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1 Million+ Step-by-step solutionsmath books Q:(a) Find to three significant(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−.Q:(a) Calculate the number of electrons(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?Q:The Nobel laureate Richard FeynmanThe 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.Q:Two protons in an atomic nucleusTwo 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?Q:(a) Two protons in a molecule(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?Q:Two small silver spheresTwo 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.)Q:Three point charges are locatedThree 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.

Three point charges are locatedQ:Suppose that 1.00 g of hydrogenSuppose 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?Q:Two identical conducting small spheresTwo 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.Q:Two small beads having positive chargesTwo 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?

Two small beads having positive chargesQ:In the Bohr Theory of the hydrogen atomIn 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?Q:Two identical particles, each havingTwo 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
Two identical particles, each havingQ:What are the magnitude and directionWhat 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.)Q:An object having a net charge of 24.0 *CAn 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?Q:In Figure P23.15, determineIn Figure P23.15, determine the point (other than infinity) at which the electric field is zero.

In Figure P23.15, determineQ:An airplane is flying throughAn 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?Q:Two point charges are located on the x axisTwo 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?Q:Three charges are at the cornersThree 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.Q:Three point charges are arrangedThree 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.

Three point charges are arrangedQ:Two 2.00-μC point chargesTwo 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.Q:Four point charges are at the cornersFour 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 resultant force on q?

Four point charges are at the cornersQ:Consider the electric dipole shown in Figure P23.22Consider 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 the electric dipole shown in Figure P23.22Q:Consider n equal positive point chargesConsider 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 passing through the center of the circle and perpendicular to the plane of the circle.
(b) Explain why this result is identical to that of the calculation done in Example 23.8.Q:Consider an infinite numberConsider 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 distribution? Suggestion: Use the fact that

Consider an infinite numberQ:A rod 14.0 cm long is uniformlyA 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 center.Q:A continuous line of charge lies alongA 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 of the electric field at the origin?Q:A uniformly charged ring of radius 10.0 cmA 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 the center of the ringQ:A line of charge starts at xA 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.Q:Show that the maximum magnitude EmaxShow 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)Q:A uniformly charged disk of radiusA 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
(d) 200 cm from the center of the diskQ:Example 23.9 derives the exactExample 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 + 5.20 μC.
(a) Using the result of Example 23.9, compute the electric field at a point on the axis and 3.00 mm from the center. What If? Compare this answer with the field computed from the near-field approximation E = 2/2) 0.
(b) Using the result of Example 23.9, compute the electric field at a point on the axis and
30.0 cm from the center of the disk. What If? Compare this with the electric field obtained by treating the disk as a +5.20-μC point charge at a distance of 30.0 cm.Q:The electric field along the axisThe 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 approaches that of a point charge Q = aπR2. (Suggestion: First show that x/(x2 + R2)1/2 = (1 + R2/x2)-1/2 and use the binomial expansion (1 + ∂) n ≈ 1 + n∂ when ∂ Q:A uniformly charged insulatingA 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 the electric field at O, the center of the semicircle.

A uniformly charged insulatingQ:(a) Consider a uniformly charged(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 of the cylinder as shown in Figure P23.34. (Suggestion: Use the result of Example 23.8 and treat the cylinder as a collection of ring charges.)
(b) What If? Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the result of Example 23.9 to find the field it creates at the same point.

(a) Consider a uniformly chargedQ:A thin rod of length ℓ and uniformA 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 perpendicular bisector, has no x component and is given by E = 2ke3 sin +0/y.
(b) What If? Using your result to part (a), show that the field of a rod of infinite length is E = 2keA/y. (Suggestion: First calculate the field at P due to an element of length dx, which has a charge 3 dx. Then change variables from x to +, using the relationships x = y tan θ and dx = y sec2 θ d θ, and integrate over θ.)

A thin rod of length ℓ and uniformQ:Three solid plastic cylinders all haveThree 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 uniform density on its curved lateral surface only. The third
(c) Carries charge with uniform density 500 nC/m3 throughout the plastic Find the charge of each cylinder.Q:Eight solid plastic cubes, each 3.00 cmEight 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 uniform density 400 nC/m3 throughout its volume; find the charge of each object.
(b) Assuming each object carries charge with uniform density 15.0 nC/m2 everywhere on its exposed surface; find the charge on each object.
(c) Assuming charge is placed only on the edges where perpendicular surfaces meet, with uniform density 80.0 pC/m, find the charge of each object.

Eight solid plastic cubes, each 3.00 cmQ:A positively charged disk has a uniformA 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.Q:A negatively charged rod of finite lengthA 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.Q:Figure P23.40 shows the electricFigure 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?

Figure P23.40 shows the electricQ:Three equal positive chargesThree 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 lines in the plane of the charges. Find the location of a point (other than 4) where the electric field is zero.
(b) What are the magnitude and direction of the electric field at P due to the two charges at the base?

Three equal positive chargesQ:An electron and a proton are eachAn 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.Q:A proton acceleratesA 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 the acceleration of the proton.
(b) How long does it take the proton to reach this speed?
(c) How far has it moved in this time?
(d) What is its kinetic energy at this time?Q:A proton is projected in the positiveA 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 acceleration of the proton,
(b) Its initial speed, and
(c) The time at which the proton comes to rest.Q:The electrons in a particle beamThe 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?Q:A positively charged bead havingA 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 at a speed of 21.0 m/s. Determine
(a) The direction of the electric field (up or down), and
(b) The charge on the bead.Q:A proton moves at 4.50 x 105 m/sA 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 interval required for the proton to travel 5.00 cm horizontally,
(b) Its vertical displacement during the time interval in which it travels 5.00 cm horizontally, and
(c) The horizontal and vertical components of its velocity after it has traveled 5.00 cm horizontally.Q:Two horizontal metal plates, each 100 mmTwo 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 of 2 000 N/C exists in the region between them. A particle of mass 2.00 x 10-16 kg and with a positive charge of 1.00 x 10-6 C leaves the center of the bottom negative plate with an initial speed of 1.00 & 105 m/s at an angle of 37.0° above the horizontal. Describe the trajectory of the particle. Which plate does it strike? Where does it strike, relative to its starting point?Q:Protons are projected with an initialProtons 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 lies at a horizontal distance of 1.27 mm from the point where the protons cross the plane and enter the electric field in Figure P23.49. Find
(a) The two projection angles + that will result in a hit and
(b) The total time of flight (the time interval during which the proton is above the plane in Figure P23.49) for each trajectory.Q:Two known charges, -12.0 μC and 45.0 μCTwo 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 unknown charge is to be placed so that each charge is in equilibrium under the action of the electric forces exerted by the other two charges. Is this situation possible? Is it possible in more than one way? Find the required location, magnitude, and sign of the unknown charge.Q:A uniform electric field of magnitudeA 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 from the negative plate.
(a) Determine the distance from the positive plate at which the two pass each other. (Ignore the electrical attraction between the proton and electron.)
(b) What If? Repeat part (a) for a sodium ion (Na+) and a chloride ion (Cl-).Q:Three point charges are alignedThree 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).

Three point charges are alignedQ:A researcher studying the propertiesA 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 q, mass m, and initial velocity vi, is turned through an angle of 90° as each ion undergoes displacement Ri + Rj . The ions enter a chamber as shown in Figure P23.53, and leave through the exit port with the same speed they had when they entered the chamber. The electric field acting on the ions is to have constant magnitude.
(a) Suppose the electric field is produced by two concentric cylindrical electrodes not shown in the diagram, and hence is radial. What magnitude should the field have? What If?
(b) If the field is produced by two flat plates and is uniform in direction, what value should the field have in this case?

A researcher studying the propertiesQ:A small, 2.00-g plastic ball is suspendedA 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 the vertical, what is the net charge on the ball?

A small, 2.00-g plastic ball is suspendedQ:A charged cork ball of mass 1.00 gA 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 at 0 = 37.0°. Find
(a) The charge on the ball and
(b) The tension in the string.

A charged cork ball of mass 1.00 gQ:A charged cork ball of mass mA 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 ball is in equilibrium at the angle θ. Find
(a) The charge on the ball and
(b) The tension in the string.

A charged cork ball of mass mQ:Four identical point charges (q = +10.0 μC)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 magnitude and direction of the resultant electric force exerted on the charge at the lower left corner by the other three charges.

Four identical point charges (q = +10.0 μC)Q:Inez is putting up decorationsInez is putting up decorations for her sister’s quinceañera (fifteenth birthday party). She ties three light silk ribbons together to the top of a gateway and hangs a rubber balloon from each ribbon (Fig. P23.58). To include the effects of the gravitational and buoyant forces on it, each balloon can be modeled as a particle of mass 2.00 g, with its center 50.0 cm from the point of support. To show off the colors of the balloons, Inez rubs the whole surface of each balloon with her woolen scarf, to make them hang separately with gaps between them. The centers of the hanging balloons form a horizontal equilateral triangle with sides 30.0 cm long. What is the common charge each balloon carries?

Inez is putting up decorationsQ:Two identical metallic blocksTwo 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. A total charge Q is slowly placed on the system, causing the spring to stretch to an equilibrium length L, as shown in Figure P23.59b. Determine the value of Q, assuming that all the charge resides on the blocks and modeling the blocks as point charges.

Two identical metallic blocksQ:Consider a regular polygon with 29 sidesConsider 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 the polygon. What is the magnitude and direction of the force experienced by the charge Q? (Suggestion: You may use the result of Problem 63 in Chapter 3.)Q:Identical thin rods of length 2a carryIdentical 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 that the magnitude of the force exerted by the left rod on the right one is given by

Identical thin rods of length 2a carryQ:Two small spheres, each of mass 2.00 gTwo 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 x 10-8 C and +5.00 x 10-8 C. Determine the electric field that enables the spheres to be in equilibrium at an angle 0 = 10.0°.

Two small spheres, each of mass 2.00 gQ:A line of positive charge is formedA 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 total charge on the semicircle is 12.0 μC. Calculate the total force on a charge of 3.00 μC placed at the center of curvature.

A line of positive charge is formedQ:Three charges of equal magnitudeThree 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 the forces exerted by the three fixed charges. Find a value for s for which Q is in equilibrium. You will need to solve a transcendental equation.

Three charges of equal magnitudeQ:Two small spheres of mass m are suspendedTwo 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 θ2 with the vertical.
(a) How are θ1 and θ2 related?
(b) Assume θ1 and θ2 are small. Show that the distance r between the spheres is given byQ:Four identical particles, each having chargeFour 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 passing through the center of the square (Fig. P23.66)
(a) Show that the force exerted by the other four charges on -Q is Note that this force is directed toward the center of the square whether z is positive (-Q above the square) or negative (-Q below the square).
(b) If z is small compared with L, the above expression reduces to F = – (constant) zk. Why does this imply that the motion of the charge -Q is simple harmonic, and what is the period of this motion if the mass of -Q is m?

Four identical particles, each having chargeQ:A 1.00-g cork ball with charge 2.00 *CA 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 ball is displaced slightly from the vertical, it oscillates like a simple pendulum.
(a) Determine the period of this oscillation.
(b) Should gravity be included in the calculation for part
(a)? Explain.Q:Two identical beads each have a massTwo 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 apart (Fig. P23.68). Determine the charge on each bead.

Two identical beads each have a massQ:Eight point charges, each of magnitude qEight 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 other charges on the charge located at point A.
(b) What are the magnitude and direction of this resultant force?Q:Consider the charge distributionConsider 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 of the electric field at the center of the top face of the cube

Consider the charge distributionQ:A negatively charged particleA 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 axis, is displaced a small distance x along the axis (where x Q:A line of charge with uniform density 35.0 nC/mA 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.Q:An electric dipole in a uniform electricAn 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 inertia of the dipole is I. Assuming the dipole is released from this position, show that its angular orientation exhibits simple harmonic motion with a frequency

An electric dipole in a uniform electricQ:An electric field with a magnitude of 3.50 kN/CAn 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 parallel to the yz plane;
(b) The plane is parallel to the xy plane;
(c) The plane contains the y axis, and its normal makes an angle of 40.0° with the x axis.Q:A vertical electric field of magnitudeA 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 roadway sloping downward at 10.0°. Determine the electric flux through the bottom of the car.Q:A 40.0-cm-diameter loop is rotatedA 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 magnitude of the electric field?Q:Consider a closed triangular box restingConsider 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 surface,
(b) The slanted surface, and
(c) The entire surface of the box.

Consider a
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