IIT JEE Advanced & Mains Physics 2018 : Optics : Rank file / expected questions : I

IIT JEE Advanced & Mains Physics 2018 : Optics : Rank file / expected questions / Physicsmynd Elite Series  /  Page  I

   

             P   U   B   L   I   S   H   I   N   G                  S   O   O   N

 

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IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions : IX

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73 – 75 ] JEE Physics Previous

A point charge q moves from point P to point S along the path PQRS (Fig.) in a uniform electric filed E pointing parallel to the positive direction of the X-axis. The coordinates of points P,Q,R and S are (a,b,0), (2a,0,0) (a,-b,0) (0,0,0) respectively. Find work done by the field in the above process is .

 

74 ]  A rigid insulated wire frame in the form of a right angled triangle ABC, is set in a vertical plane as shown in figure. Two beads of equal masses m each and carrying charges {q}_{1} and {q}_{2} are connected by a cord of length I and can slide without friction on the wires.

Considering the case when the beads are stationary determine
[ A ]  (i) The angle \alpha
          (ii) The tension in the cord
         (iii) The normal reaction on the beads
[ B ] If the cord is now cut what are the value of the charges for which the beads continue to remain stationary?

 

75 ] Two capacitors A and B with capacitors 3\mu{F} and 2\mu{F} are charged to a potential difference of 100 V and 180 V respectively. The plates of the capacitors are connected as shown in the figure with one wire of each capacitor free. The upper plate of A is positive and that of B is negative. An uncharged 2\mu{F} capacitor C with lead wires falls on the free ends to complete the circuit. Calculate :

[ A ] the final charge on the three capacitors and
[ B ] the amount of electrostatic energy stored in the system before and after completion of the circuit.

 

76 ] Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges {Q}_{1},{Q}_{2},{Q}_{3}, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, {Q}_{1}:{Q}_{2}:{Q}_{3}, is

A ]  1:2:3
B ]  1:3:5
C ]  1:4:9
D ] 1:8:18

 

77 ] Two copper balls, each weighting 10 g are kept in air 10 cm apart. If one electron from every {10}^{6} atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is 63.5)

A ]  {2.0}\times{10}^{10}N
B ]  {2.0}\times{10}^{4}N
C ]  {2.0}\times{10}^{8}N
D ]  {2.0}\times{10}^{6}N

 

78 – 79 ] Consider four equal charges Q  placed at the four corners of a square of side  ‘a’. Then potential at the center of the square is – 

A ] {V}_{0}=2(\frac {Q}{4\pi {\epsilon }_{{0}}\left({a∕\sqrt{{3}}}\right)})

B ] {V}_{0}=4(\frac {Q}{4\pi {\epsilon }_{{0}}\left({a∕\sqrt{{2}}}\right)})

C ] {V}_{0}=(\frac {Q}{4\pi {\epsilon }_{{0}}\left({a∕\sqrt{{3}}}\right)})

D ] {V}_{0}=3(\frac {Q}{4\pi {\epsilon }_{{0}}\left({a∕\sqrt{{2}}}\right)})

 

79 ] In the above case , the work done in removing a charge -Q from its center to infinity is

A ]  0
B ]  \frac {\sqrt{{2}}{Q}^{{2}}}{4\pi {\epsilon }_{{0}}a}
C ]  \frac {\sqrt{{2}}{Q}^{{2}}}{\pi {\epsilon }_{{0}}a}
D ] \frac {{Q}^{{2}}}{2\pi {\epsilon }_{{0}}a}

 

80 ] Two point charges 100 \mu{C} and 5\mu{C} are placed at points A and B respectively with AB=40 cm. The work done by external force in displacing the charge 5 \mu{C} from B to C, where BC= 30 cm , angle ABC =\frac {\pi }{2} and \frac {1}{4\pi {\epsilon }_{{0}}}={9}\times{10}^{9}N{m}^{2}/{C}^{2}

[ A ]  9J
[ B ]  \frac {81}{20}J
[ C ]  \frac {9}{25}J
[ D ]  -\frac {9}{4}J

 

81 ] The work done on rotating a point charge q around a charge Q in a circle of radius r is –  

[ A ]  {q}\times{2}\pi{r}
[ B ]  \frac {q\times 2\pi Q}{r}
[ C ]  zero
[ D ]  \frac {Q}{2{\epsilon }_{{0}}r}

 

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions : VIII

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Page  : 8

64 ] Figure ( below ) shows a charge placed at one corner of a cube. Find the flux of the shaded side ?

 

65 ] Four point charges q1 ,q2 ,q3 and q4 are brought to the positions indicated , forming the sides of a geometrical figure ,where q4 is the last to be brought in , as shown in the image below . Then the energy used for this is – 

A ] {W}_{4}=\frac {1}{4\pi {\epsilon }_{{0}}}{q}_{{4}}\left({\frac {{q}_{{1}}}{{r}_{{14}}}+\frac {{q}_{{2}}}{{r}_{{24}}}+\frac {{q}_{{3}}}{{r}_{{34}}}}\right)

B ] {W}_{4}=\frac {1}{4\pi {\epsilon }_{{0}}}{q}_{{4}}\left({\frac {{q}_{{1}}}{{r}_{{14}}}+\frac {{q}_{{2}}}{{r}_{{24}}}-\frac {{q}_{{3}}}{{r}_{{34}}}}\right)

C ] {W}_{4}=\frac {1}{4\pi {\epsilon }_{{0}}}{q}_{{4}}\left({\frac {{q}_{{1}}}{{r}_{{14}}}-\frac {{q}_{{2}}}{{r}_{{24}}}+\frac {{q}_{{3}}}{{r}_{{34}}}}\right)

D ] None of the above

 

66 ] Figure below shows a square loop of side a carrying uniform line  charge \lambda . Calculate the electric field at a point P , distance z above the center of this square loop. 

 

67 ]  Electric field vanishes in the interior of a conductor . this implies that 

a ) The volume charge density \rho also vanishes in the interior. 

b )  Divergence of the electric field inside the conductor is zero.

c )  Just outside the conductor , E is zero. 

Ans :- 

A ] a ,b & c

B ]  a and c

C  ] a and b

D ]  b and c 

 

68 ] Calculate the potential  an isolated metal sphere with a radius R in the air can be charged to if the intensity of the electric field that causes a break in the air is {E}_{0}= 39,000{V/cm}

 

69 ] Inside a test chamber is kept a 3 m earthed sphere , which is charged to a potential of  {10}^{5} V . Calculate the quantity of heat which will be generated in the test chamber ? 

 

70 – 72 ] JEE Physics Previous questions

Two equal negative charges -q are fixed at points (0,-a) and (0,a) on y-axis. A positive charge Q is relaeased from rest at the point (2a, 0) on the x-axis. The charge Q will
 (a) execute simple harmonic motion about the origin
 (b) move to the origin and remain at rest
 (c) move to infinity
 (d) execute oscillatory but not simple harmonic motion

 

71 ]  Seven capacitors each of capacitance 2\mu{F} are connected in a configuration to obtain an effective capacitance \frac{10}{11}\mu{F} Which of the following combination will achieve the desired result?

 

72 ] The magnitude of electric field \vec{E} in the annular region of a charged cylindrical capacitor
 (a) is same throughout
 (b) is higher near the outer cylinder than near the inner cylinder
 (c) varies as 1/r where r is the distance from the axis
 (d) varies as 1/{r}^{2} where r is the distance from the axis

 

 

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions : VII

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Page  : 7

 

55 – 56 ] Consider  four charges q, q,−q,−q that are located at the corners of a square of side a . At a distance r from the center of this arrangement ,  a point P is chosen in the same plane. Here  r\gg a.

 Prove that the electric field varies inversely as the fourth power of r.

 

56 ] In the above arrangement , E at P is given by – 

A ] E=\frac {3q{a}^{{2}}}{4\pi {\epsilon }_{{0}}{r}^{{4}}}

B ] E=\frac {2q{a}^{{2}}}{3\pi {\epsilon }_{{0}}{r}^{{5}}}

C ] E=\frac {3q{a}^{{3}}}{4\pi {\epsilon }_{{0}}{2r}^{{4}}}

D ] E=\frac {q{a}^{{5}}}{4\pi {\epsilon }_{{0}}{r}^{{4}}}

 

57 ] On a silk thread attached to a vertical uniformly charged sheet hangs a tiny sphere of mass 3 mg carrying a charge of 9\times {{10}}^{{-8}}{C} .Both gravity and the electric force causes  it to makes an angle of  45^{\circ}with the sheet.Then the charge of the mass is proportional to the surface charge density of the sheet as –

A ] \frac{1}{{q}^{{4}}}

B ] \frac{1}{{q}^{{3}}}

C ] \frac{1}{{q}^{{2}}}

D ] \frac{1}{{q}}

 

58 ] In the above case , calculate the surface charge density . 

 

59 – 62 ] Consider an infinite slab of thickness 2d whose other two dimensions are infinite.If it’s  volume charge density is \rho , find the electric field at a point on it’s surface .

 

60 ] If 1/3 rd of the value of the electric field of the above case is calculated , it’s the same as that of a ————- of the same volume charge density  \rho

A ]  cylinder

B ]  sphere

C ]  cone

D ]  hemisphere

 

61 ] In fact comparing the electric field of the slab ( sl )  of question 60 with that of a cylinder ( cy ) and  sphere ( sp) , of the same volume charge density  \rho , the field strength in descending order is – 

A ] cy > sp > sl

B } sp > cy > sl

C ] cy > sl > sp

D ] sl > cy > sp 

 

62 ] Discuss the key theoretical point which causes the difference in field strengths regarding the above case . .

63 ] Two concentric spherical shells of  inner radius  {r}_{1}, and  outer radius {r}_{2} has it’s middle region filled with a material of resistivity \rho. If  {r}_{{2}}\gg {r}_{{1}} , find the  resistance between the shells

 

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions : VI

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Page  : 6

 

46 – 47 ] A  cylindrical coaxial capacitor having an inner and outer conductors of radius a  and b respectively , is charged to a voltage V . It’s  dielectric constant K(r) of it’s dielectric  varies with it’s cylindrical radius r . Then – 

 

 Find the radial dependence of it’s dielectric constant.

 

47 ] In the above question ,the electric field E(r) is given by –

A ] E(r)=\frac {2rV}{{b}^{{3}}+{a}^{{2}}}

B ] E(r)=-\frac {2rV}{{b}^{{3}}+{a}^{{2}}}

C ] E(r)=\frac {2rV}{{b}^{{2}}-{a}^{{2}}}

D ] E(r)=-\frac {2rV}{{b}^{{2}}-{a}^{{2}}}

 

48 ] A system consists of three point charges – 3nC , 2nC and 5nC , at  locations  (0, 0, 0), (0, 0, 1), and (1, 0, 0), respectively.Then the energy of this system is –

A ]  W =9\left({\frac {10}{\sqrt{{2}}}-15}\right) nJ

B ]  W =9\left({\frac {6}{\sqrt{{2}}}-7}\right) nJ

C ]  W =9\left({\frac {5}{\sqrt{{2}}}-10}\right) nJ

D ]  W =9\left({\frac {15}{\sqrt{{2}}}-6}\right) nJ

 

49 – 50 ] A charge Q is equally divided between three identical tiny spheres of mass m which are suspended by threads of negligible masses and equal length l from a common point. If they come to equilibrium at the corners of a horizontal equilateral triangle whose sides are d ,then {Q}^{2} is proportional to –

A ]  12\pi {\epsilon } _{0}

B ]  8\pi {\epsilon } _{0}

C ]  24\pi {\epsilon } _{0}

D ]  10\pi {\epsilon } _{0}

 

50 ] In the above arrangement , find Q ? 

51 – 54 ] The figure below shows a charged ring of radius R , into the center of which , an  electron e is brought in through a distance x .  Questions 51 – 54 are based on this –

 

51] The acceleration experienced by the electron is proportional to –

A ]  \frac{1}{{R}^{{4}}}

B ]  \frac{1}{{R}^{{2}}}

C ]  \frac{1}{{R}^{{3}}}

D ]  \frac{1}{{R}}

 

52 ] At what distance from the center of the ring is the electric field maximum ? 

53 ] Does the electron experience SHM [ simple harmonic motion ] ?

54 ] If it experiences SHM ,then find the tension , T , acting on the electron ?  

 

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rankfile / expected questions : V

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Page  : 5

37 ] Figure below depicts a practical application of electrostatics ,where an ore is separated into components using an uniform electrical field . Assume that the ore particles are at zero initial velocity and displacement .Calculate the separation between the particles after falling through 49 cm.  Here E = 900 kV/m and Q/m = 10\mu{C}/kg for both positively and negatively charged particles.

 

38 ] Consider an uniformly charged circular ring of charge \rho_{L} C/m and radius r . It’s  placed on the xy-plane with it’s axis the same as that of the  z-axis.Then –  find the value of E at (o,o,h ) .

 

39 ] In the above case,the maximum value of E with relation of h ,ie .the distance from the center of the ring is at – 

A ]  h = \pm \frac {r}{\sqrt{{2}}}

B ]  h = \pm \frac {r}{\sqrt{{5}}}

C ]  h = \pm \frac {2r}{\sqrt{{3}}}

D ] None of the above

 

40 ] Regarding above case ,what would happen to E when  {r}\rightarrow{0} ?

 

41 ]  The figure shows a positive point charge Q  located at distances d1 and d2, respectively, from two grounded perpendicular conducting half-planes Find the force on Q caused by the charges induced on the planes.

 

 

42 – 43] Consider a line charge of charge density {\rho }_{{l}} placed parallel to a conducting cylinder of radius a at a distance d from it . Then find the following – 

The electric potential at a distance d from a line charge of density {\rho}_{l} [ when the cylinder is absent ]

 

 

43 ] In the above case prove that the cylindrical surface is an equipotential ?

 

44 –  45 ] The figure below shows a grounded coaxial cable .

 

Find the potential distribution in the space a\leq r\leq b 

 

45 ] The above result indicates a key theoretical point – what’s  it ? 

 

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rankfile / expected questions IV

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Page  : 4

28 ] A  spherically symmetrical charge distribution has density
{\rho}_{v}=\begin{cases}\begin{matrix}{\rho }_{{0}},0\leq r\leq R\\ 0,r> R\end{matrix}\end{cases}
Then the energy stored in region r < R is – 

A ]  \frac {4\pi {\rho }_{{0}}^{{3}}{R}^{{5}}}{45{\epsilon }_{{0}}}J

B ]  \frac {2\pi {\rho }_{{0}}^{{2}}{R}^{{5}}}{45{\epsilon }_{{0}}}J

C ]  \frac {\pi {\rho }_{{0}}^{{3}}{R}^{{5}}}{45{\epsilon }_{{0}}}J

D ]  \frac {2\pi {\rho }_{{0}}^{{2}}{R}^{{5}}}{90{\epsilon }_{{0}}}J

 

29 ] Two point charges of equal masses and charges  m and  Q respectively are suspended at a common point by two threads of negligible mass and length l .If at equilibrium, the angle of inclination of each thread to the vertical is \alpha  , then  {Q}^{2} is proportional to –

A ]  {{\sin}^{{2}}{\alpha {\tan{\alpha }}

B ] {{\sin}^{{3}}{\alpha {\tan{\alpha }}

C ] {{\tan}^{{2}}{\alpha {\cos{\alpha }}

D ] {{\tan}^{{3}}{\alpha {\sin{\alpha }}

 

30 ] In the above arrangement , if  \alpha is very small , then \alpha is given by – 

A ] \alpha=3\sqrt{{\frac {{Q}^{{2}}}{32\pi {\epsilon }_{{0}}mg{l}^{{2}}}}}

B ] \alpha=4\sqrt{{\frac {{Q}^{{2}}}{16\pi {\epsilon }_{{0}}mg{l}^{{3}}}}}

C ] \alpha=2\sqrt{{\frac {{Q}^{{2}}}{18\pi {\epsilon }_{{0}}mg{l}^{{3}}}}}

D ] \alpha=3\sqrt{{\frac {{Q}^{{2}}}{16\pi {\epsilon }_{{0}}mg{l}^{{2}}}}} 

 

31 ] Consider two conducting planes kept at a particular angle to each other in the xy axis with the point of contact being at the origin . Obviously . work must be done to bring a point charge to the region of contact between the planes. Then , finding the work done ,using the method of images [in the above case ] is  possible if the angle is [ in degrees] –

A ] 20

B ] 30

C ] 40

D ] 50

 

32 ] The issue with the angle in the above case is due to the fact that there is – 

A ] Difficulty in finding the location of the image charge.

B ] Difficulty in finding the location of the equipotential.

C ] Difficulty in finding the location of the charge at infinity .

D ] A and B 

E ] A , B and C 

 

33 ] A charge q is kept in a pyramid ,on the center of it’s base ,which is square shaped . Then the flux through any face of the pyramid is – 

A  ] zero

B ]  \frac{q}{{\epsilon}_{0}}

C ]  \frac{q}{{8\epsilon}_{0}}

D ]  \frac{2q}{{\epsilon}_{0}}

 

34 ]  A hollow cylinder of resistivity \rho has length L .It’s  inner radius is a and outer radius b  . Then the resistance produced when a  potential difference is generated between the ends of the cylinder is – 

A]  R=\frac {\rho L}{\pi \left({{b}^{{2}}-{a}^{{2}}}\right)}

B ]  R=\frac {\rho L}{\pi \left({{b}^{{4}}-{a}^{{4}}}\right)}

C ]  R=\frac {\rho L}{A}

D ]  R=\frac {\rho L}{2A}

 

35 ] In the above case – 

A ] No current flows through the cylinder . 

B ] Current flows parallel to the axis of the cylinder.

C ] Current flows radially outward from the axis of the cylinder

D ] Current flows perpendicular to the axis of the cylinder

 

36 ] Continuing with question no .34 , what if  the potential difference is applied between the inner and outer surfaces of the cylinder ? [ Choose the right combination ]

a ) Current flows parallel to the axis of the cylinder.

b ) Current flows radially outward from the axis of the cylinder

c ) Resistance remains the same .

d ) Resistance becomes \frac {\rho }{2\pi L}In\left({\frac {b}{a}}\right)

e ) Resistance becomes \frac {\rho }{\pi L}In\left({\frac {a}{b}}\right)

f )  No current flows through the cylinder

Answer : – 

A ]  a , e

B }  b , d 

C ]  d , f 

D ]  c , f 

 

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Page  : 3

19]  A cone [ of resistivity \rho ] is cut off at a height of h from it’s base.If it’s uniformly charged throughout it’s  cross-sections, then the resistance between the two end of the cut – off cone is –

A ]  \frac {\rho h}{\pi ab}

B ]  \frac {\pi h}{\rho ab}

C ]  \frac {\rho }{\pi h}

D]  \frac {\pi ab}{\rho h}

 

20 ] A charge distribution produces an electric field \vec{E}=\frac {{E}_{{0}}}{{r}^{{2}}}{e}^{{-r∕c}}\hat{r}  where c is a constant. Then the total charge in the distribution is – 

A ] 4\pi {E}_{{0}}{e}^{{\frac {R}{c}

B ] 2\pi {E}_{{0}}{e}^{{\frac {R}{c}

C ] \frac {Q}{{\epsilon }_{{0}}}

D ] \frac {4Q}{{\epsilon }_{{0}}}

 

21 ] Figure below shows the path of an electron where A B – when not under the influence of a field and B’ , C’ and D’ ,under the influence of three different electric fields 1 , 2 ,and 3 respectively . . Then the Drift Velocity of the electron under the second field is indicated by –

A ] AB + AB’

B ] ABB’

C ] AD’ –  AC’

D ] BC’

 

22 ] Earnshaw’s law states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges .Give a simple non-mathematical proof for the same . 

 

23 ] Two conductors are embedded in a material of conductivity {{30}}^{{-4}}\omega /m and dielectric constant \epsilon =90{\epsilon }_{{0}}. The resistance between the two conductors is found to be {{30}}^{{5}}\omega. Find the magnitude of the capacitance between the two conductors .

 

24] Figure below shows an hypothetical infinite conducting plane in the ( x,y,z) plane having charges Q1 , Q2 , Q3 , Q4  located in cavities.What can we predict with certainty regarding the nth cavity containing charge Qn ?

A ] V experienced by Q1 will influence the V of Qn

B ] V  of Q1  = V of Qn

C ] The whole conducting surface up to that containing Qn is an equipotential .

D ] V of the conducting plane cannot be zero .

 

25 ] Parallel to ( x ) and at a distance d .above a grounded conducting plane ( xy ) is placed an infinite wire of uniform charge  \lambda Then the  potential in the region above the plane is – 

A ] V   =\frac {\lambda }{4\pi {\epsilon }_{{0}}}In\{{\frac {{y}^{{2}}+{{\left({z+d}\right)}}^{{2}}}{{y}^{{2}}+{{\left({z-d}\right)}}^{{2}}}}\}

B ] V   =\frac {\lambda }{4\pi {\epsilon }_{{0}}}In\{{\frac {{y}^{{2}}-{{\left({z+d}\right)}}^{{2}}}{{y}^{{2}}-{{\left({z-d}\right)}}^{{2}}}}\}

C ] V   = \frac {\lambda }{2\pi {\epsilon }_{{0}}}In\{{\frac {{y}^{{2}}+{{\left({z+d}\right)}}^{{4}}}{{y}^{{4}}+{{\left({z-d}\right)}}^{{2}}}}\}

D ] V   = \frac {\lambda }{2\pi {\epsilon }_{{0}}}In\{{\frac {{y}^{{2}}-{{\left({z+d}\right)}}^{{4}}}{{y}^{{4}}-{{\left({z-d}\right)}}^{{2}}}}\}

 

26 ]  In the above case,the charge density  \sigma induced on the conducting plane is – 

A } -\frac {\lambda d}{\pi \left({{y}^{{2}}+{d}^{{2}}}\right)}

B ]  -\frac {\lambda d}{\pi \left({{y}^{{4}}+{d}^{{4}}}\right)}

C ]  \frac {\lambda d}{\pi \left({{y}^{{2}}+{d}^{{2}}}\right)}

D ] \frac {\lambda d}{\pi \left({{y}^{{4}}+{d}^{{4}}}\right)}

 

27 ] Diagram below represents a hollow conductor on which a test potential of around 90,000 V is applied.Choose the graph which correctly represents the incidence of potential inside the cavity . The x axis denotes the time elapsed in pico -seconds . 

 

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rankfile / expected questions II

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions / Physicsmynd Elite Series  /  Page  II 

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Page  : 2

 

10 .  A soap bubble of radius 1 cm , which is at a potential of 90 volts ,  collapses to a drop of radius 1 mm . Find the change in its electrostatic energy?

 

11.From a  sphere of uniform charge density \rho and radius R ,a small spherical hollow region of radius r is cut out at a distance d from the center of it .
(a) What is the  field E at the center of the hollow sphere ?

 

12 .In addition ,also find the potential \phi at above stated point.

 

13 . Suppose ,in the above case , a particle of charge q is moved from infinity to the center of the spherical shell through the cut out hole . Find the work needed ? [take the thickness of the shell to be t .]

 

14 .Find the  the electric field and potential at the center of a ring of radius r whose net  charge +Q is uniformly distributed on it. 

 

15.  Calculate the point(s) on the axis of a charged ring where the electric field is maximum.

 

16.Figure below shows the discharge curve of a Capacitor . From the graph the valve of time [ t ] when \frac {Q}{{Q}_{{0}}}=10 is-

A ] t=2.303\tau

B ] t=2.400\tau

C ] t=1.303\tau

D ] t=3\tau

 

17 ]   Drift Velocity

The primary charge carriers in sea water  are {Na}^{+} and {Cl}^{-} ions. Consider a non conducting pipe of 3 meters connected to a 15 volt battery at it’s both ends by an electrode.This pipe is then filled with seawater..Find the average drift velocity of the ions, in cm/s?

Note : The resistivity of seawater is about 25{\Omega}-m and there are about 3}\times{10}^{20}/{cm}^{3} of each ions .

 

18 ] Consider the following arrangement .-

An air-filled parallel-plate capacitor of area A , with plates a and b are kept on a smooth surface in such a manner ,that it’s one end is fixed and the other is  connected to a spring having a force constant k .The charges on the plates are respectively  Q + and  Q – .Then the expansion of the spring is – 

A ] x=\frac {{Q}^{{2}}}{2kA{\epsilon }_{{0}}}

B ] x=\frac {{Q}^{{2}}}{kA{\epsilon }_{{0}}}

C ] x=\frac {{Q}^{{3}}}{2kA{\epsilon }_{{0}}} 

D ] x=\frac {{Q}^{{2}}}{2A{\epsilon }_{{0}}}

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rankfile / expected questions

Primary Users : Students appearing for the Advanced and Mains Exam for Admission to the BTech Courses at the Indian Institutes of Technology , National Institutes of Technology , Indian Institute of Space science and Technology and other National Engineering Institutes, INDIA .

Secondary Users : GATE Physics  ,JAM Physics , Physics paper of Civil Services Exam , UGC-NET Physics , National and International Physics Olympiads,International College level Physics Exams, Indian State Board Engineering entrance exams etc.

Tertiary Users : All those who love Physics !

[ Answers with full explanations and tips & tricks to solve similar problems to be published in our site https://physicsmynd.in ]

 

To view more problems visit https://physicsmynd.in/electricity/

 

P A G E  : 1

1.THE ATOMIC HOOK

Recently an Ice berg weighing around  {9}\times{10}^{15} kgs broke off in the Weddell ice sea area in the Antarctic circle .Consider the following idea of an invention : A device consisting of two blocks – from one a proton can be extracted whose attractive force is directed towards an electron of the second block . Suppose the device is to be used as a hook  – that’s placing one block on the main ice and the second on the ice section which shows signs of breaking . What are your ideas regarding the following – [ neglect all other possible physical  forces / effects  ]

a } Would the device work as a hook preventing the breaking off of the above mentioned ice section ? If yes ,how many such devices would be needed  ?

b ]  What should be the effective weight of the blocks ?

c ] What is the effective distance needed between the blocks for such a device to work ?

d ] There is a very serious problem with the above idea .Can you point out what it is? 

 

 

2.A negatively charged particle accelerates from East to West in a uniform electric field. What are the direction and the value of the electric field if the particle has charge q=6 μC, mass m=1 mg, and if the value of its acceleration is 6 mm/{s}^{2}? Select the closest answer:

A) West, 0.001 N/C
B) East, 0.001 N/C
C) West, 3 N/C
D) East, 3 N/C
E) North, 300 N/C

 

3. A negatively charged particle with q= -3 μC is placed at the center of the uniformly charged cube with side a=1 mm and total charge Q=9 C spread out over all six faces of the cube. What is the total force acting on the particle in the center? Find the magnitude and the direction.

(A)  {0.6}\times{10}^{6}N, left
(B)  {0.6}\times{10}^{6}N, right
(C)  {2.9}\times{10}^{-9}N, top
(D)  {2.9}\times{10}^{-9}N, bottom
(E) Zero

 

4 . A tiny particle with mass m=3 mg and positive charge Q=3 mC is placed just near the ground. Find the surface charge density on the ground for keeping the particle above it in a stationary position. Consider the ground to be a non-conductor.

(A) {1.75}\times{10}^{-19} C/{m}^{2}
(B) {1.75}\times{10}^{-16} C/{m}^{2}
(C) {1.75}\times{10}^{-13} C/{m}^{2}
(D) {1.75}\times{10}^{-10} C/{m}^{2}
(E) {1.75} C/{m}^{2}

 

5. Three charges , top of 6C and bottom two of charges of the same magnitude but of opposite sign are placed at the corners of an equilateral triangle with it’s side being d = 1 cm. . Find the value and the direction of the field exactly at the center of the triangle?

(A) {0.17}\times{10}^{-16} N/C, top
(B) {2.35}\times{10}^{-6} N/C, top
(C) {8.55}\times{10}^{-1} N/C, bottom
(D) {3.2}\times{10}^{15} N/C, bottom
(E) None of the above

 

6. Some distance away from a positively charged plate with considerable surface charge density is placed an unit charge [ in mC ]  of mass  m=10 mg  on a wire  at an angle of 45 degrees.. Find the surface charge density .

(A) {1.76}\times{10}^{-16} C/{m}^{2}
(B) {1.76}\times{10}^{-12} C/{m}^{2}
(C) {1.76}\times{10}^{-8} C/{m}^{2}
(D) {1.76}\times{10}^{-4} C/{m}^{2}
(E) {1.76} C/{m}^{2}

 

7 . Charges are placed in a geometrical pattern corresponding to the  hour hands of a clock with their magnitudes being equivalent to that of the hours indicated .Calculate the resulting field ?  

 

8. Consider a semicircle of radius r with it’s left quadrant being negatively charged and the rest being positive. .Find the field generated in this negative quadrant ?

 

9. A disc of radius r has an amount of charge q  uniformly spread on it’s surface  Find the potential at any point on it’s axis of symmetry.

 

[ Answers with full explanations and tips & tricks to solve similar problems to be published in https://physicsmynd.in ]

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How to get into IITs, NITs ,IIITs and other engineering colleges from 2013.

A single entrance examination will be held from 2013 for admission to the centrally funded engineering institutes. These include the 15 Indian Institutes of Technology (IITs) and all the National Institutes of Technology (NITs). Equal weightage will be given to marks obtained in the Class XII examinations and those of the entrance tests.

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