Descripción de las clases del análisis

1. Four large parallel identical conducting plates of area A are arranged as shown. The charges on each plate are given in diagram and separation between plates is d  (d  is very small). Surface of plates are numbered (1), (2), ………

(8).

Column I Column II

(p) Surfaces having charges of same magnitude and sign

(a) 1 and 8

(q) Surfaces having positive charges

(b) 3 and 5

(r) Uncharged surfaces (c) 2 and 3

(s) Charged surfaces (d) 6 and 7

2. Inside a neutral metallic spherical shell a charge Q₁ is placed and outside the shell a chargeQ₂ is placed

Column I Column II

3. Axis of a hollow cone shown in figure is vertical. Its base radius is R. It is kept in a uniform electric field E  parallel to its axis.

Column I Column II

(p) Magnitude of flux through base of cone

(a) ^p  R E 2

(q) Magnitude of flux through curved part of cone

(b) 2

2  R E  p 

(r) Magnitude of flux through curved part MN QP of

(s) Net flux throughS ₄ (d) non-zero

86  Electrostatics: Part 1

5. Following figure shows for Gaussian surfaceS ₁,S ₂,S ₃ and

S ₄.

Now, match the following columns.

Column I Column II

6. In the figure shown a conducting spherical shell of inner radius x  and outer radius y  is concentric with a larger conducting spherical shell of inner radiusa and outer radius

b. The inner shell has a total charge +3Q and the outer shell has a total charge +5Q. Letr  be the distance of any point from the common centreO. Match column I and column II.

Column I Column II

(i) Electric field strength is zero

(p) On outer surface of the larger spherical shell

(ii) Electric field strength is non-zero

(q) On inner surface of the larger spherical shell

(iii) Magnitude of charge is 3Q

(r) On outer surface of the smaller spherical shell

(iv) Charge is + 8Q (s) Fora <r  <b

Now match the given columns and select the correct option from the codes given below.

Codes

1. Four charge particles each having chargeQ = 1 C are fixed at corners of base (at A, B,C  and D) of a square pyramid with slant length ‘a’ ( AP = BP = BP =PC  =a = 2 m), a charge -Q is fixed at pointP. A dipole with dipole moment

 p = 1 C-m is placed at centre of base and perpendi cular to its plane as shown in figure. If the force on dipole due to charge particles is

2. A ring of radius R, has charge –Q distributed uniformly over it. Calculate the charge (q) that should be placed at the centre of the ring such that the electric field becomes zero at a point on the axis of the ring distant ‘ R’ from the centre of the ring. If the value of

4

q⁼Q Ω . Find the value ofW.

3. Two identical small equally charged conducting balls are suspended from long threads secured at one point. The charges and masses of the balls are such that they are in equilibrium when the distance between them is a (the length of thread L >>a). One of the balls is then discharged.

Again for the certain value of distanceb (b <<l) between the balls the equilibrium is restored, Find the value of

3

3 . a b

 Electrostatics: Part 1 ⁸⁷

4. A simple pendulum is suspended in a lift which is going up with an acceleration of 5m/s². An electric field of magnitude 5 N/C and directed vertically upward is also present in the lift. The charge of the bob is 1mC and mass is 1 mg. Takingg =p ² and length of the simple pendulum 1 m, find the time period of the simple pendulum (in sec).

5. Six charges are kept at the vertices of a regular hexagon as shown in the figure. If magnitude of force applied by +Q on +q charge isF , then net electric force on the +Q is

nF . Find the value ofn.

6. Electric field in a region is given by E = - ⁴ xi ^ˆ +^{6 .}yj^ˆ

  The

charge enclosed in the cube of side 1 m oriented as shown in the diagram is given by a Œ0. Find the value ofa .

7. Two small metal sphere having equal charge and mass are suspended from some point on the ceiling of a damp room with silk threads of equal length. Let centre to centre distance between sphere be x , x  << l, l is length of silk thread. Due to ionization of medium, charge leaks off from each sphere and they keep on coming closer to each other at a constant rate.

Let their approach velocityv varies as ^{v µx -1/2}.

If mass of each sphere is m then the rate at which charge varies with respect to time is ^{2 0}

2

mg dq N 

dt l

pe 

µ .

Find the value of N .

8. S ₁ andS ₂ are two hollow concentric spheres with chargeq

and 2q. Space betweenS ₁ andS ₂ is filled with a dielectric of dielectric constants.

The ratio of flux throughS ₂ and flux throughS ₁ isK . Then, find the value of ⁹

11 K .

9. In Bohr’s theory of the hydrogen atom, an electron moves in a circular orbit about a proton of radius 0.53 Å. Speed of electron in Bohr’s orbit is about ¹ speed of light

69

 N _¥ ^¥ .

Find the value of N .

  10. A charged dust particle of radius 5 × 10^–7 m is moving in a horizontal electric field of intensity 6.28 × 10⁵ V/M. The surrounding medium is air with coefficient of viscosity

h = 1.6 × 10^–5 N-s/m². If this particle is moving with a uniform horizontal speed of 0.02 m/s, the number of excess electrons on the drop are 6k . Find the value ofk .

  11. Consider a uniform charge distribution with charge density 2 C/m³ throughout in space. If a Gaussian sphere has a variable radius which changes at the rate of 2 m/s, then value of rate of charge of flux is proportional tor ^k , (r  = radius of sphere). Then, find the value ofk .

88  Electrostatics: Part 1 6. If the electric flux entering and leaving an enclosed surface, respectively, are f ₁ andf ₂, the electric charge inside the surface will be with a forceF  when kept apart at some distance. A third spherical conductor, having the same radius as that of B

but uncharged, is brought in contact with B  and then in contact withC  and finally removed away from both. The new force of repulsion between B andC  is

  (a) F  /4  (b) 3F  /4

  (c) F  /8  (d) 3F  /8 (AIEEE 2004)

8. Four charges equal to – Q are placed at the four corners of a square and a charge q is placed at its centre. If the system is in equilibrium, the value of q is

  (a) (1 2 2 )

= L, respectively. 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) 2 L  (b)  L /4

  (c) 8 L  (d) 4 L (AIEEE 2005)

10. An electric dipole is placed at an angle of 30° to a non-uniform electric field. The dipole will experience

  (a) a translational force only in the direction of the field

  (b) a translational force only in a direction normal to the direction of the field

  (c) a torque as well as translational force

  (d) a torque only (AIEEE 2006)

 JEE (M

^AIN

)

Single Correct Answer Type

1. A charged particleq is placed at the centreO of a cube of length L ( ABCDEFGH ). Another same chargeq is placed at a distance L  from O. Then the electric flux through

2. If a chargeq is placed at the centre of the line joining two equal charges Q  such that the system is in equilibrium, 3. A simple pendulum of period T  has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate, its period will

(a) remain equal toT   (b) less thanT 

  (c) greater thanT   (d) infinite (AIEEE 2002) 4. If three charges are placed at the vertices of equilateral triangle of charge ‘q’ each. What is the net potential energy, if the side of equilateral triangle islcm?

(a)

 Electrostatics: Part 1 ⁸⁹

11. A thin spherical shell of radius R  has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E (r ) produced by the shell in the range 0 £ r <•, where r  is the distance from the center of the shell?

(AIEEE 2008) a solid sphere of radius R and total chargeQ. For a point

 p  inside the sphere at distance r ₁  from the centre of the sphere, the magnitude of electric field is

  (a) 0  (b) ₂

13. A charge Q is placed at each of the opposite corners of a square. A charge q  is placed at each of the other two corners. If the net electrical force on Q is zero, then the

Q / q equals

  (a) -^{2 2  (b)} –1

  (c) 1  (d)

-1

2 (AIEEE 2009)

14. A thin semi-circular ring of radiusr  has a positive charge

q distributed uniformly over it. The net field E  at the centre

O is 15.  Let there be a spherically symmetric charge distribution

with charge density varying as ^{( )} ₀ ⁵  16. Two identically charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8 g/cm³, the angle remains the same. If the density of the material of the sphere is 16 g/cm³, the dielectric constant of the liquid is

  (a) 4 (b) 3

(c) 2  (d) 1 (AIEEE 2010)

17. Two identical charged spheres suspended from a common point by two massless strings of length l  are initially a distanced (d  <<l) apart becuase of their mutual repulsion.

The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocityv. Then as a function of distance x  between them

  (a) vµ x^–1/2  (b) vµ x^–1

  (c) vµ x^1/2  (d) vµ x  (AIEEE 2011) 18. In a uniformly charged sphere of total chargeQ and radius

 R, the electric field E   is plotted as function of distance from the centre. The graph which would correspond to the above will be

90  Electrostatics: Part 1

19. This questions has Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describe the two statements.

An insulating solid sphere of radius R  has a unioformly positive charge densityr . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.

Statement 1: When a charge ‘q’ is take from the centre of the surface of the sphere its potential energy changes by

qr  /3e ₀

Statement 2: The electric field at a distancer  (r  < R) from the centre of the sphere isr r  /3e ₀

  (a) Statement 1 is true, statement 2 is true; statement 2 is not the correct explanation of statement 1.

  (b) Statement 1 is true statement 2 is false.

  (c) Statement 1 is false statement 2 is true.

  (d) Statement 1 is true, statement 2 is true, statement 2 is the correct explanation of statement 1.

(AIEEE 2012) 20. Two charges, each equal to q, are kept at x = –a  and

 x = a  on the x -axis. A particle of mass m  and charge

q₀ =q /2 is placed at the origin. If chargeq₀ is given a small displacement ( y <<a) along the y-axis, the net force acting on the particle is proportional to

  (a) – y  (b) ¹

 y

  (c) ¹

- y  ^{(d)  y} (JEE Main 2013)

21. Let [e ₀] denote the dimensional formula of the permittivity of vacuum. If M   = mass, L  = length, T   = time and A =

 ρ   where A is a constant andr  is the distance from the centre. At the centre of the spheres is a point chargeQ. The value of A such that the electric field in the region between the spheres will be constant, is

  (a) on the y-axis. A positive chargeQ is released from rest at the point (2a, 0) on the x-axis. The chargeQ 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

(IIT-JEE 1984) 2. A chargeQ is placed at the center of the line joining two equal chargesQ. The system of the three charges will be in equilibrium ifq is equal to

  (a) –Q /2  (b) –Q /4

  (c) +Q /4  (d) –Q /2

(IIT-JEE 1987) 3. A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in the figure as

  (a) 1  (b) 2

  (c) 3  (d) 4 (IIT-JEE 1996)

4. An electron of mass m_e initially at rest moves through a certain distance in a uniform electric field in time t ₁. A 5. Three positive charges of equal valueq are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in (IIT-JEE 2001)

(a) (b) (c) (d)

 Electrostatics: Part 1 ⁹¹

6. A metallic shell has a point chargeq kept inside its cavity.

Which one of the following diagrams correctly represents the electric lines of force?

(a) (b) (c) (d)

(IIT-JEE 2003) 7. Six charges of equal magnitude, three positive and three negative, are to be placed onPQRSTU  corners of a regular hexagon, such that field at the center is double that of what it would have been if only one positive charge is placed at

 R.

 P  Q

 R

T  S 

U  O

  (a) + + + − − −^{, , , , ,}   (b) − + + + − −^{, , , , ,}

  (c) − + + − + −^{, , , , ,} (d) + − + − + −^{, , , , ,}

(IIT-JEE 2004) 8. A Gaussian surface in the figure is shown by dotted line.

The electric field on the surface will be

q₁ q₂ q₁

(a) due to q1 and q2 only

  (b) due to q₂ only

  (c) zero

(d) due to all (IIT-JEE 2004)

9. Three infinitely long charge sheets are placed as shown in the figure. The electric field at point P is

  (a) 0

2 /s e  k ˆ  (b) 0

4 /s e  k ˆ

  (c) 0

2 /s e  k ˆ

-   ^(d) 0

4 /s e  k ˆ

- (IIT-JEE 2005)

10. Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

  (a) negative and distributed uniformly over the surface of the sphere

  (b) negative and appears only at the point on the sphere closest to the point charge

  (c) negative and distributed nonuniformly over the entire surface of the sphere

  (d) zero (IIT-JEE 2007)

11. A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the empty space is

  (a) zero everywhere

  (b) nonzero and uniform

(c)  nonuniform

  (d) zero only at its center (IIT-JEE 2007)  12. A disk of radius ^{a/ 4} having a uniformly distributed charge 6 C is placed in the xy plane with its center at ⁽ −^{a/ 2, 0, 0)}. A rod of length carrying a uniformly distributed charge 8 C is placed on the ^x-axis from  ^x =^{a/ 4} to ^x =^{5 / 4a} . Two point charges –7 C and 3 C are placed at ( / 4, ^a −^a/ 4, 0)

and ( 3 / 4,3 / 4,0)− ^{a a} , respectively. Consider a cubical surface formed by six surfaces  ^x = ±^{a/ 2},  ^{y = ±a/ 2},

/ 2

 z = ±a . The electric flux through this cubical surface is

  (a) –2C  / e ₀  (b) 2C  / e ₀

(c) 10C  / e ₀ (d) 12C  / e ₀ (IIT-JEE 2009)  13. Three concentric metallic spherical shells of radii R, 2 R, and 3 R  are given charges Q1, ^Q2, and ^Q3,  respectively.

It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio

Q1 : Q₂ : Q₃ of the charges given to the shells is

92  Electrostatics: Part 1

  (a) 1:2:3  (b) 1:3:5

  (c) 1:4:9 (d) 1:8:18

(IIT-JEE 2009) 14.  A uniformly charged thin spherical shell of radius R

carries uniform surface charge density of s  per unit area.

It is made of two hemispherical shells, held together by pressing them with forceF .F  is proportional to

 F   15. A tiny spherical oil drop carrying a net chargeq is balanced in still air with a vertical uniform electric field of strength (81p  /7) ¥ 105 Vm^–1. When the field is switched off, the

The flux through the shaded area (as shown in the figure) due to this field is  17. A wooden block performs SHM on a frictionless surface with frequency n ₀. The block carries a charge +Q on its surface. If a uniform electric field E   is switched on as shown, then the SHM of the block will be

 E  +Q

  (a) of the same frequency and with shifted mean position

  (b) of the same frequency and with the same mean position

  (c) of changed frequency and with shifted mean position

  (d) of changed frequency and with the same mean positio n

(IIT-JEE 2011)  18. ChargesQ, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R /2, R and 2 R

respectively, as shown in figure. If magnitudes of the electric fields at pointP at a distance R from the centre of spheres 1, 2 and 3 are E ₁, E ₂ and E ₃ respectively, then

  (a)  E ₁ > E 2 > E ₃  (b)  E ₃ > E ₁ > E ₂   (c)  E ₂ > E ₁ > E ₃  (d)  E ₃ > E ₂ > E ₁

(JEE Advanced 2014) 19.  The figure below depict two situations in which two infinitely long static line charges of constant positive line charge densityl  are kept parallel to each other. In their resulting electric field, point chargesq and –q are kept in equilibrium between them. The point charges are confined to move in the x -direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is (are):

  (a) Both charges execute simple harmonic motion.

  (b) Both charges will continue moving in the direction of their displacement.

 20. Consider a uniform spherical charge distribution of radius

 R₁ centred at the originO. In this distribution, a spherical cavity of radius R₂, centred at P with distance OP= a =

 R₁ – R₂ (see figure) is made. If the electric field inside the cavity at positionr 

 is E r ( )



 , then the correct statement(s) is(are)

 Electrostatics: Part 1 ⁹³

  (a)  E 

 is uniform, its magnitude is independent of R₂ but its direction depends on r 



 is uniform, its magnitude is independent of a but its direction depends on ^a

  (d)  E 

  is uniform, and both its magnitude and direction

depends on ^a (JEE Advanced 2015)

Multiple Correct Answers Type

1. A positively charged thin metal ring of radius R is fixed in the xy plane with its center at the originO. A negatively charged particle P  is released from rest at the point

(0, 0, ) ^z 0 , where _z 0 > . Then the motion of0 P is

  (a) periodic, for all values of  z 0 satisfying 0< < ∞_z 0

  (b) simple harmonic, for all values of  z 0  satisfying

0< ≤z 0 R

  (c) approximately simple harmonic, provided  z 0 <<R

  (d) such that P crosses ^O and continues to move along the negative z-axis toward  ^z  = −∞.

(IIT-JEE 1998) 2. A nonconducting solid sphere of radius R  is uniformly charged. The magnitude of the electric field due to the sphere at a distancer  from its center

  (a) increases asr  increases, for r < R

  (b) decreases asr  increases, for ⁰< < ∞r 

  (c) decreases asr  increases, for  R < < ∞r 

  (d) is discontinuous atr  = R (IIT-JEE 1998) 3. A few electric field lines for a system of two charges Q₁

andQ₂ fixed at two different points on the x -axis are shown in the figure. These lines suggest that

Q₁ Q₂

4. A cubical region of side a has its center at the origin. It encloses three fixed point charges, –q  at (0, –a /4, 0), +

5. Two nonconducting solid spheres of radii R and 2 R, having uniform volume charge densitiesr ₁ andr ₂, respectively, touch each other. The net electric field at a distance 2 R

from the center of the smaller sphere, along the line joining the center of the spheres is zero. The ratio r r 1  /  2 can be wire with constant linear charge densityl , and an infinite plane with uniform surface charge density s . If E ₁(r ₀) center of the nucleus as shown in the figure. The electric field is only along the radial direction. (IIT-JEE 2008)

94  Electrostatics: Part 1

1. The electric field at r =  isR

  (a) independent ofa

  (b) directly proportional toa   (c) directly proportional toa²   (d) inversely proportional toa

2. Fora = 0, the value ofd  (maximum value ofr  as shown in

3. The electric field within the nucleus is generally observed to be linearly dependent onr . This implies

  (a) a = 0  (b) respectively. A positive chargeq is placed on the positive

 y axis at a distanceb > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists.

are constants andr  is the distance from its centre. If the electric field at r =R^{/ 2} is 1/8 times that at r = , findR

the value ofa. (IIT-JEE 2009)

2. An infinitely long solid cylinder of radius R has a uniform volume charge densityr . It has a spherical cavity of radius

 R /2 with its center on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point

P, which is at a distance 2 R from the axis of the cylinder, is given by the expression 23 r  R /16k e 0.The value ofk  is

(IIT-JEE 2012) 3.  An infinitely long uniform line charge distribution of charge per unit length l  lies parallel to the y-axis in the

 y- z  plane at ³

2

 z = a  (see figure). If the magnitude of the flux of the electric field though the rectangular surface

 ABCD lying in the x – y plane with its centre at the origin is

0

 Electrostatics: Part 1 ⁹⁵

ANSWERS

C

ONCEPT 

 A

PPLICATION

 E

XERCISE

 1

1. (b) 2. (d) 3. (c, d) 4. 0.50 C

5. 0.19 MC 6. 1.3 × 10⁷ C

7. (a) positron; (b) electron 8. +16e

9. (a) 2.00 × 10¹⁰ electrons; (b) 1.33 × 10¹⁰ electrons

  10. –1.28 × 10¹³ C 11. 1.3 days

In document Analisis del Registro de Enfermedades de Declaracion Obligatoria (REDO) del Sistema de Informacion para la salud. (página 92-107)