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Question & Answer:

  • (a) Find to three significant digits the charge and the mass of an ionized hydrogen atom, represented as H+. Suggestion: Begin by looking up the mass of a neutral atom on the periodic table of the elements.
    (b) Find the charge and the mass of Na+, a singly ionized sodium atom.
    (c) Find the charge and the average mass of a chloride ion Cl− that joins with the Na+ to make one molecule of table salt.
    (d) Find the charge and the mass of Ca++ = Ca2+, a doubly ionized calcium atom.
    (e) You can model the center of an ammonia molecule as an N3− ion. Find its charge and mass.
    (f) The plasma in a hot star contains quadruply ionized nitrogen atoms, N4+. Find their charge and mass.
    (g) Find the charge and the mass of the nucleus of a nitrogen atom.
    (h) Find the charge and the mass of the molecular ion H2O−.
  • (a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 10.0 g. Silver has 47 electrons per atom, and its molar mass is 107.87 g/mol.
    (b) Electrons are added to the pin until the net negative charge is 1.00 mC. How many electrons are added for every 109 electrons already present?
  • The Nobel laureate Richard Feynman once said that if two persons stood at arm’s length from each other and each person had 1% more electrons than protons, the force of repulsion between them would be enough to lift a “weight’’ equal to that of the entire Earth. Carry out an order-of-magnitude calculation to substantiate this assertion.
  • Two protons in an atomic nucleus are typically separated by a distance of 2 x 10−15 m. The electric repulsion force between the protons is huge, but the attractive nuclear force is even stronger and keeps the nucleus from bursting apart. What is the magnitude of the electric force between two protons separated by 2.00 x 10−15 m?
  • (a) Two protons in a molecule are separated by 3.80 x 10−10 m. Find the electric force exerted by one proton on the other.
    (b) How does the magnitude of this force compare to the magnitude of the gravitational force between the two protons?
    (c) What If? What must be the charge-to-mass ratio of a particle if the magnitude of the gravitational force between two of these particles equals the magnitude of electric force between them?
  • Two small silver spheres, each with a mass of 10.0 g, are separated by 1.00 m. Calculate the fraction of the electrons in one sphere that must be transferred to the other in order to produce an attractive force of 1.00 x 104 N (about 1 ton) between the spheres. (The number of electrons per atom of silver is 47, and the number of atoms per gram is Avogadro’s number divided by the molar mass of silver, 107.87 g/mol.)
  • Three point charges are located at the corners of an equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-μC charge.

  • Suppose that 1.00 g of hydrogen is separated into electrons and protons. Suppose also that the protons are placed at the Earth’s North Pole and the electrons are placed at the South Pole. What is the resulting compressional force on the Earth?
  • Two identical conducting small spheres are placed with their centers 0.300m apart. One is given a charge of 12.0 nC and the other a charge of −18.0 nC.
    (a) Find the electric force exerted by one sphere on the other.
    (b) What If? The spheres are connected by a conducting wire. Find the electric force between the two after they have come to equilibrium.
  • Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x = d. As shown in Figure P23.10, a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium?

  • In the Bohr Theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is 0.529 x 10-10 m.
    (a) Find the electric force between the two.
    (b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron?
  • Two identical particles, each having charge #q, are fixed in space and separated by a distance d. A third point charge -Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between the two fixed charges (Fig. P23.12)
    (a) Show that if x is small compared with d, the motion of -Q will be simple harmonic along the perpendicular bisector. Determine the period of that motion.
    (b) How fast will the charge -Q be moving when it is at the midpoint between the two fixed charges, if initially it is released at a distance a << d from the midpoint?

  • What are the magnitude and direction of the electric field that will balance the weight of?
    (a) An electron and
    (b) A proton? (Use the data in Table 23.1.)
  • An object having a net charge of 24.0 *C is placed in a uniform electric field of 610 N/C directed vertically. What is the mass of this object if it “floats’’ in the field?
  • In Figure P23.15, determine the point (other than infinity) at which the electric field is zero.

  • An airplane is flying through a thundercloud at a height of 2 000 m. (This is a very dangerous thing to do because of updrafts, turbulence, and the possibility of electric discharge.) If a charge concentration of +40.0 C is above the plane at a height of 3 000 m within the cloud and a charge concentration of -40.0 C is at height 1 000 m, what is the electric field at the aircraft?
  • Two point charges are located on the x axis. The first is a charge +Q at x = - a. The second is an unknown charge located at x = + 3a. The net electric field these charges produce at the origin has a magnitude of 2keQ/a2. What are the two possible values of the unknown charge?
  • Three charges are at the corners of an equilateral triangle as shown in Figure P23.7.
    (a) Calculate the electric field at the position of the 2.00-μC charge due to the 7.00-μC and -4.00-μC charges.
    (b) Use your answer to part
    (a) To determine the force on the 2.00-μC charge.
  • Three point charges are arranged as shown in Figure P23.19.
    (a) Find the vector electric field that the 6.00-nC and "3.00-nC charges together create at the origin.
    (b) Find the vector force on the 5.00-nC charge.

  • Two 2.00-μC point charges are located on the x axis. One is at x = 1.00 m, and the other is at x = -1.00 m.
    (a) Determine the electric field on the y axis at y = 0.500 m.
    (b) Calculate the electric force on a -3.00-μC charge placed on the y axis at y = 0.500 m.