Electric Field and Potential Questions and Answers

A positive charge Q is fixed at a point in space There is another charge q which moves in a circular path of radius r around the given fixed charge Assume that the electrostatic force between them is the only force acting on them Calculate time period of revolution of charge

find the electric field at the location of qa in the figure below given that qb qc qd 1 35 nC q 1 00 nC and the square is 16 0 cm on a side the x axis is directed to the right a what is the magnitude in N C b what is the angle counterclockwise from the x axis i am also attaching the figure below 9a 4 9b

Hence flux through plane surface 15 An electric dipole moment P is lying along a uniform electric field E The work done in rotating the dipole by 90 is AIPMT Prelims 2006 1 2 pE 4 2 2 0 pE 2 3 2pE ish undations imited volt m also in the

12 A thin conducting ring of radius R is given a charge Q The electric field at the centre 0 of the ring due to the charge on the part AKB of the ring is E The electric field at the centre due to the charge on the part ACDB of the ring is APMT Prelims 2008 1 3E along OK a A sh 2 SE along 4 E along KO dations

Mark the correct statement 1 A solid conducting sphere holds more charge than a hollow conducting sphere of the same radius 2 Two equipotential surfaces may intersect 3 When a conductor is earthed charge always flows from conductor to earth 4 No work is done in taking a positive charge from one point to another point inside a oborand metallic sphere

The linear charge density of the semicircular ring on both side is same in magnitude The electric field intensity at centre O is along T 1 F 3 j AY 2 i 4 1 X Dh 011 4762

Three charges and q are placed at 2 the corner of an equilateral triangle of side a as shown in the figure The net electric dipole moment of the system will be 9 q 2 a a a q 2

A long straight metal rod has a radius of 2 0 mm and a surface charge of density 6 nC m Determine the magnitude of the electric field 6 mm from the axis O A 226 N C O B 452 N C C ON C D 71 97 N C E 113 N C

An electric dipole of moment p placed in uniform electric field has minimum potential energy The work done by external agent to rotate this dipole very slowly upto which it has maximum potential energy PE 2PE PE 2

a and b 3 a b and c 4 The distance between the plates of a parallel plate condenser is 4 mm and potential difference between them is 200V The condenser is placed in a magnetic field B An electron is projected vertically upwards parallel to the plates with a velocity of 10 m s The electron passes undeviated through the space between the plates The magnitude and direction of magnetic field B will be di H e iu

statement 9 d figure mark the correct Solid neutral conductor R 1 Potential of the conductor is q 4neod 2 Potential of the conductor is q 4neo d R 3 Potential at point B due to the induced qR charges is 4neod d R

A thick spherical shell of inner radius R and outer radius 2R has charge Q uniformly distributed in its volume Electric potential at center of shell is 9Q nie R Answer 1 9 0 8 2 3 Find the value of 4 5 6 7 28

14 Answer the following questions based on case study Potential due to an electric dipole The electric field of a dipole at a point with position vector r depends not just the magnitude r but also on the angle between r and p Further the field falls off at large distance not as 1 r typical of the field produced by a point charge but as 1 r The electric field obeys the superposition principle Since potential is related to the work done by the field electrostatic potential also follows the superposition principle The important contrasting features of electric potential of a dipole from that due to a single charge are a The potential due to a dipole depends not just on r but also on the angle between the position vector r and the dipole moment vector p It is however axially symmetric about p That is if you rotate the position vector r about p keeping e fixed the points corresponding to P on the cone so generated will have the same potential as at P b The electric dipole potential falls off at large distances as 1 r not as 1 r characteristic of the potential due to a single charge Potential due to an electric dipole 2a i The potential due to a dipole plane 0 0 x is a Directly proportional to r and zero respectively b Inversely proportional to r and zero respectively P c Both varies as V 40 12 d None of the above ii Two charges 10 C and 10 8 C are located 15 cm apart At what distance on the line joining the two charges inside the system is electric potential zero Take the potential at infinity to be zero a 15 cm b 7 5 cm c 9 0 cm

Two charges Q and Q2 placed at 0 0 0 and a 0 0 are such that x component of field is zero at 2 a o of field will be zero at 0 0 a 2 2a 0 0 a 0 0 8 2 0 a 2a 0 0 y componer

Three large conducting sheets placed close and parallel to each other contain charges Q 2Q and 3Q respect Find the electric field at points A B C and D Q 2Q 3Q HII A B C D

Two equal charges q are placed at a distance of 2a and a third charge 2q is placed at the midpoint The potential energy of the system is 1 3 q SEDA 6q STED 7q STED 99 hs

Five point masses m each are kept at five vertices of a regular pentagon Distance of centre of pentagon from any one of the vertices is a Find gravitational potential and field strength at centre In the above problem if any one point mass is removed then what is gravitational potential and magnitude of field strength at centre

An electric field line emerges from a positive point charge q at an angle a to the 91 91 Fig 74 FLO straight line connecting it to a negative point charge 92 Fig 74 At what angle will the field line enter the charge 92

36 Determine the electric field strength vector if the potential of this field depends on x y coordinates as a a x y b axy where a is a constant Draw the approximate shape of these fields using lines of force in the x y plane

on the bob Ans 16 4 Three charges 27 125 and 64 C are situated at the corners A B and C respectively of a rectangle ABCD having sides AB 8 x 10 2 m and BC 6 x 10 2 m Find the force on a charge 5 C placed at D Ans zero zero Find also the potential at D O 5 A spherical ball of mass m with charge q can revolve in a vertical plane at the end of a string of length on and magnitude to that

Fig 3 4 40 A point dipole with an electric moment p oriented in the positive direction of the z axis is located at the origin of coordinates Find the projections and E of the electric field strength vector on the plane perpendicu to the z axis at the point S see Fig 3 4 At which points is perpendicular to p

Two equal and oppositely charged particles are kept at some distance apart from each other A spherical surface having radius equal to separation between the particles and concentric with their mid point is considered Then a electric field is normal to the surface at two points only b electric field is zero at no point c electric potential is zero at every point of one circle only d All of the above

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

Two point charges 8q and 2q are located at x 0 and x Lrespectively The location of a point on the x axis at which the net electric field due to these two point charges is zero is a L 4 b 2L c 4 L d 8 L

Two concentric metallic shell s of radius R and 2R out of which the inner shell is having charge C and outer shell is uncharged If they are connected with a conducting wire Then A Q amount of charge will flow from inner to outer shell B Q e number of electrons will flow from outer to inner shell where e charge on electron KQ C amount of heat is produced in the wire amount of heat is produced in the wire D 4R KQ 2R

An alpha nucleus of energy mv bombards a heavy 2 nuclear target of charge Ze Then the distance of closest approach for the alpha nucleus will be proportional to a v c 2 b E m

the body is vely charged 4 Calculate the charge on a body if two billion electrons are added t 10 10 lomb

A coil is suspended in a uniform magnetic field with the plane of the coil parallel to the magnetic lines of force When a current is passed through the coil it starts oscillating it is very difficult to stop But if an aluminium plate is placed near to the coil it stops This is due to Question Type Single Correct Type 1 Electromagnetic induction in the aluminium plate giving rise to electromagnetic damping 2 Development of air current when the plate is placed 3 Induction of electrical charge on the plate Shielding of magnetic lines of force as aluminium is a paramagnotic material

A rod of finite length having linear charge density A subtends an angle of 15 symmetrically at a point P which is also the centre of curvature of a circular arc having same linear charge density as shown in the figure If the net electric field at the point P is bki R then find the value of b k A B R 478

d The relationship between the change of resistance and RTD is given by the following Eq Q 5 d RT RT20 1 20AT Where UHAN UNTU20 0 00392 for platinum UNERSITI TEKNOPerature for a platinum temperature difference between the measured temperature and the KERANA Eq Q 5 d reference temperature 20 C RT20 resistance of the sensor at the reference temperature 20 C A platinum resistance 50 C TEKNO as a resistance of 150 2 at 20 C Calculate its resistance at

A thin spherical conducting shell of radius R has a charge q Another charge Q is placed at the centre of the shell The electrostatic potential at a point P at a distance R 2 from the centre fo the shell is 1 20 4 R 2Q 4 R q 4 R 2Q 2 4TE R 4 ER 4 2q 4 E R q Q 2 4TE R

If the electric potential of the inner metal sphere is 10 volt that of the outer shell is 5 volt then the potential at the centre will be 1 10 volt var 15 volt a 2 5 volt 4 0

Line x 2 z 2 carries charge of linear charge density 2 nC m while plane x 2 carries charge of surface charge density nC m Find the force N on a 2 point charge 3 C located at origin 1 9x 10 Sl unit 4 TE

Two small balls having equal positive charge Q each are suspended by two insulating strings of equal length L from a hook fixed to a stand The whole set up is taken in a satellite into space The tension in each string is 0 8 48L 1 Q 4 21 1 Q 4TE 41

uniform linear charge densities 2 and Radius of inner cylinder is a and that of outer cylinder is b A charged particle of mass m charge q revolves in a circle of radius r Then its speed v is Neglect gravity and assume the radii of both the cylinders to be very small in comparison to their length q 2 Eo m 20 a VV b 2 2 q V Eo m a

Two parallel metal plates disconnected from battery having charges Q and Q face each other at a certain distance between them If the plates are now dipped in kerosene oil tank the electric field between the plates will Remain same Become zero Increase door

Q 4 How much work is done to move a charge of 0 05 C between two points on a certain equipotential surface 1 Q 5 The electro static force of 0 2 Newton acts on a small sphere of charge 2 x 10 C due to another sphere of charge 9 x 106 C Calculate the distance between the spheres Given 1 4780 9 x 10 Nm C 2

9 A non conducting ring of radius R has uniformly distributed positive charge Q A small part of ring of length d is removed d R The electric field at the centre of ring will be 1 Directed towards the gap inversly porportional to R 2 Directed towards the gap inversly porportional to R 3 Directed away from the gap inversly porportional to R 4 Di

Two charges of equal magnitudes and kept at a distance r from each other exert a force F on each other If eac of the charges are doubled and distance between them is made one third of initial distance then the new force acting on each charge is OF 8 O 36 F O 6 F O F 16

A thin uniform rod of length I and mass m is uniformly charged with a total charge q The rod is rotated about a point at a distance from 1 3 midpoint of the rod The magnitude of the magnetic moment of the rod if the angular velocity is is 1 2 3 90 72 7290 590 90 36 Zaml

small balls each of mass each of them on are swo light insulating Two q through length I expression of the m and char Static suspended string of for string from a point angle o made by any with vertical couilibrium Find the q

Two isolated charged metallic conductors of capacitance C and C having charges Q and Q respectively are connected to each other After connection there is No change in the energy of the system An increase in the energy of the system Always a decrease in the energy of the system A decrease in energy of the system except when qC q C

From V IR it can be said that current density is proportional to A conductivity of a metal B electric field D neither A nor B Kirchoff s first law is a law of conservation of C both A and B

In the circuit shown in figure when the input voltage of the base resistance is 10 V V is zero and V is ce also zero Value of is RU B V 0 W 100 k 1636 OU 133 10 V 9 R 3 ks2 O 2 154 C VBE 0 OVUCE

The output of the combination of gates shown in figure is A I 3 A A B A B AB Read More A B A B

Which one value of electric field is possible due to Uniformly charge ring Question Type Single Correct Type 1 2 3 3 KQ 7 R 7 KQ 19 R 7 KQ 13 R

Point charge q 2 C and 92 1 C are kept at points x 0 and x 6 respectively Electrical potential will be zero at points Question Type Single Correct Type 1 2 3 4 x 2 and x 9 x 1 and x 5 x 4 and x 12 x 2 and x 2

5 The arc AB with the long wire having linear charge density are lying in the same plane The minimum amount of work to be done to move a point charge 90 from point A to B through a circular path AB of radius a is equal to o A 90 2 EO 90 B 20 loge loge 90 C 2 EO 20 D q 2 TEO loge 2 3 2a B a A

Which of the following statement is false for a perfect conductor in electrostatic condition The surface of the conductor is an equipotential surface The electric field lines just outside the surface of a conductor is perpendicular to the surface The electric field is continuous across the surface of conductor The electric field is discontinuous across the surface of conductor

For an isolated uniformly charged spherical Conductor the electrostatic Potential is zero everywhere inside the conductor Field is zero inside the conductor Field is non zero and uniform inside conductor Field is non zero and non uniform inside the conductor