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physics
electricity and magnetism

Fundamentals of Physics 10th Extended edition Jearl Walker, Halliday Resnick - Solutions

Find (a) "north cross west," (b) "down dot south," (c) "east cross up," (d) "west dot west," and (e) "south cross south." Let each "vector" have unit magnitude.
A vector , with a magnitude of 8.0 m, is added to a vector , which lies along an x axis. The sum of these two vectors is a third vector that lies along the y axis and has a magnitude that is twice the magnitude of . What is the magnitude of ?
A man goes for a walk, starting from the origin of an xyz coordinate system, with the xy plane horizontal and the x axis eastward. Carrying a bad penny, he walks 1300 m east, 2200 m north, and then drops the penny from a cliff 410 m high.(a) In unit-vector notation, what is the displacement of the
In Fig. 3-38, the magnitude of is 4.3, the magnitude of is 5.4, and ( = 46(. Find the area of the triangle contained between the two vectors and the thin diagonal line.
A magnetic field forces an electron to move in a circle with radial acceleration 3.0 ( 1014 m/s2. (a) What is the speed of the electron if the radius of its circular path is 15 cm? (b)What is the period of the motion?
A graphing surprise. At time t = 0, a burrito is launched from level ground, with an initial speed of 16.0 m/s and launch angle. Imagine a position vector continuously directed from the launching point to the burrito during the flight. Graph the magnitude r of the position vector for (a) (0 = 40.0(
A cannon located at sea level fires a ball with initial speed 82 m/s and initial angle 45°.The ball lands in the water after traveling a horizontal distance 686 m. How much greater would the horizontal distance have been had the cannon been 30 m higher?
Some state trooper departments use aircraft to enforce highway speed limits. Suppose that one of the airplanes has a speed of 135 mi/h in still air. It is flying straight north so that it is at all times directly above a north-south highway. A ground observer tells the pilot by radio that a 70.0
A helicopter is flying in a straight line over a level field at a constant speed of 6.20 m/s and at a constant altitude of 9.50 m. A package is ejected horizontally from the helicopter with an initial velocity of 12.0 m/s relative to the helicopter and in a direction opposite the helicopter's
A car travels around a flat circle on the ground, at a constant speed of 12.0 m/s. At a certain instant the car has an acceleration of 3.00 m/s2 toward the east.What are its distance and direction from the center of the circle at that instant if it is traveling (a) clockwise around the circle and
You throw a ball from a cliff with an initial velocity of 15.0 m/s at an angle of 20.0° below the horizontal. Find (a) its horizontal displacement and (b) its vertical displacement 2.30 s later.
A baseball is hit at Fenway Park in Boston at a point 0.762 m above home plate with an initial velocity of 33.53 m/s directed 55.0° above the horizontal. The ball is observed to clear the 11.28-m-high wall in left field (known as the "green monster") 5.00 s after it is hit, at a point just inside
A transcontinental flight of 4350 km is scheduled to take 50 min longer westward than eastward. The airspeed of the airplane is 966 km/h, and the jet stream it will fly through is presumed to move due east. What is the assumed speed of the jet stream?
If the 1 kg standard body has an acceleration of 2.00 m/s2 at 20.0( to the positive direction of an x axis, what are (a) the x component and (b) the y component of the net force acting on the body, and (c) what is the net force in unit-vector notation?
In Fig. 5-59, 4.0 kg block A and 6.0 kg block B are connected by a string of negligible mass. Force = (12 N) acts on block A; force = (24 N) acts on block B. What is the tension in the string?
A 2.00 kg object is subjected to three forces that give it an acceleration = - (8.00 m/s2 + (6.00 m/s2) . If two of the three forces are = (30.0 N) + (16.0 N) and = - (12.0 N) + (8.00 N) , find the third force.
A roller-coaster car at an amusement park has a mass of 1200 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 18 m, assume that its speed is not changing. At the top of the hill, what are the (a) magnitude FN and (b) direction (up or down) of the
Continuation of Problems 8 and 37. Another explanation is that the stones move only when the water dumped on the playa during a storm freezes into a large, thin sheet of ice. The stones are trapped in place in the ice. Then, as air flows across the ice during a wind, the air-drag forces on the ice
A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches 30(, the box starts to slip, and it then slides 2.5 m
In Fig. 7-32, a constant force of magnitude 82.0 N is applied to a 3.00 kg shoe box at angle ( = 53.0(, causingthe box to move up a frictionless ramp at constant speed. How much work is done on the box by when the box has moved through vertical distance h = 0.150 m?
(b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement?
In Problem 6, what are the magnitudes of (a) the horizontal component and (b) the vertical component of the net force acting on the block at point ? (c) At what height h should the block be released from rest so that it is on the verge of losing contact with the track at the top of the loop? (On
The string in Fig. 8-38 is L = 120 cm long, has a ball attached to one end, and is fixed at its other end. The distance d from the fixed end to a fixed peg at point P is 75.0 cm. When the initially stationary ball is released with the string horizontal as shown, it will swing along the dashed arc.
A conservative force = (6.0x - 12) N, where x is in meters, acts on a particle moving along an x axis.The potential energy U associated with this force is assigned a value of 27 J at x = 0. (a) Write an expression for U as a function of x, with U in joules and x in meters. (b) What is the maximum
In Fig. 8-45, a chain is held on a frictionless table with onefourth of its length hanging over the edge. If the chain has length L = 28 cm and mass m = 0.012 kg, how much work is required to pull the hanging part back onto the table?
In Fig. 8-46, a spring with k = 170 N/m is at the top of a frictionless incline of angle ( = 37.0(. The lower end of the incline is distance D = 1.00 m from the end of the spring, which is at its relaxed length. A 2.00 kg canister is pushed against the spring until the spring is compressed 0.200 m
In Fig. 8-42, a block of mass m = 3.20 kg slides from rest a distance d down a frictionless incline at angle ( = 30.0( where it runs into a spring of spring constant 431 N/m. When the block momentarily stops, it has compressed the spring by 21.0 cm. What are (a) distance d and (b) the distance
An unmanned space probe (of mass m and speed v relative to the Sun) approaches the planet Jupiter (of mass M and speed VJ relative to the Sun) as shown in Fig. 9-84. The spacecraft rounds the planet and departs in the opposite direction. What is its speed (in kilometers per second), relative to the
A cue stick strikes a stationary pool ball, with an average force of 32 N over a time of 14 ms. If the ball has mass 0.20 kg, what speed does it have just after impact?
Figure 9-35 shows a three-particle system, with masses m1 = 3.0 kg, m2 = 4.0 kg, and m3 = 8.0 kg. The scales on the axes are set by xs = 2.0 m and ys = 2.0 m. What are (a) The x coordinate and (b) The y coordinate of the system's center of mass? (c) If m3 is gradually increased, does the center of
In Fig. 9-61, a ball of mass m = 60 g is shot with speed vi = 22 m/s into the barrel of a spring gun of mass M = 240 g initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. Assume that the increase in thermal energy due to
Starting from rest, a wheel has constant ( = 3.0 rad/s2. During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval?
A seed is on a turntable rotating at 33 1/3 rev/min, 6.0 cm from the rotation axis.What are (a) the seed's acceleration and (b) the least coefficient of static friction to avoid slippage? (c) If the turntable had undergone constant angular acceleration from rest in 0.25 s, what is the least
In Fig. 10-31, wheel A of radius rA = 10 cm is coupled by belt B to wheel C of radius rC = 25 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s2. Find the time needed for wheel C to reach an angular speed of 100 rev/min, Assuming the belt does not slip. (If the
Figure 10-35 shows three 0.0100 kg particles that have been glued to a rod of length L = 6.00 cm and negligible mass. The assembly can rotate around a perpendicular axis through point O at the left end. If we remove one particle (that is, 33% of the mass), by what percentage does the rotational
In Fig. 10-41, block 1 has mass m1 = 460 g, block 2 has mass m2 = 500 g, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 5.00 cm. When released from rest, block 2 falls 75.0 cm in 5.00 s without the cord slipping on the pulley.(a) What is the magnitude
In Fig. 12-48, the driver of a car on a horizontal road makes an emergency stop by applying the brakes so that all four wheels lock and skid along the road. The coefficient of kinetic friction between tires and road is 0.40.The separation between the front and rear axles is L = 4.2 m, and the
In Fig. 12-7 and the associated sample problem, let the coefficient of static friction (s between the ladder and the pavement be 0.53. How far (in percent) up the ladder must the firefighter go to put the ladder on the verge of sliding?
Figure 12-55 shows the stress-strain curve for a material. The scale of the stress axis is set by s = 300, in units of 106 N/m2. What are (a) the Young's modulus and (b) the approximate yield strength for this material?
The system in Fig. 12-77 is in equilibrium. The angles are (1 =60° and (2 = 20°, and the ball has mass M = 2.0 kg. What is the tension in (a) string ab and (b) string bc?
A trap door in a ceiling is 0.91 m square, has a mass of 11 kg, and is hinged along one side, with a catch at the opposite side. If the center of gravity of the door is 10 cm toward the hinged side from the door's center, what are the magnitudes of the forces exerted by the door on (a) the catch
In Fig. 13-37a, particle A is fixed in place at x = 0.20 m on the x axis and particle B, with a mass of 1.0 kg, is fixed in place at the origin. Particle C (not shown) can be moved along the x axis, between particle B and x = (. Figure 13-37 b shows the x component Fnet,x of the net gravitational
In Fig. 14-51, the fresh water behind a reservoir dam has depth D = 15 m. A horizontal pipe 4.0 cm in diameter passes through the dam at depth d = 6.0 m. A plug secures the pipe opening.(a) Find the magnitude of the frictional force between plug and pipe wall.(b) The plug is removed. What water
The L-shaped fish tank shown in Fig. 14-33 is filled with water and is open at the top. If d = 5.0 m, what is the (total) force exerted by the water (a) on face A and (b) on face B?
In Fig. 14-37, a spring of spring constant 3.00 ( 104 N/m is between a rigid beam and the output piston of a hydraulic lever. An empty container with negligible mass sits on the input piston. The input piston has area Ai, and the output piston has area 18.0Ai. Initially the spring is at its rest
The tension in a string holding a solid block below the surface of a liquid (of density greater than the block) is T0 when the container (Fig. 14-57) is at rest. When the container is given an upward acceleration of 0.250g, what multiple of T0 gives the tension in the string?
A 2.0 kg block is attached to the end of a spring with a spring constant of 350 N/m and forced to oscillate by an applied force F = (15 N) sin((dt), where (d = 35 rad/s. The damping constant is b = 15 kg/s. At t = 0, the block is at rest with the spring at its rest length. (a) Use numerical
For a simple pendulum, find the angular amplitude (m at which the restoring torque required for simple harmonic motion deviates from the actual restoring torque by 1.0%. (See "Trigonometric Expansions" in Appendix E.)
The coil in Fig. 28-50 carries current i 2.00 A in the direction indicated, is parallel to an xz plane, has 3.00 turns and an area of 4.00 x 103 m2, and lies in a uniform magnetic fieldWhat are?(a) The orientation energy of the coil in the magnetic field and (b) The torque (in unit-vector notation)
At one instant,is the velocity of a proton in a uniform magnetic field At that instant, what are?
Figure 28-56 shows a homo-polar generator, which has a solid conducting disk as rotor and which is rotated by a motor (not shown). Conducting brushes connect this emf device to a circuit through which the device drives current. The device can produce a greater emf than wire loop rotors because they
In Fig. 28-58, an electron of mass m, charge e, and low (negligible) speed enters the region between two plates of potential difference V and plate separation d, initially headed directly toward the top plate. A uniform magnetic field of magnitude B is normal to the plane of the figure. Find the
A particle of charge q moves in a circle of radius r with speed v. Treating the circular path as a current loop with an average current, find the maximum torque exerted on the loop by a uniform field of magnitude B.
In a Hall-effect experiment, express the number density of charge carriers in terms of the Hall-effect electric field magnitude E, the current density magnitude J, and the magnetic field magnitude B.
An electron that is moving through a uniform magnetic field has velocityWhen it experiences a
A wire with current i = 3.00 A is shown in Fig. 29-53. Two semi-infinite straight sections, both tangents to the same circle, are connected by a circular arc that has a central angle Î¸ and runs along the circumference of the circle. The arc and the two straight sections all lie in the
The current-carrying wire loop in Fig. lies all in one plane and consists of a semicircle of radius 10.0 cm, a smaller semicircle with the same center, and two radial lengths. The smaller semicircle is rotated out of that plane by angle u, until it is perpendicular to the plane (Fig. 29-60b).
A long solenoid with 10.0 turns / cm and a radius of 7.00 cm carry a current of 20.0 mA. A current of 6.00A exists in a straight conductor located along the central axis of the solenoid.(a) At what radial distance from the axis will the direction of the resulting magnetic field be at 45.0° to the
Figure 30-78 shows a wire that has been bent into a circular arc of radius r = 24.0 cm, centered at O.A straight wire OP can be rotated about O and makes sliding contact with the arc at P. Another straight wire OQ completes the conducting loop. The three wires have cross-sectional area 1.20 mm2 and
A circular region in an xy plane is penetrated by a uniform magnetic field in the positive direction of the z axis. The field's magnitude B (in teslas) increases with time t (in seconds) according to B at, where a is a constant. The magnitude E of the electric field set up by that increase in the
In Fig. 30-62, & = 100 V, R1 = 10.0 Î© ,R2 = 20.0 Î©,R3 = 30.0 Î©, and L = 2.00 H. Immediately after switch S is closed, what are (a) i1 and (b) i2? (Let currents in the indicated directions have positive values and currents in the opposite directions have negative
Suppose the emf of the battery in the circuit shown in Fig. 30-16 varies with time t so that the current is given by i(t) 3.0 + 5.0t, where i is in amperes and t is in seconds. Take R = 4.0 Î© and L = 6.0 H, and find an expression for the battery emf as a function of t.
In the circuit of Fig. 30-76, R1 = 20 kÎ©, R2 = 20Î©, L = 50 mH, and the ideal battery has & = 40 V. Switch S has been open for a long time when it is closed at time t = 0. Just after the switch is closed, what are?(a) The current ibat through the battery(b) The rate dibat/dt?
In Fig. 31-28, R = 14.0Î©, C = 6.20 Î¼F, and L 54.0 mH, and the ideal battery has emf34.0 V. The switch is kept at a for a long time and then thrown to position b. What are the (a) frequency and (b) current amplitude of the resulting oscillations?
A single-loop circuit consists of a 7.20 resistor, a 12.0 H inductor, and a 3.20 mF capacitor. Initially the capacitor has a charge of 6.20 mC and the current is zero. Calculate the charge on the capacitor N complete cycles later for (a) N = 5, (b) N = 10, (c) N = 100.
A 1.50 μF capacitor is connected as in Fig. 31-10 to an ac generator with &m = 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is? (a) 1.00 kHz (b) 8.00 kHz
A 50.0 Î© resistor is connected as in Fig. 31-8 to an ac generator with &m = 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is?(a) 1.00 kHz(b) 8.00 kHz
An ac generator has emf & = &m sin(ωdt - π/4), where &m = 30.0 V and ωd = 350 rad/s. The current produced in a connected circuit is i(t) = I sin(ωt 3π/4), where I = 620 mA. At what time after t = 0 does (a) The generator emf first reaches a maximum (b) The current first reach a maximum? (c)
In Fig. 31-7, set R = 200 Î©, C = 70.0 Î¼F, L = 230 mH, fd = 60.0 Hz, and &m = 36.0 V. What are?(a) Z,(b) Ï•(c) I?(d) Draw a phasor diagram.
In Fig. 31-7, R = 15.0 Î©, C = 4.70 Î¼F, and L = 25.0 mH. The generator provides an emf with rms voltage 75.0 V and frequency 550 Hz.(a) What is the rms current? What is the rms voltage across(b) R,(c) C,(d) L,(e) C and L together, and(f) R, C, and L together? At what
At what rate must the potential difference between the plates of a parallel-plate capacitor with a 2.0 μF capacitance be changed to produce a displacement current of 1.5 A?
The circuit in Fig. 32-31 consists of switch S, a 12.0 V ideal battery, a 20.0 M resistor, and an air-filled capacitor. The capacitor has parallel circular plates of radius 5.00 cm, separated by 3.00 mm. At time t = 0, switch S is closed to begin charging the capacitor. The electric field between
Uniform displacement-current density figure 32-30 shows a circular region of radius R = 3.00 cm in which a displacement current is directed out of the page. The displacement current has a uniform density of magnitude Jd = 6.00 A/m2.What is the magnitude of the magnetic field due to the displacement
Non-uniform displacement-current density figure 32-30 shows a circular region of radius R = 3.00 cm in which a displacement current is directed out of the page. The magnitude of the density of this displacement current is Jd = (4.00 A/m2) (1 - r/R), where r is the radial distance (r ‰¤
Non-uniform displacement current figure 32-30 shows a circular region of radius R = 3.00 cm in which a displacement current id is directed out of the figure. The magnitude of the displacement current is id = (3.00 A) (r/R), where r is the radial distance (r ‰¤ R) from the center. What
As a parallel-plate capacitor with circular plates 20 cm in diameter is being charged, the current density of the displacement current in the region between the plates is uniform and has a magnitude of 20 A/m2. (a) Calculate the magnitude B of the magnetic field at a distance r = 50 mm from the
In Fig. 32-34, a uniform electric field collapses. The vertical axis scale is set by Es = 6.0 x 105 N/C, and the horizontal axis scale is set by ts = 12.0 Î¼s. Calculate the magnitude of the displacement current through a 1.6 m2 area perpendicular to the field during each of the time
A sample of the paramagnetic salt to which the magnetization curve of Fig. 32-14 applies is to be tested to see whether it obeys Curie's law. The sample is placed in a uniform 0.50 T magnetic field that remains constant throughout the experiment. The magnetization M is then measured at temperatures
A sample of the paramagnetic salt to which the magnetization curve of Fig. 32-14 applies is held at room temperature (300 K). At what applied magnetic field will the degree of magnetic saturation of the sample be?(a) 50%(b) 90%?(c) Are these fields attainable in the laboratory.
A parallel-plate capacitor with circular plates of radius R = 16 mm and gap width d = 5.0 mm has a uniform electric field between the plates. Starting at time t = 0, the potential difference between the two plates is V = (100 V)e-t/τ, where the time constant τ = 12 ms. At radial distance r =
A parallel-plate capacitor with circular plates of radius 55.0 mm is being charged. At what radius (a) Inside and (b) Outside the capacitor gap is the magnitude of the induced magnetic field equal to 50.0% of its maximum value?
A sample of the paramagnetic salt to which the magnetization curve of Fig. 32-14 applies is immersed in a uniform magnetic field of 2.0 T. At what temperature will the degree of magnetic saturation of the sample be?(a) 50%(b) 90%
What are the measured components of the orbital magnetic dipole moment of an electron with? (a) ml = 3 (b) ml = -4
The magnetic component of a polarized wave of light is given by(a) In which direction does the wave travel?(b) Parallel to which axis is it polarized, (c) What is its intensity?(d) Write an expression for the electric field of the wave, including a value for the angular wave number.(e) What is the
In Fig. 33-78, where n1 = 1.70, n2 = 1.50, and n3 = 1.30, light refracts from material 1 into material 2. If it is incident at point A at the critical angle for the interface between materials 2 and 3, what are?(a) The angle of refraction at point B(b) The initial angle Î¸? If, instead,
In Fig. 33-41, a beam of un-polarized light, with intensity 43 W/m2, is sent into a system of two polarizing sheets with polarizing directions at angles Î¸1 = 70° and Î¸ 2 = 90° to the y axis. What is the intensity of the light transmitted by the system?
In Fig. 33-50a, a beam of light in material 1 is incident on a boundary at an angle Î¸1 = 40°. Some of the light travels through material 2, and then some of it emerges into material 3. The two boundaries between the three materials are parallel. The final direction of the beam
In Fig. 33-51, light is incident at angle Î¸1 40.1 on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If n1 = 1.30, n2 = 1.40, n3 = 1.32,
In Fig. 33-52a, a beam of light in material 1 is incident on a boundary at an angle of Î¸1 = 30°.The extent of refraction of the light into material 2 depends, in part, on the index of refraction n2 of material 2. Figure 33-52b gives the angle of refraction Î¸2 versus n2
Figure 33-74 shows a cylindrical resistor of length l, radius a, and resistivity r, carrying current i.(b) Show that the rate P at which energy flows into the resistor through its cylindrical surface, calculated by integrating the Poynting vector over this surface, is equal to the rate at which
A thin, totally absorbing sheet of mass m, face area A, and specific heat cs is fully illuminated by a perpendicular beam of a plane electromagnetic wave. The magnitude of the maximum electric field of the wave is Em. What is the rate dT/dt at which the sheet's temperature increases due to the
Two polarizing sheets, one directly above the other, transmit p% of the initially un-polarized light that is perpendicularly incident on the top sheet. What is the angle between the polarizing directions of the two sheets?
A laser beam of intensity I reflect from a flat, totally reflecting surface of area A, with a normal at angle θ with the beam. Write an expression for the beam's radiation pressure pr (θ) on the surface in terms of the beam's pressure when θ = 0o.
A laser beam of intensity I reflect from a flat, totally reflecting surface of area A, with a normal at angle θ with the beam. Write an expression for the beam's radiation pressure pr (θ) on the surface in terms of the beam's pressure when θ = 0o.
A beam of intensity I reflect from a long, totally reflecting cylinder of radius R; the beam is perpendicular to the central axis of the cylinder and has a diameter larger than 2R.What is the beam's force per unit length on the cylinder?
In Fig. 34-52, an object is placed in front of a converging lens at a distance equal to twice the focal length f1 of the lens. On the other side of the lens is a concave mirror of focal length f2 separated from the lens by a distance 2(f1 + f2). Light from the object passes rightward through the
A pinhole camera has the hole a distance 12 cm from the film plane, which is a rectangle of height 8.0 cm and width 6.0 cm. How far from a painting of dimensions 50 cm by 50 cm should the camera be placed so as to get the largest complete image possible on the film plane?
Light travels from point A to point B via reflection at point O on the surface of a mirror. Without using calculus, show that length AOB is a minimum when the angle of incidence θ is equal to the angle of reflection ϕ.
In Fig. 35-34, a light ray is incident at angle Î¸1 = 50° on a series of five transparent layers with parallel boundaries. For layers 1 and 3, L1 = 20 mm, L3 = 25 mm, n1 = 1.6, and n3 =1.45.(a) At what angle does the light emerge back into air at the right?(b) How much time does the light take
In Fig. 35-59, an oil drop (n = 1.20) floats on the surface of water (n = 1.33) and is viewed from overhead when illuminated by sunlight shining vertically downward and reflected vertically upward.(a) Are the outer (thinnest) regions of the drop bright or dark? The oil film displays several spectra

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