Electric Field and Potential Questions and Answers

A conducting loop has a charge of q 4 C The thickness of the loop is negligible and its radius is r 6 cm What is the electric field E on the axis of symmetry of the loop at a distance of x 8cm from the centre of the loop

A point charge q is placed at th concentric cavity of a neutral metallic sphere a Kq 1 kala 2 3 O b R A Find the electric field at point A K 2 1 4T EO Kq R 4 None of these

The volume charge density of a sphere carrying charge Q and of radius Ris proportional to the square of the distance from the centre The ratio of the magnitude of the electric field at a distance 2R from the centre to that at a distance of from the centre is 0 5 Correct Answer 2

The diagram shows three infinitely long uniform lin charges placed on the X Y and Z axis The work don in moving a unit positive charge from 1 1 1 to 0 1 is equal to Z A n2 2 T C 32 m2 2TE Y 3 X 27 B 2 2 TE D None

shows three electric field lines If FA FB and Fc are forces on a test charge q at positions A B and C respectively then A 1 FA FB FC 3 SIE B 2 FA FB FC

Figure shows electric field lines due to a charge configuration from this we conclude that 9 92 1 q and q are positive and q q 9 92 2 q and q are positive and q 9 2 3 q and q are negative and lq 1 19 1 2 4 and q are negative and 19 1 19 1

Four charge particles A B C D of mass m and charge q each are connected by light silk threads of length d forming a tetrahedron floating in gravity free space The thread connecting particles A and B 1 suddenly breaks The maximum speed of particle A after that will be Given K 47 A Kq 2md 1 3 3 B Kq md 1 3 3 Kq 3 1 2md D Kq 3 1 md

30 180 O 20e A ball with charge 20e is placed at the centre of a hollow spherical shell which has net charge of 40e The charge on the shell s outer surface O 40e Mark for Review 60e 02 56 hr min

As shown in the figure the electric field lines on the right have twice the separation of those on the left If a charge particle takes time t to move a distance x in left region then how much time will it take to travel same distance in right side region 1 1 2 3 2t 2 t 4 2t 15 ilm Find

O AF Two small charged spheres separated by a distance d exert a force Fon each other If they are immersed in a liquid of dielectric constant 4 then new force on any of the spheres will be distance between the charge remains same 4 F hr OF 2 mi

02 09 hr mi The electric field created by a line charge falls with distance from line charge as 01 04 20 Or

226 Three identical charges are placed at corners of an equilateral triangle of side 1 If force between any two charges is F then the work required to double the dimensions of triangle is a 3F1 c 4a 3 2 Fl b 3Fl 3 d Fl 2 6

The intensity of electric field inside capacitor is E The work done to move a charge q in a closed rectangular loop once is 1 E 2a 2b 2 E 2a 3 Ea a b

An electric dipole of moment p placed in uniform electri field E has minimum potential energy The work done by external agent to rotate this dipole very slowly upto which it has maximum potential energy O PE O 2PE COPPER P 2 02 50 hr min O Zero

The electric field Eat a point just outside a perfect conducto is O Parallel to the surface O Zero O Perpendicular to the surface 02 59 hr min O Can have any direction

When one proton is taken towards the other proton then electric potential energy of the system O Decrease O Increase O Remains unchanged 02 hr Becomes zero

O 2Th An electric dipole is situated in electric field of uniform intensity Ewhose dipole moment is P and moment of inertia If the dipole is slightly disturbed from the equilibrium position then the time period of oscillation about its centre is PE O 2 O 2T 2 PE 2PE Mark Tor Review o 2 2PE 02 58 hr mi

Electric potential at any point V 4x 3y 5z then magnitude of electric field in the space will be O 5 N C O 10 N C O 5 2 N C O 6N C hr

Magnitude q each are placed at the vertices of a square of side length a with origin O at centroid Find the electrostatic potential at point P given OP r r a YA qa 1 4 r qa 2 E r O O 45 P X

17 Figure a shows a uniformly charged ring of radius R Its axis is along the x axis and the ring is in the yz plane Point P lies on the axis and P in the xy plane Y XA P P A E 0 E 0 E 0 B E 0 E 0 E 0 0 E 0 C E 0 E X D E 0 E P b c Figure b shows a uniformly charged disc of radius R Its axis is along the x axis and the disc is in the yz plane Point P lies on the axis and P in the xy plane Sec Sr Super60 All Space for rough work P 0 E 0 X Sri Chaitanya IIT Academy 06 06 2021 Sr Super60 All Jee Adv 2018 P2 GTA 08 Q P Figure c shows an infinite line charged uniformly P is a point on x axis and p in the xy plane Match the Column I with Column II Column I P P Y Column II p Point P in Figure c q Point P in Figure b r Point P in Figure c s Point P in Figure a and b Page 8

225 A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure Find the amount of heat produced when switch is closed 1 4 a c Kq 2a 2 Ka K b d 2 Kq 3a 2 Kq S 3a 2a

112 Electric 6 The linear charge density on the semicir in magnitude is same The electric field at the centre is LAX AL YA Kavis C 1 Along x axis 2 Along x axis ini ne 3 Along y axis us to t 145 X V Et

1 A long thin inextensible light thread is wound on a fixed cylinder of Ja radius r and a positively charged bead P of mass m is attached to the free end of the thread A uniform magnetic field of induction B directed along the axis of the cylinder exists in the region surrounding the cylinder as shown in the figure Initially the thread is fully wound on the cylinder and the bead touches it If the bead is projected with a velocity v radially away from the cylinder it will eventually touch the cylinder tangentially What should be the magnitude of charge on the bead to fulfil the above mentioned conditions Ars mu 2rB 20 angular 8 8 8 8p O 8 3 26 8 P 2 4

11 Two parallel metal plates each of area S carry iden tical charge Q The distance between the plates is much less than their linear dimensions What are the values of electric field at A and B show in the figure 2 1 What is di electric constant

11 Four charges of 6 C 2 C 12 C and 4 C are placed at the corners of a square of side 1m The square is in xy plane and its center at its origin Electric potential due to these charges is zero everywhere on the line A x y z 0 B x 0 z C x 0 y D x z y 0

Two concentric spheres of radii R and r have similar charges with equal surface charge densities o What is the electr potential at their common centre aleo R r 2 3 0 R r EO None of these

Two identical metallic balls A and B have charges 40 and 10 C respectively The distance between them is 2 0 m What is the magnitude and type of force acting between them They are touched to each other and again separated by a distance of 2 0 m from each other Calculate the new force between them What will be the force if one ball is connected to earth Ans 0 90 N attraction 0 51 N repulsion zero

Q 14 The electrostatic flux through a rectangular area of 1 m lying in a plane 2x 3y 6z 10 due to an electric field 81 63 10k V m will be in V m Your Answer 3 5 Correct Answer 0 5 Rate this questic

1 An uniform electric field of magnitude E is set up is a region of gravity free space in upward direction An electron of mass m is projected at an angle 0 with the field with a speed u at time t 0 If the electron is at same height at t and t The value of t t will be 1 2m usine eE mousine 2 meu cos e eE 2m u cos 0 Fi 1

1 Two metallic concentric shells are shown Before closing the switch charge on inner shell is Q and charge on outer shell is 2Q and potential at point A is V What will be potential at same point after closing the switch 1 V 2 2V 3 314 2 3 V 4 V 2a A S

Consider the circuit shown below Is is constant current source meaning that no matter what device is connected between points A and B the current provided by the constant current source is always Is the same 4R 0 2R 4R A B 2R 2R 34R of an ideal voltmeter is connected b w A B what is the reading 2 au ideal ammeter is connected what is the reading Page No Date

In a certain region of space a uniform and constant electric field and a magnetic field parallel to each other are present A proton is fired from a point A in the field with speed v 4 x 10 m s at an angle of a with the field direction The proton reaches a point B in the field where its velocity makes an sin a angle with the field direction If A 16 V C 90 V 3 Find the electric potential difference between the points sin A and B Take m mass of proton 1 6 10 27 kg and e magnitude of electronic charge 1 6 x 10 C 19 B 16 3 V D 30 V

9 The electric field in a region is given by E ax i Here a is a constant of proper dimensions Z D H F X x 1 x 21 y 0 y 1 z 0 z 1 The charge contained inside the above cube is A 2 1 B a 1 C 4a 1 D 3a 1

17 Three concentric metal shells A B and C of respective radii a b and c a b c have surface charge densities o o and o respectively The potential of shell B is ob c 1 3 17 4 ob c C b 0 O b 0 a a 2 a c 2 0 Ma a C a b b to C

Two uniformly charged solid spheres of total charge Q and Q with radius R ar placed along the x axis with centers at x 0 and x 2Rrespectively A What is the electric field due to both charge spheres at x R B What is the electric field due to both spheres at x R 2 y Q 62 RAR 70 x

Consider the configuration of a system of four charges each of value q Find the work done by external agent in changing the configuration of the system from figure i to fig ii tq a fig 1 TO a 9 fig ii

Two electric dipoles are placed parallel to ea other as shown in figure The potential at a po P at equitorial position of dipoles is P 1 3 29 39 K 2q K 3q r 12 90 90 29 39 K 5q 2 2 2 2 4 Zero

99 The potential difference between points A and B at the periphery of a spherical cavity of radius r made in a solid nonconducting sphere of uniform charge density p is 3 par 1 20 2 par a B 2 2 par 0 par

lentical point charges of 2 3 C are fixed to diagonally opposite corners of a square A third charge is then fixed at the center of the square such that it causes the potentials at the empty orners to change signs without changing magnitudes Find the sign and magnitude of the third charge Units umber he tolerance is 9

6 The ratio of field energy stored inside and outside a uniformly charged solid sphere of radius R and volume charge density p is 11 1 5 3 1 5 2 4 516 6 5 3 5

Ram and Ali have been fast friends since childhood Ali neglected studies and now has no means to earn money other than a camel whereas Ram has become an engineer Now both are working in the same factory Ali uses camel to transport the load within the factory Due to low salary and degradation in health of camel Ali becomes worried and meets his friends Ram and discusses his problems Ram collected some data and with some assumptions concluded the following i The load used in each trip is 1000 kg and has friction coefficient k 0 1 and s 0 2 ii Mass of camel is 500 kg iii Load is accelerated for first 50 m with constant acceleration then it is pulled at a constant speed of 5ms for 2 km and at last stopped with constant retardation in 50 m iv From biological data the rate of consumption of energy of camel can be expressed as P 18X10 v 104 js where P is the power and v is the velocity of the camel After calculations on different issues Ram suggested proper food speed of camel etc to his friend For the welfare of Ali Ram wrote a letter to the management to increase his salary Assuming that the camel exerts a horizontal force on the load The total energy consumed by the camel during the trip of 2100m is

Consider two concentric spherical shell s S1 and S2 with radii R and 2R respecti vely R 2 units S1 encloses point char ge Q and point charge 4Q is placed i n the space between S1 and S2 as sho wn in the figure If both the point charg es are movable and the space between S1 and S2 is filled with a medium havin g k 5 then find the electric flux through S1 and S2 S2 S1 2R 4Q R k 5

Mass per unit area of a circular dise of radius a depends on the distance r from its centre as o r A Br The moment of inertia of the dise about the the axis perpendicular to the plane and passing through its centre is 1 2 2 3 2na 2mad A aB A B 5 aA B 4 A B

If charge is distributed uniformly in xy plane with charge density to in first quardrant and o in remaining three quadrants then work done by electric field in moving a point charge q from 0 0 d to 0 0 2d is a C oq 480 09 280 d d b d 480 09 d 09 d 0

A light rod of length L with two point charges qand q both of mass m are attached at its end is placed in a region of uniform electric field with intensity E The rod can rotate in the horizontal plane about a fixed axis passing through its mid point If it is slightly displaced from unstable equilibrium then the maximum angular velocity of the rod is

03 A charge particle is free to move in an electric field It will travel IIT 1979 A B C R always along a line of force along a line of force if its initial velocity is zero along a line of force if it has some initial velocity in the direction of an acute angle with the line of force opposite to a line of force

The point charges 3 Cand 4 Care placed at a separation of 7 m The medium between them is of two types as shown in figure the electric force acting between them is 3 C 9 3m 16 4m Choose only 1 answer B 4 C A 1 75 x 10 N 1 73 x 10 4 N C 0 18 x 10 4 N D 0 18 10 N 3

In the figure shown a coil of single turn is wound on a sphere of radius r and mass m The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere If sphere is in rotational equilibrium the value of B is current in the coil is i mg mg sin e B Tir i A C mgr sin 0 i D none of these IB 0

Find the electric flux in units of N m C through the surface in the figure dashed line given that Q 87 9 pC use 80 8 8542x10 12 F m 30 2Q Select one A 0 00 B 49 64 C 69 49 D 69 49 30 50 70

The electric field at distance 2R from the centre of a uniformly charged non conducting sphere of radius R is E The electric field at a distance R 2 from the centre will be a Zero b ZE c 4E d 16E