Electric force – Coulomb’s law – Exercises

ELECTRIC FORCE – COULOMB’S LAW – EXERCISES

Electric force – Coulomb’s law

Exercises

01-(UNIFESP-SP) Two particles with electric charges

Q 1 = 4.0 × 10 -16 C eq‚ = 6.0 × 10 -16 C

are separated in vacuum by a distance of 3.0.10 -9 m. If k = 9.0.10 9 Nm 2 /C 2 , the intensity of the interaction force between them, in newtons, is

  1. a) 1,2.10-5. b) 1,8.10 -4 . c) 2,0.10 -4 .
    d) 2,4.10 -4 . e) 3,0.10 -3 .

02-(UEL-PR) Two equal charges of 2.10 -6 C , repel each other in a vacuum with a force of 0.1 N. Knowing that the electric constant of the vacuum is 9.10 9 Nm 2 /C 2 , the distance between the charges, in meters, is:

  1. a) 0.9 b) 0.6 c) 0.5
  2. d) 0.3 e) 0.1

03-(UNESP-SP) Which of the graphs represents the way in which the electrical force between two point charges varies as a function of the distance separating them, when they are brought closer to or further away from each other?

04-(MACKENZIE-SP) Two electrified corpuscles with identical electrical charges are located in a vacuum (K o =9.0.10 9 N.m 2 /C 2 ) and

1 m apart. The intensity of the electrostatic interaction force between them is 3.6.10 -2 N. The electric charge of each of these corpuscles can be (in μC):

  1. a) 9 b) 8 c) 6
  2. d) 4 e) 2

05-(PUC-MG) Two point electric charges are separated by a distance of 4.0 cm and repel each other with a force of 3.6 × 10 -5 N. If the distance between the charges is increased to 12.0 cm, the force between the charges will be:

  1. a) 1.5 × 10-6N
    b) 4.0 × 10 -6 N c) 1.8 × 10 -6 N
    d) 7.2 × 10 -6 N

06-(UNESP-SP)) Two point bodies at rest, separated by a certain distance and electrically charged with charges of equal signs, repel each other according to Coulomb’s Law.

  1. a) If the amount of charge on one of the bodies is tripled, will the electrical repulsion force remain constant, increase (how many times?) or decrease (how many times?)?
  2. b) If the initial charges are maintained, but the distance between the bodies is doubled, will the electrical repulsion force remain constant, increase (how many times?) or decrease (how many times?)?

07-(UFRN-RN) If q 1 and q 2 are two electric charges, for the situation outlined we will necessarily have:

  1. a) q1= q 2
    b) q 1 = – q 2 c) q 1 . q 2 > 0
    d) q 1 . q 2 < 0 e) q 1 >0, q 2 < 0

08-(UEPG-PR) The electrostatic interaction between two electric charges q 1 and q 2 , separated from each other by a distance r, is F 1 . The charge q 2 is removed and, at a distance 2r from the charge q 1 , a charge q 3 is placed whose intensity is one third of q 2 . In this new configuration, the electrostatic interaction between q 1 and q 3 is – F 2 . Based on this data, mark the correct statement.

(01) The charges q1 and q2 have opposite signs.

(02) The charges q 2 and q 3 have opposite signs.

(04) The charges q 1 and q 3 have the same sign.

(08) The force F 2 is repulsive and the force F 1 is attractive.

(16) The intensity of F 2 = F 1 /12

09- (UERJ-RJ) Let f be the repulsive force between two particles with the same charge q, separated by a distance r. Thus, which of the two figures below best illustrates the repulsive forces between two particles with charges 2q and 3q, separated by the same distance r?

10-(PUC-RJ) Two charged spheres, 1 m apart, attract each other with a force of 720 N. If one sphere has twice the charge of the second, what is the charge of the two spheres? (Consider k = 9 . 10 9 Nm 2 /C 2 )

11-(FGV-SP) With ka being the electrostatic constant and G the universal gravitational constant, a system of two identical bodies, of

 

same mass M and charges of the same intensity +Q, will be subject to a zero resultant force when the ratio M/Q is equal to

  1. a) k/G. b) G/k. c) √(k/G).
    d) √(G/k).e) (k/G)2 .

12-(FUVEST-SP) At a distance d from each other, there are two identical metal spheres, of negligible dimensions, with charges -Q and +9Q. They are brought into contact and then placed at a distance 2d. The ratio between the magnitudes of the forces acting after contact and before contact is

  1. a) 2/3 b) 4/9 c) 1
    d) 9/2 e) 4

13-(UFPE) The following graph represents the force F between two positive point charges of the same value, separated by

distance r. Consider K=9.10 9 Nm 2 C 2 and determine the value of the charges, in units of 10 -7 C.

  1. a) 1.0 b) 2.0 c) 3.0
    d) 4.0 e) 5.0

14-(UFRGS) An electric charge of +5.10-5 C is uniformly deposited on a small non-conducting sphere. A particle with a charge of -3.10-6 C , placed 30 cm from the sphere, experiences an attractive force of module 15 N. Another particle, with a charge of -6.10-6 C , placed 60 cm from the sphere, will experience an attractive force of module, in N:

  1. a) 3.8 b) 7.5 c) 15.0
    d) 30.0 e) 60.0

15-(FATEC-SP) Two small spheres are initially electrically neutral. From one of the spheres 5.0 × 10 14 are removed.

electrons that are transferred to the other sphere. After this operation, the two spheres are separated by 8.0 cm, in a vacuum

Data: elementary charge e = 1.6 × 10 -19 C — electrostatic constant in vacuum k o = 9.0 × 10 9 N.m 2 /C 2

The electrical interaction force between the spheres will be

  1. a) attraction and intensity 7.2 × 105 b) attraction and intensity 9.0 × 10 3 N.
    c) attraction and intensity 6.4 × 10 3 N. d) repulsion and intensity 7.2 × 10 3 N. e) repulsion and intensity 9.0 × 10 3 N.

16- (UFGO) Charges of the same value Q, but of alternating signs, are placed at four vertices of a regular pentagon,

as shown in the figure. At the 5th and last vertex of the pentagon, a test charge q0 > 0 is placed, which will be under the action of all the others. Which of the vectors , , , or represents the resultant of the actions of the charges + Q and – Q on q0?

  1. a)b)c)
    d) d)
    zero resultant

17- (UNESP-SP) Consider an experiment in which three point charges of equal magnitude are aligned and equally spaced, that charges A and C are fixed, and that the signs of charges A, B and C obey one of the following three configurations:

Consider, further, that you want load B to be loose and in balance. To this end, from the configurations presented, you can use

  1. a) only 1.
    b) only 2.
    c) only 3.
    d) both 1 and 3.
    e) both 1 and 2.

18-(PUCCAMP-SP) At the abscissa points x=2 and x=5 the charges Q and 4Q are fixed, respectively, as shown in the diagram below.

next: A third charge –Q, will be in equilibrium, under the action only of the electrical forces exerted by Q and 4Q, when placed at the abscissa point equal to:

  1. a) 0 b) 1 c) 3
    d) 4 e) 6

19-(UFC-CE) A particle with positive charge +q is fixed at a point, attracting another particle with negative charge -q and mass m, which moves in a circular path of radius R, around the positive charge, with a constant velocity (see the figure below). Consider that there is no form of energy dissipation, so that conservation of mechanical energy is observed in the system of charges. Neglect any effect of gravity. The electrostatic constant is equal to k.

  1. a) Determine the speed v at which the negative charge moves around the positive charge.
  2. b) Determine the period of circular motion of the negative charge around the positive charge.

20-(UNESP-SP) Three small spheres are electrically charged with charges q 1 , q 2 and q 3 and aligned on a frictionless horizontal plane (in a vacuum), as shown in the figure.

In this situation they are in equilibrium. The charge of the sphere q2 is positive and is 2.7.10 -4 C.

Requested:

  1. a) Determine the signs of the charges q1and q  Justify.
  2. b) Calculate the values ​​of the charges q1and q 3 .
  3. c) If the positions of q1and q 3 are fixed , what will be the type of equilibrium (stable,
    unstable or indifferent) of the sphere with charge q 2 ?

21-(UFRS-RS) Three identical point electric charges, Q 1 , Q 2 and Q 3 , are kept fixed in their positions on a straight line,

as shown in the following figure. Knowing that the magnitude of the electric force exerted by Q 1 on Q 2 is 4.0.10 -5 N, what is the magnitude of the resulting electric force on Q 2 ?

  1. a) 4.0.10-5
    b) 8.0.10 -5 N. c) 1.2.10 -4 N.
    d) 1.6.10 -4 N. e) 2.0.10 -4 N.

22-(UFRS-RS) The following figure represents two positive point electric charges, +q and +4q, kept fixed in their

positions. In order for the resulting electrostatic force on a third point charge to be zero, this charge must be placed at the point

  1. a) A.
    b) B. c) C. d) D.
    e) E.

23-(UFMG-MG) Two small insulating spheres – I and II -, electrically charged with charges of opposite signs, are fixed in the positions represented in this figure:

The charge of sphere I is positive and its magnitude is greater than that of sphere II.

Guilherme positions a positive point charge, of negligible weight, along the line that joins these two spheres, so that it is in balance.

Considering this information, it is CORRECT to state that the point that best represents the equilibrium position of the point load, in the situation described, is the

  1. a) R.
    b) P. c) S.
    d) Q.

24-(FUVEST-SP) Three objects with identical electric charges are aligned as shown in the figure. Object C exerts a force on B equal to 3.0.10 -6 N. The electric force resulting from the effects of A and C on B is:

  1. a) 2.0.10-6
    b) 6.0.10 -6 N. c) 12.10 -6 N.
    d) 24.10 -6 N. e) 30.10 -6 N.

25-(FUVESP-SP) Two equal insulating bars, A and B, placed on a table, have at their ends spheres with electric charges of equal modules and opposite signs. Bar A is fixed, but bar B can rotate freely around its center O, which remains fixed.
In situations I and II, bar B was placed in equilibrium, in opposite positions. For each of these two situations, the equilibrium of bar B can be considered to be, respectively,

  1. a) indifferent and unstable.
    b) unstable and unstable. c) stable and indifferent.
    d) stable and stable. e) stable and unstable.

26-(PUC-RJ) Before the first trip to the Moon, several NASA scientists were concerned about the possibility of the lunar spacecraft encountering a cloud of dust charged over the surface of the Moon.

Suppose the Moon has a negative charge. Then it would exert a repulsive force on the negatively charged dust particles. On the other hand, the Moon’s gravitational force would exert an attractive force on these dust particles.

Suppose that 2 km from the surface of the Moon the gravitational attraction exactly balances the electrical repulsion, so that the dust particles float.

If the same dust cloud were 5 km from the surface of the Moon:

  1. a) gravity would still balance the electrostatic force, but only if the dust lost charge.
  2. b) gravity would still balance the electrostatic force, and the dust particles would also float.
  3. c) gravity would still balance the electrostatic force, but only if the dust lost mass.
  4. d) gravity would be greater than the electrostatic force, and the dust would fall.
  5. e) gravity would be less than the electrostatic force, and the dust would be lost in space.

27-(UFMG-MG)) Observe the figure that represents an equilateral triangle. In this triangle, three point electric charges of the same absolute value are at its vertices. The vector that best represents the resulting electric force on the charge at vertex 1 is

28-(UFMG-MG) The figure shows three particles with identical charges such that│q 1 │such that│q 1 │=│q 2 │=│q 3 │=1μC,

occupying the vertices of an equilateral triangle ABC with sides of 3 m. Determine the intensity, direction and sense of the resulting electric force acting on the charge located at vertex A. Consider K = 9.10 9 N.m 2 /C 2

29-(UNIFESP-SP) The figure shows two small spheres of the same mass, m=0.048kg, electrified with charges of the same sign, repelling each other, in the air. They are suspended by very light, inextensible insulating wires of the same length L=0.090m. It can be seen that, over time, these spheres come closer together and the wires tend to become vertical.

  1. a) What causes these spheres to come closer together? During this approach, are the angles that the wires form with the vertical always equal or can they become different from each other?
  2. b) Suppose that, in the situation in the figure, the angle α is such that senα=0.60; cosα=0.80 and tgα=0.75 and the spheres have equal charges. What is, in this case, the electric charge of each sphere? (Assume g=10 m/s2and K=9.0.10 9 m 2 /C 2 ).

30-(UFPE) Four point electric charges, with intensities Q and q, are fixed at the vertices of a square, as shown in the figure. Determine the ratio Q/q so that the force on each of the charges Q is zero.

  1. a) -√2/4
    b) -√2/2 c) -√2
    d) -2√2 e) -4√2

31-(UFRJ-RJ) Two charges, q and
-q, are kept fixed at a distance d from each other. A third charge q o
is placed at the midpoint between the first two, as illustrated in figure A.
In this situation, the magnitude of the resulting electrostatic force on charge q o
is F A .

The charge q o is then
moved away from this position along the perpendicular bisector between the other two until it reaches
point P, where it is fixed, as illustrated in figure B. Now, the three charges are
at the vertices of an equilateral triangle. In this situation, the magnitude of the
resulting electrostatic force on the charge q o is F B .

Calculate the ratio F A /F B .

32-(PUC-RJ-09) Two
identical spherical metallic objects, containing electric charges of 1 C and 5 C, are placed in contact and then separated at a distance of 3 m. Considering the Coulomb Constant k = 9.10 9 N m 2 /C 2 , we can
say that the force acting between the charges after contact is:

  1. a) attractive and has a magnitude of 3.109
    b) attractive and has a magnitude of 9.109 N. c) repulsive
    and has a magnitude of 3.10 9 N.
  2. d) repulsive and has a magnitude of 9.109
    e) zero.

33- (PUC-RJ-09) Two identical spheres, charged with
charges Q = 30 μC, are suspended from the same point by two

insulating wires of the same
length as shown in the figure.

In equilibrium, the angle
θ formed by the two insulating wires with the vertical is 45°. Knowing that the
mass of each sphere is 1 kg, that the Coulomb Constant is k = 9.10 9
N m 2 /C 2 and that the acceleration of gravity is g = 10 m/s 2 ,
determine the distance between the two spheres when in equilibrium.

Remember that μ = 10 -6 .

  1. a) 1.0 mb) 0.9 mc) 0.8 md) 0.7 m) 0.6 m

34-(UNICAMP-SP-09) The fact that
atomic nuclei are formed by protons and neutrons raises the question of
cohesion

nuclear, since
protons, which have a positive charge q = 1.6.10 -19 C , repel each other
through the electrostatic force. In 1935, H. Yukawa proposed a theory for the
strong nuclear force, which acts at short distances and holds nuclei together.

  1. a) Consider that the magnitude of the
    strong nuclear force between two protonsFNis equal to twenty times the
    magnitude of the electrostatic force between them F E , that is, FN =
    20 F E . The magnitude of the electrostatic force between two protons
    separated by a distance d is given by F E = K(q 2 /d 2 ),
    where K = 9.0.10 9 Nm 2 /C 2 . Obtain the magnitude of the
    strong nuclear force FN between the two protons, when separated by
    a distance = 1.6.10 -15 m, which is a typical distance between protons in the
  2. b) Nuclear forces are
    much greater than the forces that accelerate particles in large accelerators
    like the LHC. In a

first stage of
accelerator, charged particles move under the action of an electric field
applied in the direction of movement. Knowing that an electric field of module

E = 2.0.10 5 N/C
acts on a proton in an accelerator, calculate the electrostatic force acting on the
proton.

35-(UNIFESP-SP-09) Consider
the following “unit” of measurement: the intensity of the electric force between
two charges q, when separated by a distance d, is F. Suppose then
that a charge q 1 = q is placed in front of two other charges, q 2
= 3q and

q 3 = 4q, according to the
arrangement shown in the figure. The intensity of the resulting electric force on
the charge q 1 , due to the charges q 2 and q 3 , will be

  1. a) 2F. b) 3F. c) 4F. d) 5F. e) 9F.

36-(FGV-SP-010)
Rigidly positioned on the vertices of a cube with an edge of 1 m, there are eight positive electric charges

of the same module. If k
is the value of the electrostatic constant of the medium surrounding the charges, the
resulting force on a ninth electric charge, also positive and with the same module as
the first eight, left at rest in the center of the cube, will have an intensity:

  1. a) zero. b) kQ2.
    c) kQ 2 . d)
    Q 4 . e) 8k.Q 2 .

37- (PUC-RJ-010) Three
electric charges are in equilibrium along a straight line so that a
positive charge (+Q) is

in the center and two
negative charges (–q) and (–q) are placed on opposite sides and at the same distance (d)
from the charge Q. If we bring the two negative charges closer to d/2 distance from the
positive charge, how much do we have to increase the value of Q (the final value will be
Q’), so that the balance of forces is maintained?

  1. a) Q’ = 1 Q b)
    Q’ = 2 Q c) Q’ = 4 Q d) Q’ = Q / 2 e)
    Q’ = Q / 4

38-(PUC-RJ-010) What
happens to the force between two electric charges (+Q) and (–q) placed at a
distance (d) if we change the charge (+ Q) by (+ 4Q), the charge (–q) by (+3q) and the
distance (d) by (2d)?

  1. a) It maintains its module and becomes
  2. b) It maintains its module and becomes
  3. c) Its module is doubled and
    it becomes repulsive.
  4. d) Its module is tripled
    and it becomes repulsive.
  5. e) Its module is tripled
    and becomes attractive.

39-(ITA-SP-010)

Consider a balance with
unequal arms, of lengths ℓ 1 and ℓ 2 ,
as shown in the figure. On the left side there is a load of
magnitude Q and negligible mass hanging, located at a certain distance from another load,
q. On the right side there is a mass m on a plate of negligible mass.
Considering the charges as point charges and the mass of the plate on the right negligible,
the value of q to balance the mass m is given by

40-(UFU-MG-011)

Two charges +q are fixed
to an insulating rod and are separated by a distance 2d. Another
insulating rod is fixed perpendicular to the first one at the midpoint between these two
charges. The system is placed so that this last rod points upwards
. A third small sphere of mass m and charge +3q with holes is passed
through the vertical rod so that it can slide without friction along it, as
shown in the following figure. The equilibrium distance of the mass m along the
vertical axis is z.

Based on this information,
the value of the mass m in question can be written as a function of d, z, g and k, where g
is the gravitational acceleration and k is the electrostatic constant.

The expression for the mass m
will be given by:

41-(MACKENZIE-SP-011)

Two point electric charges, when separated by
a distance d, repel each other with a

force of intensity F. By moving these charges apart, so as
to double the distance between them, the intensity of the repulsion force will be
equal to

a)
√2F b) 2F c) F/2 d)
F/4 e) F/8

42-(IME-RJ-011)

A positive charge is attached
to a flat mirror. The mirror approaches, without rotation, at a
constant speed parallel to the x axis, a negative charge hanging from the ceiling by an
inextensible string. At the instant illustrated in the figure, the charge

negative charge moves in the
opposite direction to the positive charge, with the same scalar speed as the mirror.
Determine, for this instant:

  1. a) the x and y components of the
    velocity vector of the image of the negative charge reflected in the mirror;
  2. b) the tangential
    and centripetal accelerations of the negative charge;

Data:

  • angle between the x-axis and
    the mirror: α;
  • angle between the x-axis and the
    line segment formed by the charges: β;
  • module of
    electric charges; Q;
  • difference between the
    y coordinates of the charges: d;
  • wire length: L;
  • mirror speed
    : V;
  • mass of negative charge: m;
  • electric constant of the medium:
    k

43-Interdisciplinary questions:

The world population today is around 7 billion people and
is expected to reach 10 billion by the middle of the 21st century. According to the scenarios
chosen for energy demand, global primary energy consumption
could reach two to three times the current consumption.

In 1990, primary energy consumption per inhabitant per year
was 5.1 TOE in industrialized countries and only 10% in developing countries
.

1TOE (Tonne of Oil Equivalent) is the unit of measurement
for energy consumption and is equivalent to 10×109 cal.

1BEP (Barrel of Oil Equivalent), variation of TEP,
equivalent to 1.45×10 9 cal.

Or even that:

An energy source capable of substantially meeting
this demand is nuclear energy, through nuclear FISSION and FUSION.
Let’s see:

This phenomenon of electrical repulsion constitutes one of the Principles
of Electrostatics, whose force module can be determined by Coulomb’s Law
F=k.|Q 1 |. |Q 2 |./d 2 .
.

The extent to which this force acts is related to the charge, the medium and the
distance between the centers of the nuclei of the particles that are interacting.
If the nuclei were able to get close enough, with the
strong interaction prevailing, the phenomenon of nuclear fusion would occur.

The control of this nuclear fusion continues to be the subject of research.
This fusion is the process in which two nuclei of light atoms (for example,
hydrogen – whose nucleus consists of 1 proton with an
elementary electric charge of 1.6.10 -19 C ) combine, or
fuse, forming a heavier element. The nuclei, then,
positively charged, must come close enough to each other, that is, overcome
the electrostatic repulsion force between them.

For fusion reactions to be produced at a
suitable rate, extremely high temperatures are required, in the order of 100 million
degrees Celsius, and the pressure causes the hydrogen atoms
to be compressed.

The centers of their nuclei must be within 1.10 -15 meters of each other for fusion to occur.
At this stage, they turn into plasma. A special feature of this state is that matter reacts to electrical and magnetic influences.

As modest as the hopes of achieving fusion may be,
it is estimated that it will still take 30 years to have a commercial reactor and, however
expensive the research may be, the advantages of fusion are seductive.

According to all calculations, future nuclear fusion plants
will be able to extract from 1 cubic meter of water an amount of energy equal to that of 2 thousand barrels of oil.

  1. a) According to expectations, after the installation of a
    commercial reactor with a daily capacity of 100 cubic meters of water for nuclear fusion, what would be its daily production, corresponding to
    Barrels of Oil Equivalents? (assume that 1 barrel [159L] of oil of
    average composition contains 1.5×106kcal)
  2. b) Determine the value of the repulsive electric force between two
    hydrogen nuclei when placed in a vacuum and separated by the distance necessary for nuclear fusion to occur.