C ONCLUSIONES - Analisis de un IDE para multiples plataformas con tecnologias y herramientas l

Level 1

1. A and B are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are far away from the dipole and at equal distances from it. The fields at A and B are _E^Æ_A and E _B

is perpendicular to E _A

2. In a gravity-free space, uniform electric field E has been applied in the vertical direction as shown. A particle of massm and chargeq is projected horizontally with velocity

V . The time after which the velocity vector makes an angle 45° with the initial velocity vector, is equal to

(a) mV / qE (b) 2mV / qE (c) 3mV /2qE (d) 3mV /4qE

3. A cylinder of length L and radiusb had its axis coincident with the x-axis. The electric field in this region is^E^Æ⁼²⁰⁰ⁱ^ˆ . Find the flux through the left end of cylinder.

(a) 0 (b) 200p b²

4. Charge on an originally uncharged conductor is separated by holding a positively charged rod very closely nearby, as in figure. Assume that the induced negative charge on the conductor is equal to the positive chargeq on the rod.

Then, flux through surfaceS ₁ is

(a) zero (b) q / e ₀

Electrostatics: Part 1 ⁷⁷

(a) kq / a² at an angle 45° above the + x -axis

(b) kq / a² at an angle 45° below the – x -axis

(d) 3kq / a² at an angle 45° below the + x -axis

10. Four electrical charges are arranged on the corners of a 10 cm square as shown.

What would be the direction of the resulting electric field at the centre point P?

(a) → (b) ↑

11. Two pith balls each with mass m are suspended from insulating threads.

When the pith balls are given equal positive chargeQ, they hang in equilibrium as shown. We now increase the charge on the left pith ball fromQ to 2Q while leaving its mass essentially unchanged. Which of the following diagrams best represents the new equilibrium configuration?

(a) (b)

12. Three charges each Q are placed at the three corners of an equilateral triangle. A fourth chargeq is placed at the

centre of triangle. The ratio ^q

Q so as to make the system in equilibrium is:

(a) 1: 3 (b) ^{1 : 3}

13. The maximum electric field at a point on the axis of a uniformly charged ring is E ₀. At how many points on the axis will the magnitude of electric field be E ₀ /2

(a) 1 (b) 2

14. An electric chargeq exerts a forceF on a similar electric chargeq separated by a distance r . A third chargeq /4 is placed mid-way between the two charges. Now, th e force

F will

(a) become

F (b) become

9 F

F (d) remainF

15. The electric field intensity at the centre of a uniformly charged hemispherical shell is E ₀. Now two portions of the hemisphere are cut from either side and remaining portion is shown in figure.

If 3

a b ⁼ ⁼p , then electric field intensity at centre due to remaining portion is

(a) ⁰

3 E

(b) ⁰

6 E

2 E

(d) Information insufficient

16. A block of mass m is suspended in vertical orientation with a spring of spring constantk . The block is made to oscillate in gravitation field. Its time period is found to be

78 Electrostatics: Part 1

T . Now the space between the plates is made gravity free and an electric field E is produced in vertical downward direction. Now the block is given chargeq. The new time period of oscillation is

(a) T (b) T + 2p ^qE

md (c) 2p ^qE

md (d) none of the above

17. The figure below shows the forces that three charged particles exert on each other. Which of the four situations shown can be correct?

(I) (II)

(III) (IV)

(a) all of the above (b) none of the above

18. An electroscope is given a positive charge, causing its foil leaves to separate. When an object is brought near the top plate of the electroscope, the foils separate even further.

We conclude

(a) that the object is positively charged

(b) that the object is electrically neutral

(d) none of these

19. A point negative charge –Q is placed at a distancer from a dipole with dipole momentPin x − y plane as shown in figure. The x component of force acting on the charge –Q

(a) ^PkQ^cos i^ˆ r

- q ^(b)

cos ˆ

PkQ i

2PkQcos ˆ

r i

- q ^(d) 3

2PkQ cos ˆ

i r

Level 2

20. Two chargesq₁ andq₂ are kept on x -axis and electric field at different points an x -axis is plotted against x . Choose correct statement about nature and magnitude of q₁ and

q₂.

(a) q₁ +ve,q₂ –ve ; |q₁| > |q₂|

(b) q₁ +ve,q₂ –ve ; |q₁| < |q₂|

(d) q₁ –ve,q₂ +ve ; |q₁| < |q₂|

21. Three identical point charges, each of mass m and charge

q, hang from three strings as shown in figure. The value ofq in terms ofm, L andq.

(a) ^q⁼ ^(16/5)^pe₀^{mg L}²^sin²^q^tan^q (b) ^q⁼ ^(16/15)^pe₀^{mg L}²^sin²^q ^tan^q (c) q⁼ (15/16) ^pe₀mg L²sin ²^q tan^q (d) none of these

22. A metallic shell has a point charge ‘q’ kept inside its cavity.

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

(a) (b)

Electrostatics: Part 1 ⁷⁹

23. The direction (q ) of E

 at point P due to uniformly charged finite rod will be

(a) at angle 30° from x -axis

(b) 45° from x -axis

(d) none of these

24. Find the force experienced by the semicircular rod charged with a chargeq, placed as shown in figure. Radius of the wire is R and the line of charge with linear charge density λ is passing through its centre and perpendicular to the plane of wire.

25. A large sheet carries uniform surface charge densitys . A rod of length 2l has a linear charge densityl on one half and –l on the second half. The rod is hinged at mid-point

O and makes an angleq with the normal to the sheet. The torque experienced by the rod is

(a) 0 (b)

26. A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the centre. What is the ratio of the magnitude of the electric field at a distance 2 R from the centre to the magnitude of the electric field at a distance of R /2 from the centre?

(a) 1 (b) 2

27. An uncharged conducing large plate is placed as shown.

Now an electric field E towards right is applied. Find the induced charge density on right surface of the plate.

(a) –e ₀ E (b) e ₀ E

28. An uncharged aluminium block has a cavity within it. The block is placed in a region where a uniform electric field which is directed upwards. Which of the following is a correct statement describing conditions in the interior of the block’s cavity?

(a) The electric field in the cavity is directed upwards

(b) The electric field in the cavity is directed downwards

(d) The electric field in the cavity is of varying magnitude and is zero at the exact centre

29. The diagram shows a uniformly charged hemisphere of radius R. It has volume charge densityr . If the electric field at a point 2 R distance above its centre is E then what is the electric field at the point which is 2 R below its centre?

(a) r R /6e ₀ + E (b) ρ R /12e ₀ – E (c) –r R /6e ₀ + E (d) r R /12e ₀ + E

30. Consider an infinite line charge having uniform linear charge density and passing through the axis of a cylinder.

80 Electrostatics: Part 1

What will be the effect on the flux passing through curved surface if the portions of the line charge outside the cylinder is removed?

(a) Decreases (b) Increases

31. One fourth of a sphere of radius R is removed as shown.

An electric field E exists parallel to x − y plane. Find the flux through remaining curved part.

(a) ^p R E ² (b) _{2 R E}p ²

32. A non-conducting sphere of radius R is filled with uniform volume charge density –r . The centre of this sphere is displaced from the origin by ^d^. The electric field E

 at any point P having position vector, inside the sphere is

(a)

33. A charged large metal sheet is placed into uniform electric field, perpendicularly to the electric field lines. After placing the sheet into the field, the electric field on the left side of the sheet is E ₁ = 5 × 10⁵ V/m and on the right it is

E ₂= 3 × 10⁵ V/m. The sheet experiences a net electric force of 0.08 N. Find the area of one face of the sheet. Assume external field to remain constant after introducing the large sheet.

34. A positively charged sphere of radiusr ₀ carries a volume charge densityr (figure). A spherical cavity of radiusr ₀ /2 is then scooped out and left empty, as shown.C ₁ is the centre of sphere andC ₂ that of cavity. What is the direction and magnitude of the electric field at point B?

(a) ⁰

35. Four very large metal plates are given the charges as shown in figure. The middle two are then connected through a wire. Find the charge that will flow through the wire.

(a) 5Q from A to B (b) 5Q /2 from A to B (c) 5Q from B to A (d) no charge will flow

36. A conic surface is placed in a uniform electric field E as shown such that field is perpendicular to the surface on the side AB. The base of the cone is of radius R and height of the cone ish.

Electrostatics: Part 1 ⁸¹

The angle of cone isq as shown. Find the magnitude of that flux which enters the cone curved surface from left side. Don’t count the outgoing flux. (q < 45°).

(a) ER[h cosq +p ( R /2) sinq ]

(b) ER[h sinq +p ( R /2) cosq ]

(d) none of these

37. Flux passing through shaded surface of sphere when a point chargeq is placed at the centre is (radius of the sphere is

(a) q / e ₀ (b) q /2e ₀

38. A uniformly charged and infinitely long line having a linear charge density ‘l ’is placed at a normal distance y from a point O. Consider a sphere of radius R withO as centre and R > y. Electric flux through the surface of the sphere is

39. Two infinite sheets having charge densitiess ₁ands ₂ are placed in two perpendicular planes whose two-dimensional view is shown in the figure. The charges are distributed uniformly on sheets in electrostatic equilibrium condition.

Four points are marked I, II, III and IV. The electric field intensities at these points are _{E E E}1 , 2, 3

  

and E 4



respectively. The correct expression for electric field intensities is

40. Three large identical conducting parallel plates carrying charge +Q, -Q and +2Q respectively are placed as shown in the figure. If E _A, E _Band E _C refer the magnitude of electric field at points A, B and C respectively then:

(a) E _A > E _B > E _C (b) E _A = E _B> E _C (c) E _A = 0 and E _B > E _C (d) E _A = 0 and E _B = E _C 41. The number of electric field lines crossing an area DS

is n₁ when DS E ,

 

 while number of field lines crossing same area isn₂ when _D_E^^ makes an angle of 30º with E ^,



then:

(a) n₁ =n₂ (b) n₁ >n₂

M

ULTIPLE

C

ORRECT

A

NSWERS

T

YPE

1. When an electron moves in a circular path around a stationary nucleus charge at the centre:

(a) the acceleration of the electron changes

(b) the velocity of the electron changes

(b) the chargeq is in equilibrium at the origin

(d) for any position ofq other than origin the force is directed away from origin

3. A conducting ball is positively charged and another positive point charge is brought closer to the ball.

(a) the ball may attract the point charge

(b) the ball may repel the point charge

82 Electrostatics: Part 1

(d) the ball will only repel the point charge and in no condition it can attract the point charge

4. We have two electric dipoles. Each dipole consists of two equal and opposite point charges at the ends of an insulating rod of lengthd . The dipoles sit along the x -axis a distance

r apart, oriented as shown below.

Their separationr >>d . The dipole on the left:

(a) will feel a force to the left

(b) will feel a force to the right

(d) will feel no torque

5. Imagine a short dipole is at the centre of a spherical surface.

If magnitude of electric field at a certain point on the surface of sphere is 10 N/C, then which of the following cannot be the magnitude of electric field anywhere on the surface of sphere

(a) 4 N/C (b) 8 N/C

(c 16 N/C (d) 32 N/C

6. Consider a Gaussian spherical surface, covering a dipole of chargeq and –q, then

(a) q_in = 0 (Net charge enclosed by the spherical surface)

(b) f _net = 0 (Net flux coming out the spherical surface)

(d)

Ú

E d s^· ^ =0 (Surface integral of over the spherical surface)

7. Two large thin conducting plates with small gap in between are placed in a uniform electric field ‘ E ’ (perpendicular to the plates). Area of each plate is A and charges +Q and –Q

are given to these plates as shown in the figure. If points

R,S andT as shown in the figure are three points in space, then the

8. ChargesQ1 andQ2 lie inside and outside respectively of a closed surfaceS . Let E be the field at any point onS and of a spherical cavity of radius 3 cm of piece of metal. Th e electric field at

(a) A (2 cm from the charge) is 0

(b) A (2 cm from the charge) is 1.125 × 10⁷ N/C

(d) B (5 cm from the charge) is 1.8 × 10⁶ N/C

10. A right circular imaginary cone is shown in the adjacent figure. A, B andC are the points in the plane containing the base of the cone, while D is the point at the vertex of the cone. Iff _A, f _B, f _Candf _Drepresent the flux through curved surface of the cone when a point charge Q is at point A, B,C and D, respectively, then

L

^INKED

C

OMPREHENSION

T

^YPE

For Problems (1–2)

1. A simple pendulum of mass m charged negatively to q

coulomb oscillates with a time period Tin a downward electric field E such thatmg > qE . If the electric field is withdrawn, the new time period

Electrostatics: Part 1 ⁸³

(a) =T (b) >T (c) <T

(d) any of the above three is possible

2. At equilibrium of the bob the change in tension in string will be (assuming rest condition)

(a) mg (b) qE

For Problems (3–5)

There is an insulator rod of length Land of negligible mass with two small balls of mass mand electric charge Qattached to its ends. The rod can rotate in the horizontal plane around a vertical axis crossing it at an L /4 distance from one of its ends.

3. At first the rod is in unstable equilibrium in a horizontal uniform electric field of field strength E . Then we gently displace it from this position. Determine the maximum velocity attained by the ball which is closer to the axis in the subsequent motion.

4. In what position is the rod to be set so that if displaced a little from that position it begins a harmonic oscillation about the axis A?

(a) (b)

5. What is the time period of the SHM as mentioned in above question?

Positive and negative charges of equal magnitude lie along the symmetry axis of a cylinder. The distance from the positive charge to the left end-cap of the cylinder is the same as the distance from the negative charge to the right end-cap.

6. What is the flux of the electric field through the closed cylinder?

(a) 0 (b) +Q /e ₀

7. What is the sign of the flux through the right end-cap of the cylinder?

(a) Positive

(b) Negative

For Problems (8–9)

There are two non-conducting spheres having uniform volume charge densities r and –r . Both spheres have equal radius R. The spheres are now laid down such that they overlap as shown in the figure. Take ^d^Æ⁼^{O O}_{1 2}^Æ

8. The electric field _E^ in the overlap region is

(a) non-uniform (b) zero

(c)

9. The potential differenceDV between the centres of the two spheres ford = R is although are equivalent ways of describing the relation between charge and electric field in static conditions. Gauss’s law is e ₀f

=q_enclin whichq_enclis the net charge inside an imaginary closed surface called Gaussian surface f = ^

Ú

^{ }^{E d}^. a gives electric flux

84 Electrostatics: Part 1

of through Gaussian surface. The two equations hold only when the net charge is in vacuum or air.

10. A Gaussian surface encloses two of the 4 positively charged particles. The particles which contribute to the electric field at point p on the surface are

(a) q₁andq₂ (b) q₂ andq₃ (c) q₄ andq₃ (d) q₁,q₂,q₃ andq₄ 11. The net flux of the electric field through the surface is

(a) due toq₁andq₂ only

(b) due toq₃andq₄ only

(d) cannot say

12. The net flux of the electric field through the surface due toq₃andq₄ is

(a) zero (b) positive

13. If the charge q₃ and q₄ are displaced (always remaining outside the Gaussian surface), then consider the following two statements

A: Electric field at each point on Gaussian surface will remain same.

A spherical conductor A contains two spherical cavities as shown in figure. The total charge on conductor itself is zero. However, there is a point charge q₁ at centre of one cavity and q₂ at the centre of other cavity. Another charge q₃ is placed at large distance ‘r ’ from the centre of the spherical conductor.

14. Which of the following statements are true?

(a) Chargeq₃ applies larger force on charge q₂ than on chargeq₁

(b) Chargeq₃ applies smaller force on charge q₂ than on chargeq₁

(d) Chargeq₃ applies no force on any of the charges

15. If q₁ is displaced from its centre slightly (being always inside the cavity) then the correct representation of field lines inside the same cavity is:

(a) (b)

(d)

16. The force acting on conductor A will be

(a) zero (b) ³ ¹ ₂²

17. Find the tensions in the string AB.

(a) zero (b)

18. Find the tensions in the string BC .

(a) zero (b)

19. If the particleC is discharged then tension in string BC

(a) zero (b)

Electrostatics: Part 1 ⁸⁵

20. If the particle B is discharged then the tension in string

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