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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

A 2.0 × 10-3 V/m electric field creates a 3.5 × 1017 electrons/s current in a 1.0-mm-diameter aluminum wire. What are(a) The drift speed(b) The mean time between collisions for electrons in this
The electron drift speed is 2.0 × 10-4 m/s in a metal with a mean time between collisions of 5.0 × 10-14 s. What is the electric field strength?
1.0 × 1016 electrons flow through a cross section of a silver wire in 320 μs with a drift speed of 8.0 × 10-4 m/s. What is the diameter of the wire?
1.0 × 1020 electrons flow through a cross section of a 2.0 mm-diameter iron wire in 5.0 s. What is the electron drift speed?
Estimate the electric fields E1and E2at points 1 and 2 in Figure Q26.4. Don€™t forget that E is a vector. ov OV 10 V 20 V 30 V 40 V 2 m 0m 4 m FIGURE Q26.4
a. Suppose that E = 0 V/m throughout some region of space. Can you conclude that V = 0 V in this region? Explain.b. Suppose that V = 0 V throughout some region of space. Can you conclude that E = 0
Figure Q26.2 shows the electric potential as a function of x. Draw a graph of Exversus x in this same region of space. V (V) 100 x (m) FIGURE Q26.2
Figure Q26.1 shows the x-component of E as a function of x.Draw a graph of V versus x in this same region of space. Let V = 0 V at x = 0 m and include an appropriate vertical scale. E, (V/m) 100 - x
FIGURE P23.44 shows a thin rod of length L with total charge Q. Find an expression for the electric field E at point P. Give your answer in component form. P х FIGURE P23.44 + + + + + + + + +
FIGURE P23.43 shows a thin rod of length L with total charge Q. a. Find an expression for the electric field strength at point P on the axis of the rod at distance r from the center.b. Verify that
FIGURE P23.42 is a cross section of two infinite lines of charge that extend out of the page. The linear charge densities are ±Î».Find an expression for the electric field strength
FIGURE P23.41 is a cross section of two infinite lines of charge that extend out of the page. Both have linear charge density Î».Find an expression for the electric field strength E at
Derive Equation 23.11 for the field Edipole in the plane that bisects an electric dipole. y Lines of charge coming out of the page FIGURE P23.41
Charges -q and +2q in FIGURE P23.39 are located at x = ±a. Determine the electric field at points 1 to 4. Write each field in component form. y 2a +1 2 3 х -2a +29 2a -a- -2a +4 FIGURE P23.39
FIGURE P23.38 shows three charges at the corners of a square. Write the electric field at point P in component form. -Q FIGURE P23.38 PO-
What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.37? Give your answer (a) In component form. (b) As a magnitude and angle measured cw or
What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.36? Give your answer (a) In component form. (b) As a magnitude and angle measured cw or
What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.35? Give your answer(a) In component form.(b) As a magnitude and angle measured cw or ccw
An ammonia molecule (NH3) has a permanent electric dipole moment 5.0 × 10-30 C m. A proton is 2.0 nm from the molecule in the plane that bisects the dipole. What is the electric force of the
A point charge Q is distance r from a dipole consisting of charges ±q separated by distance s. The dipole is initially oriented so that Q is in the plane bisecting the dipole. Immediately after the
The permanent electric dipole moment of the water molecule (H2O) is 6.2 × 10-30 C m. What is the maximum possible torque on a water molecule in a 5.0 × 108 N/C electric field?
A 1.0-μm-diameter oil droplet (density 900 kg/m3) is negatively charged with the addition of 25 extra electrons. It is released from rest 2.0 mm from a very wide plane of positive charge, after
An electron in a vacuum chamber is fired with a speed of 8300 km/s toward a large, uniformly charged plate 75 cm away.The electron reaches a closest distance of 15 cm before being repelled. What is
The surface charge density on an infinite charged plane is -2.0 × 10-6 C/m2. A proton is shot straight away from the plane at 2.0 × 106 m/s. How far does the proton travel before reaching its
An electron traveling parallel to a uniform electric field increases its speed from 2.0 × 107 m/s to 4.0 × 107 m/s over a distance of 1.2 cm. What is the electric field strength?
Honeybees acquire a charge while flying due to friction with the air. A 100 mg bee with a charge of +23 pC experiences an electric force in the earth’s electric field, which is typically 100 N/C,
A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder?
A thin rod of length L and total charge Q has the nonuniform linear charge distribution λ(x) = λ0 x/L, where x is measured from the rod’s left end.a. What is λ0 in terms of Q and L?b. What is
Two 2.0-mm-diameter beads, C and D, are 10 mm apart, measured between their centers. Bead C has mass 1.0 g and charge 2.0 nC. Bead D has mass 2.0 g and charge -1.0 nC. If the beads are released from
Bead A has a mass of 15 g and a charge of -5.0 nC. Bead B has a mass of 25 g and a charge of -10.0 nC. The beads are held 12 cm apart (measured between their centers) and released. What maximum speed
A proton and an alpha particle (q = +2e, m = 4 u) are fired directly toward each other from far away, each with an initial speed of 0.010c. What is their distance of closest approach, as measured
An electric dipole consists of 1.0 g spheres charged to ±2.0 nC at the ends of a 10-cm-long massless rod. The dipole rotates on a frictionless pivot at its center. The dipole is held perpendicular
You are given the equation(s) used to solve a problem. For each of these,a. Write a realistic problem for which this is the correct equation(s).b. Finish the solution of the problem. (9.0 × 10°
You are given the equation(s) used to solve a problem. For each of these,a. Write a realistic problem for which this is the correct equation(s).b. Finish the solution of the problem. (1.67 X 10-27
You are given the equation(s) used to solve a problem. For each of these,a. Write a realistic problem for which this is the correct equation(s).b. Finish the solution of the problem. (9.0 × 10°
The wire in FIGURE P25.73 has linear charge density Î». What is the electric potential at the center of the semicircle? 2R 2R FIGURE P25.73
A disk with a hole has inner radius Rin and outer radius Rout.The disk is uniformly charged with total charge Q. Find an expression for the on-axis electric potential at distance z from the center of
FIGURE P25.71 shows a thin rod with charge Q that has been bent into a semicircle of radius R. Find an expression for the electric potential at the center. Center Charge Q
FIGURE P25.69 shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance z away from the center of rod on the line that bisects the rod. -Point on bisecting
FIGURE P25.69 shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod. -Point on bisecting line
The arrangement of charges shown in FIGURE P25.68 is called a linear electric quadrupole. The positive charges are located at y = ±s. Notice that the net charge is zero. Find an expression for
Two positive point charges q are located on the y-axis at y = ±1/2s.a. Find an expression for the potential along the x-axis.b. Draw a graph of V versus x for - ∞ < x < ∞ . For comparison,
FIGURE P25.66 shows two uniformly charged spheres. What is the potential difference between points a and b? Which point is at the higher potential? 100 cm 100 nC 25 nC a b e 10 cm FIGURE P25.66 60 cm
A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm.a. How
Two spherical drops of mercury each have a charge of 0.10 nC and a potential of 300 V at the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?
a. Find an algebraic expression for the electric field strength E0 at the surface of a charged sphere in terms of the sphere’s potential V0 and radius R.b. What is the electric field strength at
Electrodes of area A are spaced distance d apart to form a parallel-plate capacitor. The electrodes are charged to ±q.a. What is the infinitesimal increase in electric potential energy dU if an
Two 10-cm-diameter electrodes 0.50 cm apart form a parallelplate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. What are the charge on each electrode, the
Two 10-cm-diameter electrodes 0.50 cm apart form a parallelplate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. After a long time, the capacitor is
One form of nuclear radiation, beta decay, occurs when a neutron changes into a proton, an electron, and a neutral particle called a neutrino: n → p+ + e- + ν where ν is the symbol for a
In the form of radioactive decay known as alpha decay, an unstable nucleus emits a helium-atom nucleus, which is called an alpha particle. An alpha particle contains two protons and two neutrons,
A proton is fired from far away toward the nucleus of a mercury atom. Mercury is element number 80, and the diameter of the nucleus is 14.0 fm. If the proton is fired at a speed of 4.0 × 107 m/s,
A proton is fired from far away toward the nucleus of an iron atom. Iron is element number 26, and the diameter of the nucleus is 9.0 fm. What initial speed does the proton need to just reach the
Your lab assignment for the week is to measure the amount of charge on the 6.0-cm-diameter metal sphere of a Van de Graaff generator. To do so, you’re going to use a spring with spring constant
A 2.0-mm-diameter glass bead is positively charged. The potential difference between a point 2.0 mm from the bead and a point 4.0 mm from the bead is 500 V. What is the charge on the bead?
Three electrons form an equilateral triangle 1.0 nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges?
An electric dipole has dipole moment p. If r >> s, where s is the separation between the charges, show that the electric potential of the dipole can be writtenwhere r is the distance from the
What is the escape speed of an electron launched from the surface of a 1.0-cm-diameter glass sphere that has been charged to 10 nC?
Two 2.0 g plastic buttons each with +50 nC of charge are placed on a frictionless surface 2.0 cm (measured between centers) on either side of a 5.0 g button charged to +250 nC. All three are released
A group of science and engineering students embarks on a quest to make an electrostatic projectile launcher. For their first trial, a horizontal, frictionless surface is positioned next to the
A room with 3.0-m-high ceilings has a metal plate on the floor with V = 0 V and a separate metal plate on the ceiling. A 1.0 g glass ball charged to +4.9 nC is shot straight up at 5.0 m/s. How high
The electron gun in an old TV picture tube accelerates electrons between two parallel plates 1.2 cm apart with a 25 kV potential difference between them. The electrons enter through a small hole in
A proton moves along the x-axis where some arrangement of charges has produced the potential V(x) = V0sin(2πx/λ, where V0 = 5000 V and λ = 1.0 mm.a. What minimum speed must the proton have at x =
An arrangement of source charges produces the electric potential V = 5000x2 along the x-axis, where V is in volts and x is in meters.What is the maximum speed of a 1.0 g, 10 nC charged particle that
Living cells “pump” singly ionized sodium ions, Na+, from the inside of the cell to the outside to maintain a membrane potential ΔVmembrane = Vin - Vout = - 70 mV. It is called pumping
A proton€™s speed as it passes point A is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton€™s speed at point B? BI -10 V 30 V 10 V FIGURE P25.43
The four 1.0 g spheres shown in FIGURE P25.42 are released simultaneously and allowed to move away from each other. What is the speed of each sphere when they are very far apart? 10 nC 10 nC 1.0 cm
Two small metal cubes with masses 2.0 g and 4.0 g are tied together by a 5.0-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2.0 μC.a. What is the energy of
A -3.0 nC charge is on the x-axis at x = -9 cm and a +4.0 nC charge is on the x-axis at x = 16 cm. At what point or points on the y-axis is the electric potential zero?
A +3.0 nC charge is at x = 0 cm and a -1.0 nC charge is at x = 4 cm. At what point or points on the x-axis is the electric potential zero?
A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis.a. What is the electric potential at the point on the x-axis where the electric field is zero?b. What is the
Two point charges 2.0 cm apart have an electric potential energy -180 μJ. The total charge is 30 nC. What are the two charges?
A 5.0-cm-diameter metal ball has a surface charge density of 10 μC/m2. How much work is required to remove one electron from this ball?
The two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot? ++++++++ FIGURE EX25.35
Two point charges qaand qbare located on the x-axis at x = a and x = b. FIGURE EX25.34 is a graph of V, the electric potential. a. What are the signs of qa and qb?b. What is the ratio |qa/qb|?c.
A -2.0 nC charge and a +2.0 nC charge are located on the x-axis at x = -1.0 cm and x = +1.0 cm, respectively.a. Other than at infinity, is there a position or positions on the x-axis where the
The electric potential at the dot in FIGURE EX25.32 is 3140 V.What is charge q? -5.0 nC 2.0 cm 4.0 cmi 5.0 nC FIGURE EX25.32
What is the electric potential at the point indicated with the dot in FIGURE EX25.31? 1.0 nC 3.0 cm,' 3.0 cm 3.0 cm -2.0 nC -2.0 nC FIGURE EX25.31
What is the electric potential at the point indicated with the dot in FIGURE EX25.30? 2.0 nC -1.0 nC 3.0 cm 14.0 cm +, 2.0 nC FIGURE EX25.30
In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm.a. What is the electric potential of the proton at the position of the electron?b. What is the
A 1.0-mm-diameter ball bearing has 2.0 × 109 excess electrons.What is the ball bearing’s potential?
a. What is the electric potential at points A, B, and C in FIGURE EX25.27?b. What are the potential differences Î”VAB= VB- VAand Î”VCB= VB- VC? 2,0 cm, 1.0 cm в +, 2.0 nC
In FIGURE EX25.26, a proton is fired with a speed of 200,000 m/s from the midpoint of the capacitor toward the positive plate. a. Show that this is insufficient speed to reach the positive plate.b.
Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is 5.0 × 105 V/m.a. What is the voltage across the capacitor?b. An electron is
Two 2.00 cm × 2.00 cm plates that form a parallel-plate capacitor are charged to ±0.708 nC. What are the electric field strength inside and the potential difference across the capacitor if the
A 3.0-cm-diameter parallel-plate capacitor has a 2.0 mm spacing. The electric field strength inside the capacitor is 1.0 × 105 V/m.a. What is the potential difference across the capacitor?b. How
a. What is the potential of an ordinary AA or AAA battery?b. An AA battery is connected to a parallel-plate capacitor having 4.0 cm × 4.0 cm plates spaced 1.0 mm apart. How much charge does the
Show that 1 V/m = 1 N/C.
Physicists often use a different unit of energy, the electron volt, when dealing with energies at the atomic level. One electron volt, abbreviated eV, is defined as the amount of kinetic energy
A student wants to make a very small particle accelerator using a 9.0 V battery. What speed will(a) A proton(b) An electron have after being accelerated from rest through the 9.0 V potential
In proton-beam therapy, a high-energy beam of protons is fired at a tumor. As the protons stop in the tumor, their kinetic energy breaks apart the tumor’s DNA, thus killing the tumor cells. For one
Through what potential difference must a proton be accelerated to reach the speed it would have by falling 100 m in vacuum?
An electron with an initial speed of 500,000 m/s is brought to rest by an electric field.a. Did the electron move into a region of higher potential or lower potential?b. What was the potential
A proton with an initial speed of 800,000 m/s is brought to rest by an electric field.a. Did the proton move into a region of higher potential or lower potential?b. What was the potential difference
What potential difference is needed to accelerate a He+ ion (charge +e, mass 4 u) from rest to a speed of 2.0 × 106 m/s?
What potential difference is needed to accelerate an electron from rest to a speed of 2.0 × 106 m/s?
What is the speed of an electron that has been accelerated from rest through a potential difference of 1000 V?
Reproduce FIGURE Q25.12 on your paper. Then draw a dot (or dots) on the figure to show the position (or positions) at which the electric potential is zero. | FIGURE Q25.12
What is the speed of a proton that has been accelerated from rest through a potential difference of -1000 V?
FIGURE Q25.11 shows three points near two point charges. The charges have equal magnitudes. For each part, rank in order, from most positive to most negative, the potentials Vato Vc.a.b. +, +) b a

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