moving a charge 3 C from B to A is Take 1 4 10 Nm C 5 C A 1 2 Question Type Single Correct Type 3 2 8 J 3 5 J 5cm 4 5 J B 2 C 15cm

ucting plates Q 20 75 Two large no are fixed parallel to each other with a very small distance between them The plates are charged uniformly with charge per unit area and 20 as shown If the electric field at the points A and B is and respectively then the correct relation is B 11 2a