The cube in the figure (Figure 1)has sides of length L = 10.0 cm. The electric field is uniform, has a magnitude E = 4.00×103 N/C, and is parallel to the xy-plane at an angle of 36.9∘ measured from the +x− axis toward the +y - axis. Figure 1 of 1 Part A What is the electric flux through the cube face S1 ? Φ1 = N⋅m2 /C Submit Request Answer Part B What is the electric flux through the cube face S2 ? Φ2 = N⋅m2 /C Submit Request Answer Part C What is the electric flux through the cube face S3 ? Φ3 = N⋅m2 /C Submit Request Answer Part D What is the electric flux through the cube face S4 ? Submit Request Answer Part E What is the electric flux through the cube face S5 ? Submit Request Answer Part F What is the electric flux through the cube face S6 ? Submit Request Answer Part G What is the total electric flux through all faces of the cube? Submit Request Answer
Negative charge -Q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin. Part A Find the x-component of the net electric field at the origin. Express your answer in terms of the variables Q, a, and constant k. Submit Request Answer Part B Find the y-component of the net electric field at the origin. Express your answer in terms of the variables Q, a, and constant k.
The three small spheres shown in (Figure 1) carry charges q1 = 4.30 nC, q2 = −7.50 nC, and q3 = 2.40 nC. Figure 1 of 1 Part A Find the net electric flux through the closed surface S1 shown in cross section in the figure. Express your answer in newton times meters squared per coulomb. Submit Request Answer Part B Find the net electric flux through the closed surface S2 shown in cross section in the figure. Express your answer in newton times meters squared per coulomb. Part C Find the net electric flux through the closed surface S3 shown in cross section in the figure. Express your answer in newton times meters squared per coulomb. Submit Request Answer Part D Find the net electric flux through the closed surface S4 shown in cross section in the figure. Express your answer in newton times meters squared per coulomb. art E Find the net electric flux through the closed surface S5 shown in cross section in the figure. Express your answer in newton times meters squared per coulomb. Φ = N⋅m2 /C Submit Request Answer Part F Do your answers to parts A through E depend on how the charge is distributed over each small sphere? depend do not depend
A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 19.0 cm, giving it a charge of −13.0 μC. Part A Find the electric field just inside the paint layer. Express your answer using three significant figures. Part B Find the electric field just outside the paint layer. Express your answer using three significant figures. Submit Request Answer Part C Find the electric field 9.00 cm outside the surface of the paint layer. Express your answer using three significant figures. |E| =
A conductor with an inner cavity, like that shown in (Figure 1), carries a total charge of +5.30 nC. The charge within the cavity, insulated from the conductor, is q = −6.60 nC. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of A conductor with a cavity. Figure 1 of 1 Part A How much charge is on the inner surface of the conductor? Submit Request Answer Part B How much charge is on the outer surface of the conductor?
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +α, where α is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +α. Part A Calculate the electric field in terms of α and the distance r from the axis of the tube for r < a. Express your answer in terms of the variables α, r, and constant ϵ0. Part B Calculate the electric field in terms of α and the distance r from the axis of the tube for a < r < b. Express your answer in terms of the variables α, r, and constant ϵ0. Submit Request Answer Part C Calculate the electric field in terms of α and the distance r from the axis of the tube for r > b. Express your answer in terms of the variables α, r, and constant ϵ0. Part D What is the charge per unit length on the inner surface of the tube? Enter your answer numerically. Submit Request Answer Part E What is the charge per unit length on the outer surface of the tube? Enter your answer numerically.
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d ( Figure 1). The inner shell has total charge +2q, and the outer shell has charge −2q. Figure 1 of 1 Part A Calculate the magnitude of the electric field in terms of q and the distance r from the common center of the two shells for r < a. Express your answer in terms of the given quantities, and appropriate constants. Submit Request Answer Part B Calculate the magnitude of the electric field for a < r < b. Express your answer in terms of the given quantities, and appropriate constants. Part C Calculate the magnitude of the electric field for b < r < c. Express your answer in terms of the given quantities, and appropriate constants. E3 = Part D What is the direction of the electric field for b < r < c ? toward the center outward the center Submit Request Answer Part E Calculate the magnitude of the electric field for c < r < d. Express your answer in terms of the given quantities, and appropriate constants. E4 = Part F Calculate the magnitude of the electric field for r > d. Express your answer in terms of the given quantities, and appropriate constants. E5 = Part G What's the total charge on the inner surface of the small shell? Express your answer in terms of the given quantities, and appropriate constants. qi = Submit Request Answer Part H What's the total charge on the outer surface of the small shell? Express your answer in terms of the given quantities, and appropriate constants. qo = Part I What's the total charge on the inner surface of the large shell? Express your answer in terms of the given quantities, and appropriate constants. qi = Request Answer Part J What's the total charge on the outer surface of the large shell? Express your answer in terms of the given quantities, and appropriate constants.
A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r) = ρ0(1 − r/R) for r ≤ R ρ(r) = 0 for r ≥ R where ρ0 = 3Q/πR3 is a positive constant. Part A Find the total charge contained in the charge distribution. Express your answer in terms of some or all of the variables r, R, Q, and appropriate constants. Part B Obtain an expression for the electric field in the region r ≥ R. Express your answer in terms of some or all of the variables r, R, Q, and appropriate constants. E1 = Submit Request Answer Part C Obtain an expression for the electric field in the region r ≤ R. Express your answer in terms of some or all of the variables r, R, Q, and appropriate constants. Part D Find the value of r at which the electric field is maximum. Express your answer in terms of some or all of the variables r, R, Q, and appropriate constants. Submit Request Answer Part E Find the value of that maximum field. Express your answer in terms of some or all of the variables r, R, Q, and appropriate constants.
A long solenoid with n = 10 turns per centimeter has a cross-sectional area of 5.0 cm2 and carries a current of 0.25 A. A coil with five turns encircles the solenoid. When the current through the solenoid is turned off, it decreases to zero in 0.050 s. What is the average emf induced in the coil? μo = 4π×10−7 H/m 8.55×10^−5 1.57×10^−5 3.55×10^−5 2.57×10^−5
When a magnetic field is first turned on, the flux through a 20-turn loop varies with time according to Φm = 5.0t2 − 2.0t, where Φm is in milliwebers, t is in seconds, and the loop is in the plane of the page with the unit normal pointing outward. What is the emf induced in the loop as a function of time? −200t + 40 −400t + 20 −300t + 40 −100t + 80
The square armature coil of an alternating current generator has 200 turns and is 20.0 cm on side. When it rotates at 3600 rpm, its peak output voltage is 120 V. What is the frequency of the output voltage? 40 Hz 50 Hz 70 Hz 60 Hz
An automobile with a radio antenna 1.0 m long generates an emf, V1, since it is traveling at 100.0 km/h in a location where the Earth's horizontal magnetic field is 5.5×10−5 T. At some time, the radio antenna quadruples in length and the car begins traveling at a quarter of the original speed. What is the ratio of the new emf generated, V2, to the original emf, V1 ? 0.5 V1 0.75 V1 0.125 V1 1 V1
An automobile with a radio antenna 1.2 m long travels at 120.0 km/h in a location where the Earth's horizontal magnetic field is 5.6×10−5 T What is the maximum possible emf induced in the antenna due to this motion? emf = 1.5 V emf = 2.24 V emf = 2.24 mV emf = 0.15 V emf = 0.0015 V
An automobile with a radio antenna 1.0 m long travels at 100.0 km/h in a location where the Earth's horizontal magnetic field is 5.5×10−5 T. What is the maximum possible emf induced in the antenna due to this motion? 0.0015 V 0.0035 V 0.0030 V 0.0025 V
The density of gold is 19.5 g/cm3. Part A What is this value in kilograms per cubic meter? Express your answer in kilograms per cubic meter.
Part A How many years older will you be 1.30 billion seconds from now? (Assume a 365-day year. ) Express your answer in years. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Converting speed units.
In the fall of 2002, a group of scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a chain reaction. This element has a density of 19.5 g/cm3 For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Converting volume units. Part A What would be the radius of a sphere of this material that has a critical mass? Express your answer in centimeters.
The volume of a solid cylinder is given by V = πr2h, where r is the radius and h is the height. You measure the radius and height of a thin cylindrical wire and obtain the results r = 0.036 cm and h = 12.1 cm. Part A What do your measurements give for the volume of the wire in mm3 ? Use the correct number of significant figures in your answer. Express your answer in cubic millimeters.
A useful and easy-to-remember approximate value for the number of seconds in a year is π×107. Part A Determine the percent error in this approximate value. (There are 365.24 days in one year. ) Express your answer in percent.
Part A For the vectors A→ and B→ in the figure (Figure 1), use a scale drawing to find the magnitude of the vector sum A→ + B→. Express your answer in meters. Part B Find the direction of the vector sum A→ + B→. Express your answer in degrees. angle = ∘ counterclockwise from +x-axis Part C Find the magnitude of the vector difference A→−B→. Express your answer in meters. |A→−B→| = m Part D Find the direction of the vector difference A→−B→. Express your answer in degrees. Part E Use your answers to find the magnitude of −A→−B→. Express your answer in meters. |−A→−B→| = Part F Find the direction of −A→−B→. Express your answer in degrees. angle = ∘ counterclockwise from +x-axis Part G Find the magnitude of B→−A→. Express your answer in meters. Part H Find the direction of B→−A→. Express your answer in degrees. angle = ∘ counterclockwise from +x-axis Figure 1 of 1
Vector A→ has y-component Ay = +14.0 m. A→ makes an angle of 22.0∘ counterclockwise from the +y-axis. Part A What is the x-component of A→ ? Express your answer with the appropriate units. Submit Request Answer Part B What is the magnitude of A→ ? Express your answer with the appropriate units. A = Value Units
For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Using unit vectors. Figure 1 of 1 Part A Write the vector A→ in (Figure 1) in terms of the unit vectors i^ and j^. Express your answer in terms of the unit vectors i^ and j^. Use the 'unit vector' button to denote unit vectors in your answer. Express the coefficients in meters. Part B Write the vector B→ in the figure in terms of the unit vectors i^ and j^. Express your answer in terms of the unit vectors i^ and j^. Use the 'unit vector' button to denote unit vectors in your answer. Express the coefficients in meters. Part C Use unit vectors to express the vector C→, where C→ = 3.00 A→−4.00 B→. Express your answer in terms of the unit vectors i^ and j^. Use the 'unit vector' button to denote unit vectors in your answer. Express the coefficients in meters. Part D Find the magnitude of C→. Express your answer in meters. Part E Find the direction of C→. Express your answers in degrees. C = ∘ counterclockwise from +x-axis
For the vectors A→, B→, and C→ in (Figure 1), find the scalar products. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Calculating a scalar product. Figure 1 of 1 Part A Express your answer in square meters. Submit Request Answer Part B Express your answer in square meters. Submit Request Answer Part C Express your answer in square meters.
Part A Given two vectors A→ = 4.00 i^+7.00 j^ and B→ = 5.00 i^−2.00 j^, find the vector product A→×B→ (expressed in unit vectors). Express your answer in terms of the unit vectors i^, j^, and k^. Use the 'unit vector' button to denote unit vectors in your answer. A→×B→ = Submit Request Answer Part B What is the magnitude of the vector product?
Find the angle between each of the following pairs of vectors. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of finding an angle with scalar product. Part A A→ = −2.00 i^+6.00 j^ and B→ = 8.00 i^−3.00 j^. Express your answer in degrees. Part B A→ = 5.00 i^+5.00 j^ and B→ = 10.00 i^+6.00 j^. Express your answer in degrees. Submit Request Answer Part C A→ = −4.00 i^+2.00 j^ and B→ = 7.00 i^+14.00 j^. Express your answer in degrees. ϕ =
Recall that density is mass divided by volume, and consult the textbook as needed. Part B In about 5 billion years, at the end of its lifetime, our sun will end up as a white dwarf, having about the same mass as it does now, but reduced to about 15, 000 km in diameter. What will be its density at that stage? Express your answer in grams per cubic centimeter. Part B In about 5 billion years, at the end of its lifetime, our sun will end up as a white dwarf, having about the same mass as it does now, but reduced to about 15, 000 km in diameter. What will be its density at that stage? Express your answer in grams per cubic centimeter. Submit Request Answer Part C A neutron star is the remnant left after certain supernovae (explosions of giant stars). Typically, neutron stars are about 21 km in diameter and have around the same mass as our sun. What is a typical neutron star density in g/cm3 ? Express your answer in grams per cubic centimeter.
Vector A→ = 6.0 i^−4.0 k^. Part A Construct a unit vector that is parallel to A→. Enter the x, y, and z components of the vector separated by commas. ax, ay, az = Part B Construct a unit vector that is antiparallel to A→. Enter the x, y, and z components of the vector separated by commas. bx, by, bz = Submit Request Answer Part C Construct two unit vectors that are perpendicular to A→ and that have no y-component. Enter the x, y, and z components of the vectors separated by commas. cx, cy, cz, dx, dy, dz =
The work W done by a constant force F→ on an object that undergoes displacement s→ from point 1 to point 2 is W = F→⋅s→. For F in newtons (N) and s in meters (m), W is in joules ( J ). Part A If, during a displacement of the object, F→ has constant direction 60.0∘ above the −x-axis and constant magnitude 8.00 N and if the displacement is 0.800 m in the +x-direction, what is the work done by the force F→ ? Express your answer with the appropriate units.