Solved: In which of the following contexts can Gausss law

A very small ball has a mass of 5.0 3 1023 kg and a charge of 4.0 mC. What magnitude electric field directed upward will balance the weight of the ball? (a) 8.2 3 102 N/C (b) 1.2 3 104 N/C (c) 2.0 3 1022 N/C (d) 5.1 3 106 N/C (e) 3.7 3 103 N/C

Estimate the magnitude of the electric field strength due to the proton in a hydrogen atom at a distance of 5.29 3 10211 m, the expected position of the electron in the atom. (a) 10211 N/C (b) 108 N/C (c) 1014 N/C (d) 106 N/C (e) 1012 N/C

The magnitude of the electric force between two protons is 2.3 3 10226 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

A uniform electric field of 1.0 N/C is set up by a uniform distribution of charge in the xy-plane. What is the electric field inside a metal ball placed 0.50 m above the xy-plane? (a) 1.0 N/C (b) 21.0 N/C (c) 0 (d) 0.25 N/C (e) It varies depending on the position inside the ball.

Charges of 3.0 nC, 22.0 nC, 27.0 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 flux through the surface of the box? (a) 0 (b) 2560 N ? m2/C (c) 2340 N ? m2/C (d) 260 N ? m2/C (e) 170 N ? m2/C

An electron with a speed of 3.00 3 106 m/s moves into a uniform electric field of magnitude 1.00 3 103 N/C. The field lines are parallel to the electrons velocity and pointing in the same direction as the velocity. 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

A charge of 24.00 nC is located at (0, 1.00) m. What is the x-component of the electric field at (4.00, 22.00) m? (a) 1.15 N/C (b) 22.24 N/C (c) 3.91 N/C (d) 21.15 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

In which of the following contexts can Gausss law not be readily applied to find the electric field? (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 find the electric field in all these contexts.

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.

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.

Three charged particles are arranged on corners of a square as shown in Figure MCQ15.12, with charge 2Q on both the particle at the upper left corner and the particle at the lower right corner, and charge 12Q on the particle at the lower left corner. What is the direction of the electric field 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 field is exactly zero at that point.

Suppose the 12Q charge at the lower left corner of Figure MCQ15.12 is removed. Which statement is true about the magnitude of the electric field 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 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?

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

A student who grew up in a tropical country and is studying in the United States may have no experience with static electricity sparks and shocks until his or her first American winter. Explain.

A small object of mass 3.80 g and charge 218 mC is suspended motionless above the ground when immersed in a uniform electric field perpendicular to the ground. What is the magnitude and direction of the electric field?

(a) Determine the electric field strength at a point 1.00 cm to the left of the middle charge shown in Figure P15.10. (b) If a charge of 22.00 mC is placed at this point, what are the magnitude and direction of the force on it?

An electric field of magnitude 5.25 3 105 N/C points due south at a certain location. Find the magnitude and direction of the force on a 26.00 mC charge at this location.

An electron is accelerated by a constant electric field of magnitude 300 N/C. (a) Find the acceleration of the electron. (b) Use the equations of motion with constant acceleration to find the electrons speed after 1.00 3 1028 s, assuming it starts from rest.

A small block of mass m and charge Q is placed on an insulated, frictionless, inclined plane of angle u as in Figure P15.21. An electric field is applied parallel to the incline. (a) Find an expression for the magnitude of the electric field that enables the block to remain at rest. (b) If m 5 5.40 g, Q 5 27.00 mC, and u 5 25.0, determine the magnitude and direction ofthe electric field that enables the block to remain atrest on the incline.

A small sphere of charge q 5 168 mC and mass m 55.8 g is attached to a light string and placed in a uniformelectric field ESthat makes an angle u 5 37with the horizontal. The opposite end of the string isattached to a wall and the sphere is in static equilibriumwhen the string is horizontal as in Figure P15.22.(a) Construct a free body diagram for the sphere. Find(b) the magnitude of the electric field and (c) the tensionin the strin

A proton accelerates from rest in a uniform electric field of 640 N/C. At some later time, its speed is 1.20 3 106 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 field at the position of the 2.00 mC charge in Figure P15.13. (b) How would the electric field at that point be affected if the charge there were doubled? Would the magnitude of the electric force be affected?

Two equal positive charges are at opposite corners of a trapezoid as in Figure P15.25. Find symbolic expressions for the components of the electric field at the point P.

Three point charges are located on a circular arc as shown in Figure P15.26. (a) What is the total electric field at P, the center of the arc? (b) Find the electric force that would be exerted on a 25.00-nC charge placed at P.

In Figure P15.27 determine the point (other than infinity) at which the total electric field is zero.

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

Three identical charges (q 5 25.0 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 field at the center of the circle?

Figure P15.30 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?

(a) Sketch the electric field lines around an isolated point charge q . 0. (b) Sketch the electric field pattern around an isolated negative point charge of magnitude 22q.

(a) Sketch the electric field pattern around two positive point charges of magnitude 1 mC placed close together. (b) Sketch the electric field pattern around two negative point charges of 22 mC, placed close together. (c) Sketch the pattern around two point charges of 11 mC and 22 mC, placed close together.

Two point charges are a small distance apart. (a) Sketch the electric field 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.

Three equal positive charges are at the corners of an equilateral triangle of side a as in Figure P15.34. Assume the three charges together create an electric field. (a) Sketch the electric field lines in the plane of the charges. (b) Find the location of one point (other than `) where the electric field is zero. What are (c) the magnitude and (d) the direction of the electric field at P due to the two charges at the base?

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 3 1024 C. Find the strength of the electric field (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 field strength in air exceeds 3.0 3 106 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 illustrated in Figure 15.21, an atomizer (a sprayer with a fine 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 field of 3 3 104 N/C. The charge on one electron is about 1.6 3 10219 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 field 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 3 1012 m/s2. Find (a) the magnitude of the electric force on the proton at that instant and (b) the magni- tude and direction of the electric field at the surface of the generator.

A uniform electric field of magnitude E 5 435 N/C makes an angle of u 5 65.0 with a plane surface of area A 5 3.50 m2 as in Figure P15.40. Find the electric flux through this surface.

An electric field of intensity 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 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 field 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 22Q , Q, and 2Q , are sketched in Figure P15.43. (The colored lines are the intersections of the surfaces with the page.) Find the electric flux through each surface.

A charge q 5 15.80 mC is located at the center of a regular tetrahedron (a foursided surface) as in Figure P15.44. Find (a) the total electric flux through the tetrahedron and (b) the electric flux through one face of the tetrahedron.

A point charge q is located at the center of a spherical shell of radius a that has a charge 2q uniformly distributed on its surface. Find the electric field (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 3 102 mC is at the center of a cube of edge 80.0 cm. No other charges are nearby. (a) Find the flux through the whole surface of the cube. (b) Find the flux 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 22.00 nC is at the center of the sphere. If a 5 2.00 m and b 5 2.40 m, find the electric field at (a) r 5 1.50 m, (b) r 5 2.20 m, and (c) r 5 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 5 2.00 cm and oriented parallel to the xy-plane carries a charge per unit area of 22s. Find the electric field (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 3 102 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 field 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 field at the position x 5 12.0 m, y 5 0.

A small plastic ball of mass m 5 2.00 g is suspended by a string of length L 5 20.0 cm in a uniform electric field, as shown in Figure P15.52. If the ball is in equilibrium when the string makes a u 5 15.0 angle with the vertical as indicated, what is the net charge on the ball?

(a) Two identical point charges 1q are located on the y-axis at y 5 1a and y 5 2a. What is the electric field along the x-axis at x 5 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 5 0 plane with its center at the origin. What is the electric field along the x-axis at x 5 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 field that will stop these electrons in a distance d, expressing the answer symbolically in terms of K, e, and d. Should the electric field point in the direction of the motion of the electron, or should it point in the opposite direction?

A point charge 12Q is at the origin and a point charge 2Q is located along the x-axis at x 5 d as in Figure P15.55. Find symbolic expressions for the components of the net force on a third point charge 1Q located along the y-axis at y 5 d.

A 1.00-g cork ball having a positive charge of 2.00 mC is suspended vertically on a 0.500-m-long light string in the presence of a uniform downward-directed electric field of magnitude E 5 1.00 3 105 N/C as in Figure P15.56. 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 field is applied in the x-direction. If the spheres have charges of 25.0 3 1028 C and 15.0 3 1028 C, determine the electric field intensity that enables the spheres to be in equilibrium at u 5 10.

A point charge of magnitude 5.00 mC is at the origin of a coordinate system, and a charge of 24.00 mC is at the point x 5 1.00 m. There is a point on the x-axis, at x less than infinity, where the electric field 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 5 0 and negative infinity. (c) Show by conceptual arguments that the point must be between x 5 1.00 m and x 5 positive infinity. (d) Use the values given to find the point and show that it is consistent with your conceptual argument.

Two hard rubber spheres, each of mass m 5 15.0 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L 5 5.00 cm whose support points are a distance d 5 3.00 cm from each other as shown in Figure P15.59. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of u 5 10.0 with the vertical. Find the amount of charge on each sphere.

Two small beads having positive charges q1 5 3q and q2 5 q are fixed at the opposite ends of a horizontal insulating rod of length d 5 1.50 m. The bead with charge q1 is at the origin. As shown in Figure P15.60, a third small charged bead is free to slide on the rod. At what position x is the third bead in equilibrium?

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 24.00 mC. Find the electric field at (a) r 5 1.00 cm, (b) r 5 3.00 cm, (c) r 5 4.50 cm, and (d) r 5 7.00 cm from the center of this charge configuration.

Three identical point charges, each of mass m 5 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 5 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 3 10217 J. (a) What is the magnitude of the uniform electric field (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 5 9 550 m/s into a region where a uniform electric field of magnitude E 5 720 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 flight for each of the two trajectories.