Three charged particles are arranged on corners of a

The magnitude of the electric force between two protons is 2.3 _ 10_26 N. How far apart are they? (a) 0.10 m (b) 0.022 m (c) 3.1 m (d) 0.005 7 m (e) 0.48 m

Estimate the magnitude of the electric fi eld strength due to the proton in a hydrogen atom at a distance of 5.29 _ 10_11 m, the Bohr radius. (a) 10_11 N/C (b) 108 N/C (c) 1014 N/C (d) 106 N/C (e) 1012 N/C

A very small ball has a mass of 5.0 _ 10_3 kg and a charge of 4.0 mC. What magnitude electric fi eld directed upward will balance the weight of the ball? (a) 8.2 _ 102 N/C (b) 1.2 _ 104 N/C (c) 2.0 _ 10_2 N/C (d) 5.1 _ 106 N/C (e) 3.7 _ 103 N/C

An electron with a speed of 3.00 _ 106 m/s moves into a uniform electric fi eld of magnitude 1.00 _ 103 N/C. The fi eld is parallel to the electrons motion. How far does the electron travel before it is brought to rest? (a) 2.56 cm (b) 5.12 cm (c) 11.2 cm (d) 3.34 m (e) 4.24 m

Charges of 3.0 nC, _2.0 nC, _7.0 nC, and 1.0 nC are contained inside a rectangular box with length 1.0 m, width 2.0 m, and height 2.5 m. Outside the box are charges of 1.0 nC and 4.0 nC. What is the electric fl ux through the surface of the box? (a) 0 (b) _560 N _ m2/C (c) _340 N _ m2/C (d) 260 N _ m2/C (e) 170 N _ m2/C

A uniform electric fi eld of 1.0 N/C is set up by a uniform distribution of charge in the xy-plane. What is the electric fi eld inside a metal ball placed 0.50 m above the xy-plane? (a) 1.0 N/C (b) _1.0 N/C (c) 0 (d) 0.25 N/C (e) It varies depending on the position inside the ball.

A charge of _4.00 nC is located at (0, 1.00) m. What is the x-component of the electric fi eld at (4.00, _2.00) m? (a) 1.15 N/C (b) _2.24 N/C (c) 3.91 N/C (d) _1.15 N/C (e) 0.863 N/C

Two point charges attract each other with an electric force of magnitude F. If one charge is reduced to onethird its original value and the distance between the charges is doubled, what is the resulting magnitude of the electric force between them? (a) F/12 (b) F/3 (c) F/6 (d) 3F/4 (e) 3F/2

What happens when a charged insulator is placed near an uncharged metallic object? (a) They repel each other. (b) They attract each other. (c) They may attract or repel each other, depending on whether the charge on the insulator is positive or negative. (d) They exert no electrostatic force on each other. (e) The charged insulator always spontaneously discharges.

In which of the following contexts can Gausss law not be readily applied to fi nd the electric fi eld? (a) near a long, uniformly charged wire (b) above a large uniformly charged plane (c) inside a uniformly charged ball (d) outside a uniformly charged sphere (e) Gausss law can be readily applied to fi nd the electric fi eld in all these contexts.

What prevents gravity from pulling you through the ground to the center of Earth? Choose the best answer. (a) The density of matter is too great. (b) The positive nuclei of your bodys atoms repel the positive nuclei of the atoms of the ground. (c) The density of the ground is greater than the density of your body. (d) Atoms are bound together by chemical bonds. (e) Electrons on the grounds surface and the surface of your feet repel one another.

A metallic coin is given a positive electric charge. Does its mass (a) increase measurably, (b) increase by an amount too small to measure directly, (c) stay unchanged, (d) decrease by an amount too small to measure directly, or (e) decrease measurably?

Three charged particles are arranged on corners of a square as shown in Figure MCQ15.13, with charge _Q on both the particle at the upper left corner and the particle at the lower right corner, and charge _2Q on the particle at the lower left corner. What is the direction of the electric fi eld at the upper right corner, which is a point in empty space? (a) upward and to the right (b) to the right (c) downward (d) downward and to the left (e) The fi eld is exactly zero at that point.

Suppose the _2Q charge at the lower left corner of Figure MCQ15.13 is removed. Which statement is true about the magnitude of the electric fi eld at the upper right corner? (a) It becomes larger. (b) It becomes smaller. (c) It stays the same. (d) It changes unpredictably. (e) It is zero.

A glass object is charged to _3 nC by rubbing it with a silk cloth. In the rubbing process, have protons been added to the object or have electrons been removed from it?

Why must hospital personnel wear special conducting shoes while working around oxygen in an operating room? What might happen if the personnel wore shoes with rubber soles?

A person is placed in a large, hollow metallic sphere that is insulated from ground. If a large charge is placed on the sphere, will the person be harmed upon touching the inside of the sphere?

Explain from an atomic viewpoint why charge is usually transferred by electrons.

Explain how a positively charged object can be used to leave another metallic object with a net negative charge. Discuss the motion of charges during the process.

If a suspended object A is attracted to a charged object B, can we conclude that A is charged? Explain.

If a metal object receives a positive charge, does its mass increase, decrease, or stay the same? What happens to its mass if the object receives a negative charge?

Consider point A in Figure CQ15.8. Does charge exist at this point? Does a force exist at this point? Does a fi eld exist at this point? Explain.

In fair weather there is an electric fi eld at the surface of the Earth, pointing down into the ground. What is the electric charge on the ground in this situation?

A student stands on a thick piece of insulating material, places her hand on top of a Van de Graaff generator, and then turns on the generator. Does she receive a shock?

There are great similarities between electric and gravitational fi elds. A room can be electrically shielded so that there are no electric fi elds in the room by surrounding it with a conductor. Can a room be gravitationally shielded? Explain.

Why should a ground wire be connected to the metal support rod for a television antenna?

A charged comb often attracts small bits of dry paper that then fl y away when they touch the comb. Explain.

A spherical surface surrounds a point charge q. Describe what happens to the total fl ux through the surface if (a) the charge is tripled, (b) the volume of the sphere is doubled, (c) the surface is changed to a cube, (d) the charge is moved to another location inside the surface, and (e) the charge is moved outside the surface.

If more electric fi eld lines leave a Gaussian surface than enter it, what can you conclude about the net charge enclosed by that surface?

A 7.5-nC charge is located 1.8 m from a 4.2-nC charge. Find the magnitude of the electrostatic force that one charge exerts on the other. Is the force attractive or repulsive?

A charged particle A exerts a force of 2.62 mN to the right on charged particle B when the particles are 13.7 mm apart. Particle B moves straight away from A to make the distance between them 17.7 mm. What vector force does particle B then exert on A?

Two metal balls A and B of negligible radius are fl oating at rest on Space Station Freedom between two metal bulkheads, connected by a taut nonconducting thread of length 2.00 m. Ball A carries charge q, and ball B carries charge 2q. Each ball is 1.00 m away from a bulkhead. (a) If the tension in the string is 2.50 N, what is the magnitude of q? (b) What happens to the system as time passes? Explain.

(a) Find the electrostatic force between a Na_ ion and a Cl_ ion separated by 0.50 nm. (b) Would the answer change if the sodium ion were replaced by Li_ and the Chloride ion by Br_? Explain.

The nucleus of 8Be, which consists of 4 protons and 4 neutrons, is very unstable and spontaneously breaks into two alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons). (a) What is the force between the two alpha particles when they are 5.00 _ 10_15 m apart, and (b) what is the initial magnitude of the acceleration of the alpha particles due to this force? Note that the mass of an alpha particle is 4.0026 u.

A molecule of DNA (deoxyribonucleic acid) is 2.17 mm long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 1.00% upon becoming charged. Determine the effective spring constant of the molecule.

Suppose 1.00 g of hydrogen is separated into electrons and protons. Suppose also the protons are placed at the Earths North Pole and the electrons are placed at the South Pole. What is the resulting compressional force on the Earth?

Four point charges are at the corners of a square of side a as shown in Figure P15.8. Determine the magnitude and direction of the resultant electric force on q, with ke, q, and a left in symbolic form.

Two small identical conducting spheres are placed with their centers 0.30 m apart. One is given a charge of 12 _ 10_9 C, the other a charge of _18 _ 10_9 C. (a) Find the electrostatic force exerted on one sphere by the other. (b) The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached.

Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in Figure P15.10.

Three charges are arranged as shown in Figure P15.11. Find the magnitude and direction of the electrostatic force on the charge at the origin.

Three charges are arranged as shown in Figure P15.12. Find the magnitude and direction of the electrostatic force on the 6.00-nC charge.

Three point charges are located at the corners of an equilateral triangle as in Figure P15.13. Find the magnitude and direction of the net electric force on the 2.00 mC charge.

A charge of _3.00 nC and a charge of _5.80 nC are separated by a distance of 50.0 cm. Find the position at which a third charge of _7.50 nC can be placed so that the net electrostatic force on it is zero.

Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by light strings from a common point as shown in Figure P15.15. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of 5.0 with the vertical. If each string is 30.0 cm long, what is the magnitude of the charge on each sphere?

Particle A of charge 3.00 _ 10_4 C is at the origin, particle B of charge _6.00 _ 10_4 C is at (4.00 m, 0) and particle C of charge 1.00 _ 10_4 C is at (0, 3.00 m). (a) What is the x-component of the electric force exerted by A on C ? (b) What is the y-component of the force exerted by A on C ? (c) Find the magnitude of the force exerted by B on C. (d) Calculate the x-component of the force exerted by B on C. (e) Calculate the y-component of the force exerted by B on C. (f) Sum the two x-components to obtain the resultant x-component of the electric force acting on C. (g) Repeat part (f) for the y-component. (h) Find the magnitude and direction of the resultant electric force acting on C.

A small object of mass 3.80 g and charge _18 mC fl oats in a uniform electric fi eld. What is the magnitude and direction of the electric fi eld?

(a) Determine the electric fi eld strength at a point 1.00 cm to the left of the middle charge shown in Figure P15.10. (b) If a charge of _2.00 mC is placed at this point, what are the magnitude and direction of the force on it?

An airplane is fl ying through a thundercloud at a height of 2 000 m. (Flying at this height is very dangerous because of updrafts, turbulence, and the possibility of electric discharge.) If there are charge concentrations of _40.0 C at a height of 3 000 m within the cloud and _40.0 C at a height of 1 000 m, what is the electric fi eld E S at the aircraft?

An electron is accelerated by a constant electric fi eld of magnitude 300 N/C. (a) Find the acceleration of the electron. (b) Use the equations of motion with constant acceleration to fi nd the electrons speed after 1.00 _ 10_8 s, assuming it starts from rest.

A charge of _5.0 nC is at the origin and a second charge of 7.0 nC is at x _ 4.00 m. Find the magnitude and direction of the electric fi eld halfway in between the two charges.

Each of the protons in a particle beam has a kinetic energy of 3.25 _ 10_15 J. What are the magnitude and direction of the electric fi eld that will stop these protons in a distance of 1.25 m?

A proton accelerates from rest in a uniform electric fi eld of 640 N/C. At some later time, its speed is 1.20 _ 106 m/s. (a) Find the magnitude of the acceleration of the proton. (b) How long does it take the proton to reach this speed? (c) How far has it moved in that interval? (d) What is its kinetic energy at the later time?

(a) Find the magnitude and direction of the electric fi eld at the position of the 2.00 mC charge in Figure P15.13. (b) How would the electric fi eld at that point be affected if the charge there were doubled? Would the magnitude of the electric force be affected?

An alpha particle (a helium nucleus) is traveling along the positive x-axis at 1 250 m/s when it enters a cylindrical tube of radius 0.500 m centered on the x-axis. Inside the tube is a uniform electric fi eld of 4.50 _ 10_4 N/C pointing in the negative y-direction. How far does the particle travel before hitting the tube wall? Neglect any gravitational forces. Note: ma _ 6.64 _ 10_27 kg; qa _ 2e.

Two point charges lie along the y-axis. A charge of q1 _ _9.0 mC is at y _ 6.0 m, and a charge of q2 _ _8.0 mC is at y _ _4.0 m. Locate the point (other than infi nity) at which the total electric fi eld is zero.

In Figure P15.27 determine the point (other than infi nity) at which the total electric fi eld is zero.

Three charges are at the corners of an equilateral triangle, as shown in Figure P15.28. Calculate the electric fi eld at a point midway between the two charges on the x-axis.

Three identical charges (q _ _5.0 mC) lie along a circle of radius 2.0 m at angles of 30, 150, and 270, as shown in Figure P15.29. What is the resultant electric fi eld at the center of the circle?

Figure P15.30 shows the electric fi eld 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?

(a) Sketch the electric fi eld lines around an isolated point charge q _ 0. (b) Sketch the electric fi eld pattern around an isolated negative point charge of magnitude _2q.

(a) Sketch the electric fi eld pattern around two positive point charges of magnitude 1 mC placed close together. (b) Sketch the electric fi eld pattern around two negative point charges of _2 mC, placed close together. (c) Sketch the pattern around two point charges of _1 mC and _2 mC, placed close together.

Two point charges are a small distance apart. (a) Sketch the electric fi eld lines for the two if one has a charge four times that of the other and both charges are positive. (b) Repeat for the case in which both charges are negative.

(a) Sketch the electric fi eld pattern set up by a positively charged hollow sphere. Include regions inside and regions outside the sphere. (b) A conducting cube is given a positive charge. Sketch the electric fi eld pattern both inside and outside the cube.

Refer to Figure 15.20. The charge lowered into the center of the hollow conductor has a magnitude of 5 mC. Find the magnitude and sign of the charge on the inside and outside of the hollow conductor when the charge is as shown in (a) Figure 15.20a, (b) Figure 15.20b, (c) Figure 15.20c, and (d) Figure 15.20d.

The dome of a Van de Graaff generator receives a charge of 2.0 _ 10_4 C. Find the strength of the electric fi eld (a) inside the dome, (b) at the surface of the dome, assuming it has a radius of 1.0 m, and (c) 4.0 m from the center of the dome. (Hint: See Section 15.6 to review properties of conductors in electrostatic equilibrium. Also, use that the points on the surface are outside a spherically symmetric charge distribution; the total charge may be considered to be located at the center of the sphere.)

If the electric fi eld strength in air exceeds 3.0 _ 106 N/C, the air becomes a conductor. Using this fact, determine the maximum amount of charge that can be carried by a metal sphere 2.0 m in radius. (See the hint in Problem 36.)

In the Millikan oil-drop experiment, an atomizer (a sprayer with a fi ne nozzle) is used to introduce many tiny droplets of oil between two oppositely charged parallel metal plates. Some of the droplets pick up one or more excess electrons. The charge on the plates is adjusted so that the electric force on the excess electrons exactly balances the weight of the droplet. The idea is to look for a droplet that has the smallest electric force and assume it has only one excess electron. This strategy lets the observer measure the charge on the electron. Suppose we are using an electric fi eld of 3 _ 104 N/C. The charge on one electron is about 1.6 _ 10_19 C. Estimate the radius of an oil drop of density 858 kg/m3 for which its weight could be balanced by the electric force of this fi eld on one electron. (Problem 38 is courtesy of E. F. Redish. For more problems of this type, visit www.physics.umd.edu/perg/.)

A Van de Graaff generator is charged so that a proton at its surface accelerates radially outward at 1.52 _ 1012 m/s2. Find (a) the magnitude of the electric force on the proton at that instant and (b) the magnitude and direction of the electric fi eld at the surface of the generator.

A fl at surface having an area of 3.2 m2 is rotated in a uniform electric fi eld of magnitude E _ 6.2 _ 105 N/C. Determine the electric fl ux through this area (a) when the electric fi eld is perpendicular to the surface and (b) when the electric fi eld is parallel to the surface.

An electric fi eld of intensity 3.50 kN/C is applied along the x-axis. Calculate the electric fl ux through a rectangular plane 0.350 m wide and 0.700 m long if (a) the plane is parallel to the yz-plane, (b) the plane is parallel to the xy-plane, and (c) the plane contains the y-axis and its normal makes an angle of 40.0 with the x-axis.

The electric fi eld everywhere on the surface of a charged sphere of radius 0.230 m has a magnitude of 575 N/C and points radially outward from the center of the sphere. (a) What is the net charge on the sphere? (b) What can you conclude about the nature and distribution of charge inside the sphere?

Four closed surfaces, S1 through S4, together with the charges _2Q , Q , and _Q , are sketched in Figure P15.43. (The colored lines are the intersections of the surfaces with the page.) Find the electric fl ux through each surface. FIGURE P15.43

A vertical electric fi eld of magnitude 1.80 _ 104 N/C exists above Earths surface on a stormy day. A car with a rectangular size of 5.50 m by 2.00 m is traveling along a horizontal roadway. Find the magnitude of the electric fl ux through the bottom of the car.

A point charge q is located at the center of a spherical shell of radius a that has a charge _q uniformly distributed on its surface. Find the electric fi eld (a) for all points outside the spherical shell and (b) for a point inside the shell a distance r from the center.

A charge of 1.70 _ 102 mC is at the center of a cube of edge 80.0 cm. No other charges are nearby. (a) Find the fl ux through the whole surface of the cube. (b) Find the fl ux through each face of the cube. (c) Would your answers to parts (a) or (b) change if the charge were not at the center? Explain.

Suppose the conducting spherical shell of Figure 15.29 carries a charge of 3.00 nC and that a charge of _2.00 nC is at the center of the sphere. If a _ 2.00 m and b _ 2.40 m, fi nd the electric fi eld at (a) r _ 1.50 m, (b) r _ 2.20 m, and (c) r _ 2.50 m. (d) What is the charge distribution on the sphere?

A very large nonconducting plate lying in the xyplane carries a charge per unit area of s. A second such plate located at z _ 2.00 cm and oriented parallel to the xy-plane carries a charge per unit area of _2s. Find the electric fi eld (a) for z 0, (b) 0 z 2.00 cm, and (c) z _ 2.00 cm.

In deep space two spheres each of radius 5.00 m are connected by a 3.00 _ 102 m nonconducting cord. If a uniformly distributed charge of 35.0 mC resides on the surface of each sphere, calculate the tension in the cord.

A nonconducting, thin plane sheet of charge carries a uniform charge per unit area of 5.20 mC/m2 as in Figure 15.30. (a) Find the electric fi eld at a distance of 8.70 cm from the plate. (b) Explain whether your result changes as the distance from the sheet is varied.

Three point charges are aligned along the x-axis as shown in Figure P15.51. Find the electric fi eld at the position x _ _2.0 m, y _ 0. lowered to reach its equilibrium position? (b) The ball is given a charge of 0.050 0 C. If an electric fi eld directed upward is applied, increasing slowly to a maximum value of 355.0 N/C, how far below the unstretched position is the new equilibrium position of the ball?

A 2.00-mC charged 1.00-g cork ball is suspended vertically on a 0.500-m-long light string in the presence of a uniform downward-directed electric fi eld of magnitude E _ 1.00 _ 105 N/C. If the ball is displaced slightly from the vertical, it oscillates like a simple pendulum. (a) Determine the period of the balls oscillation. (b) Should gravity be included in the calculation for part (a)? Explain.

Two 2.0-g spheres are suspended by 10.0-cm-long light strings (Fig. P15.57). A uniform electric fi eld is applied in the x-direction. If the spheres have charges of _5.0 _ 10_8 C and _5.0 _ 10_8 C, determine the electric fi eld intensity that enables the spheres to be in equilibrium at u _ 10.

A small, 2.00-g plastic ball is suspended by a 20.0-cmlong string in a uniform electric fi eld, as shown in Figure P15.52. If the ball is in equilibrium when the string makes a 15.0 angle with the vertical as indicated, what is the net charge on the ball?

(a) Two identical point charges _q are located on the y-axis at y _ _a and y _ _a. What is the electric fi eld along the x-axis at x _ b? (b) A circular ring of charge of radius a has a total positive charge Q distributed uniformly around it. The ring is in the x _ 0 plane with its center at the origin. What is the electric fi eld along the x-axis at x _ b due to the ring of charge? (Hint: Consider the charge Q to consist of many pairs of identical point charges positioned at the ends of diameters of the ring.)

The electrons in a particle beam each have a kinetic energy K. Find the magnitude of the electric fi eld that will stop these electrons in a distance d, expressing the answer symbolically in terms of K, e, and d. Should the electric fi eld point in the direction of the motion of the electron, or should it point in the opposite direction?

A vertical spring with constant 845 N/m has a ball of mass 4.00 kg attached to the bottom of it, which is held with the spring unstretched. (a) How far must the ball be

A point charge of magnitude 5.00 mC is at the origin of a coordinate system, and a charge of _4.00 mC is at the point x _ 1.00 m. There is a point on the x-axis, at x less than infi nity, where the electric fi eld goes to zero. (a) Show by conceptual arguments that this point cannot be located between the charges. (b) Show by conceptual arguments that the point cannot be at any location between x _ 0 and negative infi nity. (c) Show by conceptual arguments that the point must be between x _ 1.00 m and x _ positive infi nity. (d) Use the values given to fi nd the point and show that it is consistent with your conceptual argument.

Two hard rubber spheres of mass 15 g are rubbed vigorously with fur on a dry day and are then suspended from a rod with two insulating strings of length 5.0 cm. They are observed to hang at equilibrium as shown in Figure P15.59, each at an angle of 10 with the vertical. Estimate the amount of charge that is found on each sphere. (Problem 59 is courtesy of E. F. Redish. For more problems of this type, visit www.physics.umd.edu/perg/.)

Two small silver spheres, each with a mass of 100 g, are separated by 1.00 m. Calculate the fraction of the electrons in one sphere that must be transferred to the other to produce an attractive force of 1.00 _ 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 Avogadros number divided by the molar mass of silver, 107.87 g/mol.)

A solid conducting sphere of radius 2.00 cm has a charge of 8.00 mC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge of _4.00 mC. Find the electric fi eld at (a) r _ 1.00 cm, (b) r _ 3.00 cm, (c) r _ 4.50 cm, and (d) r _ 7.00 cm from the center of this charge confi guration.

Three identical point charges, each of mass m _ 0.100 kg, hang from three strings, as shown in Figure P15.62. If the lengths of the left and right strings are each L _ 30.0 cm and if the angle u is 45.0, determine the value of q.

Each of the electrons in a particle beam has a kinetic energy of 1.60 _ 10_17 J. (a) What is the magnitude of the uniform electric fi eld (pointing in the direction of the electrons movement) that will stop these electrons in a distance of 10.0 cm? (b) How long will it take to stop the electrons? (c) After the electrons stop, what will they do? Explain.

Protons are projected with an initial speed v0 _ 9 550 m/s into a region where a uniform electric fi eld E _ 720 N/C is present (Fig. P15.64). The protons are to hit a target that lies a horizontal distance of 1.27 mm from the point where the protons are launched. Find (a) the two projection angles u that will result in a hit and (b) the total duration of fl ight for each of the two trajectories.