- (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
- (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
- 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
- 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
- (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
- 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
- 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
- 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
- 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
- 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)
- 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
- 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
- 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
- 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
- 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
- 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
- Four point charges are at the corners of a square of side a as shown in Figure P23.21.(a) Determine the magnitude and direction of the electric field at the location of charge q. (b) What is the
- Consider the electric dipole shown in Figure P23.22. Show that the electric field at a distant point on the +x axis is Ex ≈ 4keqa/x 3.
- Consider n equal positive point charges each of magnitude Q/n placed symmetrically around a circle of radius R. (a) Calculate the magnitude of the electric field at a point a distance x on the line
- Consider an infinite number of identical charges (each of charge q) placed along the x axis at distances a, 2a, 3a, 4a, . . . , from the origin. What is the electric field at the origin due to this
- A rod 14.0 cm long is uniformly charged and has a total charge of -22.0 μC. Determine the magnitude and direction of the electric field along the axis of the rod at a point 36.0 cm from its
- A continuous line of charge lies along the x axis, extending from x = + x0 to positive infinity. The line carries charge with a uniform linear charge density 3 0. What are the magnitude and direction
- A uniformly charged ring of radius 10.0 cm has a total charge of 75.0 μC. Find the electric field on the axis of the ring at (a) 1.00 cm, (b) 5.00 cm, (c) 30.0 cm, and (d) 100 cm from
- A line of charge starts at x = + x0 and extends to positive infinity. The linear charge density is A = A0x0/x. Determine the electric field at the origin.
- Show that the maximum magnitude Emax of the electric field along the axis of a uniformly charged ring occurs at x = a/√2 (see Fig. 23.18) and has the value Q/ (6√3πЄ0a2)
- A uniformly charged disk of radius 35.0 cm carries charge with a density of 7.90 & 10"3 C/m2. Calculate the electric field on the axis of the disk at (a) 5.00 cm, (b) 10.0 cm, (c) 50.0 cm, and
- Example 23.9 derives the exact expression for the electric field at a point on the axis of a uniformly charged disk. Consider a disk, of radius R = 3.00 cm, having a uniformly distributed charge of +
- The electric field along the axis of a uniformly charged disk of radius R and total charge Q was calculated in Example 23.9. Show that the electric field at distances x that are large compared with R
- A uniformly charged insulating rod of length 14.0 cm is bent into the shape of a semicircle as shown in Figure P23.33. The rod has a total charge of - 7.50 μC. Find the magnitude and direction of
- (a) Consider a uniformly charged thin-walled right circular cylindrical shell having total charge Q, radius R, and height h. Determine the electric field at a point a distance d from the right side
- A thin rod of length ℓ and uniform charge per unit length 3 lies along the x axis, as shown in Figure P23.35.(a) Show that the electric field at P, a distance y from the rod along its
- Three solid plastic cylinders all have radius 2.50 cm and length 6.00 cm. One (a) Carries charge with uniform density 15.0 nC/m2 everywhere on its surface. Another (b) Carries charge with the same
- Eight solid plastic cubes, each 3.00 cm on each edge, are glued together to form each one of the objects (i, ii, iii, and iv) shown in Figure P23.37.(a) Assuming each object carries charge with
- A positively charged disk has a uniform charge per unit area as described in Example 23.9. Sketch the electric field lines in a plane perpendicular to the plane of the disk passing through its center.
- A negatively charged rod of finite length carries charge with a uniform charge per unit length. Sketch the electric field lines in a plane containing the rod.
- Figure P23.40 shows the electric field lines for two point charges separated by a small distance.(a) Determine the ratio q1/q2.(b) What are the signs of q1 and q2?
- Three equal positive charges q are at the corners of an equilateral triangle of side a as shown in Figure P23.41.(a) Assume that the three charges together create an electric field. Sketch the field
- An electron and a proton are each placed at rest in an electric field of 520 N/C. Calculate the speed of each particle 48.0 ns after being released.
- A proton accelerates from rest in a uniform electric field of 640 N/C. At some later time, its speed is 1.20 x 106 m/s (non-relativistic, because v is much less than the speed of light). (a) Find
- A proton is projected in the positive x direction into a region of a uniform electric field E = - 6.00 x 105i N/C at t = 0. The proton travels 7.00 cm before coming to rest. Determine (a) The
- The electrons in a particle beam each have a kinetic energy K. What are the magnitude and direction of the electric field that will stop these electrons in a distance d?
- A positively charged bead having a mass of 1.00 g falls from rest in a vacuum from a height of 5.00 m in a uniform vertical electric field with a magnitude of 1.00 x 104 N/C. The bead hits the ground
- A proton moves at 4.50 x 105 m/s in the horizontal direction. It enters a uniform vertical electric field with a magnitude of 9.60 x 103 N/C. Ignoring any gravitational effects, find (a) The time
- Two horizontal metal plates, each 100 mm square, are aligned 10.0 mm apart, with one above the other. They are given equal-magnitude charges of opposite sign so that a uniform downward electric field
- Protons are projected with an initial speed vi = 9.55 x 103 m/s into a region where a uniform electric field E = -720j N/C is present, as shown in Figure P23.49. The protons are to hit a target that
- Two known charges, -12.0 μC and 45.0 μC, and an unknown charge are located on the x axis. The charge -12.0 μC is at the origin, and the charge 45.0 μC is at x = 15.0 cm. The
- A uniform electric field of magnitude 640 N/C exists between two parallel plates that are 4.00 cm apart. A proton is released from the positive plate at the same instant that an electron is released
- Three point charges are aligned along the x axis as shown in Figure P23.52. Find the electric field at(a) The position (2.00, 0) and(b) The position (0, 2.00).
- A researcher studying the properties of ions in the upper atmosphere wishes to construct an apparatus with the following characteristics: Using an electric field, a beam of ions, each having charge
- A small, 2.00-g plastic ball is suspended by a 20.0-cm-long string in a uniform electric field as shown in Figure P23.54. If the ball is in equilibrium when the string makes a 15.0° angle with
- A charged cork ball of mass 1.00 g is suspended on a light string in the presence of a uniform electric field as shown in Figure P23.55. When E = (3.00i + 5.00j) x 105 N/C, the ball is in equilibrium
- A charged cork ball of mass m is suspended on a light string in the presence of a uniform electric field as shown in Figure P23.55. When E = (Ai + Bj) N/C, where A and B are positive numbers, the
- Four identical point charges (q = +10.0 μC) are located on the corners of a rectangle as shown in Figure P23.57. The dimensions of the rectangle are L = 60.0 cm and W = 15.0 cm. Calculate the
- Inez is putting up decorations for her sister€™s quinceaÃ±era (fifteenth birthday party). She ties three light silk ribbons together to the top of a gateway and hangs a rubber
- Two identical metallic blocks resting on a frictionless horizontal surface are connected by a light metallic spring having a spring constant k as shown in Figure P23.59a and an unstretched length Li.
- Consider a regular polygon with 29 sides. The distance from the center to each vertex is a. identical charges q are placed at 28 vertices of the polygon. A single charge Q is placed at the center of
- Identical thin rods of length 2a carry equal charges +Q uniformly distributed along their lengths. The rods lie along the x axis with their centers separated by a distance b - 2a (Fig. P23.61). Show
- Two small spheres, each of mass 2.00 g, are suspended by light strings 10.0 cm in length (Fig. P23.62). A uniform electric field is applied in the x direction. The spheres have charges equal to -5.00
- A line of positive charge is formed into a semicircle of radius R = 60.0 cm as shown in Figure P23.63. The charge per unit length along the semicircle is described by the expression 3 = 30 cos +. The
- Three charges of equal magnitude q are fixed in position at the vertices of an equilateral triangle (Fig. P23.64). A fourth charge Q is free to move along the positive x axis under the influence of
- Two small spheres of mass m are suspended from strings of length ℓ that are connected at a common point. One sphere has charge Q; the other has charge 2Q. The strings make angles θ1 and
- Four identical particles, each having charge +q, are fixed at the corners of a square of side L. A fifth point charge -Q lies a distance z along the line perpendicular to the plane of the square and
- A 1.00-g cork ball with charge 2.00 *C is suspended vertically on a 0.500-m-long light string in the presence of a uniform, downward-directed electric field of magnitude E = 1.00 x 105 N/C. If the
- Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, non-conducting walls, the beads move, and at equilibrium they are a distance R
- Eight point charges, each of magnitude q, are located on the corners of a cube of edge s, as shown in Figure P23.69. (a) Determine the x, y, and z components of the resultant force exerted by the
- Consider the charge distribution shown in Figure P23.69. (a) Show that the magnitude of the electric field at the center of any face of the cube has a value of 2.18keq/s2.(b) What is the direction
- A negatively charged particle -q is placed at the center of a uniformly charged ring, where the ring has a total positive charge Q as shown in Example 23.8. The particle, confined to move along the x
- A line of charge with uniform density 35.0 nC/m lies along the line y = -15.0 cm, between the points with coordinates x = 0 and x = 40.0 cm. Find the electric field it creates at the origin.
- An electric dipole in a uniform electric field is displaced slightly from its equilibrium position, as shown in Figure P23.73, where + is small. The separation of the charges is 2a, and the moment of
- An electric field with a magnitude of 3.50 kN/C is applied along the x axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long assuming that (a) The plane is
- A vertical electric field of magnitude 2.00 x 104 N/C exists above the Earth’s surface on a day when a thunderstorm is brewing. A car with a rectangular size of 6.00 m by 3.00 m is traveling along
- A 40.0-cm-diameter loop is rotated in a uniform electric field until the position of maximum electric flux is found. The flux in this position is measured to be 5.20 x 105 Nm2/C. What is the
- Consider a closed triangular box resting within a horizontal electric field of magnitude E = 7.80 x 104 N/C as shown in Figure P24.4. Calculate the electric flux through(a) The vertical rectangular
- A uniform electric field ai + bj intersects a surface of area A. What is the flux through this area if the surface lies? (a) In the yz plane? (b) In the xz plane? (c) In the xy plane?
- A point charge q is located at the center of a uniform ring having linear charge density A and radius a, as shown in Figure P24.6. Determine the total electric flux through a sphere centered at the
- A pyramid with horizontal square base, 6.00 m on each side, and a height of 4.00 m is placed in a vertical electric field of 52.0 N/C. Calculate the total electric flux through the pyramid’s four
- A cone with base radius R and height h is located on a horizontal table. A horizontal uniform field E penetrates the cone, as shown in Figure P24.8. Determine the electric flux that enters the
- The following charges are located inside a submarine: 5.00 μC, - 9.00 μC, 27.0 μC, and -84.0 μC. (a) Calculate the net electric flux through the hull of the submarine. (b) Is
- The electric field everywhere on the surface of a thin spherical shell of radius 0.750 m is measured to be 890 N/C and points radially toward the center of the sphere. (a) What is the net charge
- Four closed surfaces, S1 through S4, together with the charges −2Q, Q, and −Q are sketched in Figure P24.11. (The colored lines are the intersections of the surfaces with the page.) Find
- (a) A point charge q is located a distance d from an infinite plane. Determine the electric flux through the plane due to the point charge. (b) What If? A point charge q is located a very small
- Calculate the total electric flux through the paraboloidal surface due to a uniform electric field of magnitude E 0 in the direction shown in Figure P24.13
- A point charge of 12.0 %C is placed at the center of a spherical shell of radius 22.0 cm. What is the total electric flux through? (a) The surface of the shell and (b) Any hemispherical surface
- A point charge Q is located just above the center of the flat face of a hemisphere of radius R as shown in Figure P24.15. What is the electric flux? (a) Through the curved surface and (b) Through
- In the air over a particular region at an altitude of 500 m above the ground the electric field is 120 N/C directed downward. At 600 m above the ground the electric field is 100 N/C downward. What is
- A point charge Q = 5.00 %C is located at the center of a cube of edge L = 0.100 m. In addition, six other identical point charges having q = -1.00 %C are positioned symmetrically around Q as shown in
- A positive point charge Q is located at the center of a cube of edge L. In addition, six other identical negative point charges q are positioned symmetrically around Q as shown in Figure P24.17.
- An infinitely long line charge having a uniform charge per unit length A lies a distance d from point O as shown in Figure P24.19. Determine the total electric flux through the surface of a sphere of
- An uncharged non-conducting hollow sphere of radius 10.0 cm surrounds a 10.0-%C charge located at the origin of a cartesian coordinate system. A drill with a radius of 1.00 mm is aligned along the z
- A charge of 170 %C is at the center of a cube of edge 80.0 cm. (a) Find the total flux through each face of the cube. (b) Find the flux through the whole surface of the cube. (c) What If? Would
- The line ag in Figure P24.22 is a diagonal of a cube. A point charge q is located on the extension of line ag, very close to vertex a of the cube. Determine the electric flux through each of the
- Determine the magnitude of the electric field at the surface of a lead-208 nucleus, which contains 82 protons and 126 neutrons. Assume the lead nucleus has a volume 208 times that of one proton, and
- A solid sphere of radius 40.0 cm has a total positive charge of 26.0 %C uniformly distributed throughout its volume. Calculate the magnitude of the electric field (a) 0 cm, (b) 10.0 cm, (c) 40.0
- A 10.0-g piece of Styrofoam carries a net charge of '0.700 %C and floats above the center of a large horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge
- A cylindrical shell of radius 7.00 cm and length 240 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm radially outward from its
- A particle with a charge of '60.0 nC is placed at the center of a non-conducting spherical shell of inner radius 20.0 cm and outer radius 25.0 cm. The spherical shell carries charge with a uniform