10:10Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector CalculusDr. Trefor Bazett588views
16:51Using Gauss's Law to Calculate the Electric Flux and Charge in a Rectangular PrismPhysics Ninja874views
10:27Gauss's Law Problems - Conducting Sphere, Spherical Conductor, Electric Flux & Field, PhysicsThe Organic Chemistry Tutor489views
12:10Gauss Law Cylinder, Infinite Line of Charge, Electric Flux & Field, Physics ProblemsThe Organic Chemistry Tutor611views
Multiple ChoiceRank the flux through surfaces A, B and C in the figure below from greatest to smallest.897views21rank2comments
Multiple ChoiceA spherical, thin conducting shell of radius 8cm has a charge of –6C. If a 4C charge were placed at the center of the shell, what is the electric field 4 cm from the center? At 12 cm?914views14rank7comments
Multiple ChoiceA cube has sides equal to 4.0cm. The net flux through the cube is 12N·m2/C outward. Is the net charge in the cube positive, negative or zero?323views
Multiple ChoiceAn electric field with strength 3500N/C exists just outside a face of a large block of aluminum. If the electric field points towards the block, what is the surface charge density on the face of the block?283views
Multiple ChoiceA sphere of radius 4.0cm has a charge of 23nC evenly distributed throughout the sphere. What is the electric field strength 1.0cm from the center of the sphere?317views1comments
Multiple ChoiceAn insulating sphere of radius 4.0cm is in the center of a conducting spherical shell with inner radius of 5.0cm and outer radius of 7.0cm. The insulating sphere has a charge of −34nC and the conducting spherical shell has a net charge of 42nC. What is the total charge on the inner surface of the conducting spherical shell?318views
Multiple ChoiceA very long insulating cylinder has radius 4.7cm. Every 3.0m length of the cylinder contains a charge of 86nC evenly distributed throughout. What is the strength of the electric field 3.0cm from the axis of the cylinder?470views
Textbook QuestionThe nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15 m. (c) The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?1453views
Textbook QuestionThe nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15 m. (a) What is the electric field this nucleus produces just outside its surface?344views1rank
Textbook QuestionSome planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of −3.63×1016 N·m2/C at the planet's surface. Calculate:(c) the charge density on Mars, assuming all the charge is uniformly distributed over the planet's surface.301views1rank
Textbook QuestionSome planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of −3.63×1016 N·m2/C at the planet's surface. Calculate: (b) the electric field at the planet's surface (refer to the astronomical data inside the back cover);729views
Textbook QuestionSome planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of −3.63×1016 N·m2/C at the planet's surface. Calculate: (a) the total electric charge on the planet;298views2rank
Textbook QuestionA hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge density of +6.37×10−6 C/m2. A charge of −0.500 μC is now introduced at the center of the cavity inside the sphere. (c) What is the electric flux through a spherical surface just inside the inner surface of the sphere?443views
Textbook QuestionA hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge density of +6.37×10−6 C/m2. A charge of −0.500 μC is now introduced at the center of the cavity inside the sphere. (b) Calculate the strength of the electric field just outside the sphere?1568views
Textbook QuestionA hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge density of +6.37×10−6 C/m2. A charge of −0.500 μC is now introduced at the center of the cavity inside the sphere. (a) What is the new charge density on the outside of the sphere?424views
Textbook QuestionYou measure an electric field of 1.25×106 N/C at a distance of 0.150 m from a point charge. There is no other source of electric field in the region other than this point charge. (a) What is the electric flux through the surface of a sphere that has this charge at its center and that has radius 0.150 m? (b) What is the magnitude of this charge?1981views
Textbook QuestionCharge q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude E = 940 N/C. What are (b) the electric field at a distance of 2.00 cm from the sphere's center?502views
Textbook QuestionCharge q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude E = 940 N/C. What are (a) the volume charge density for the sphere?2054views1rank1comments
Textbook QuestionThe earth has a vertical electric field at the surface, pointing down, that averages 100 N/C. This field is maintained by various atmospheric processes, including lightning. What is the excess charge on the surface of the earth?300views
Textbook QuestionAn infinite slab of charge of thickness 2𝒵₀ lies in the xy-plane between 𝒵 = -𝒵₀ and 𝒵 = +𝒵₀ . The volume charge density p (C/m³) is a constant. (b) Find an expression for the electric field strength above the slab (𝒵 ≥ 𝒵₀).469views
Textbook QuestionA spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r ≤ R ) is E(r) = r⁴ Eₘₐₓ / R⁴ . (b) Find an expression for the volume charge density ρ(r) inside the ball as a function of r.321views
Textbook QuestionFIGURE EX24.18 shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a) 2q / ϵ₀ , (b) q / ϵ₀ , (c) 0, and (d) 5q / ϵ₀ .228views
Textbook QuestionA conductor with an inner cavity, like that shown in Fig. 22.23c, carries a total charge of +5.00 nC. The charge within the cavity, insulated from the conductor, is −6.00 nC. How much charge is on (a) the inner surface of the conductor and (b) the outer surface of the conductor?1288views
Textbook QuestionA very large, horizontal, nonconducting sheet of charge has uniform charge per unit area σ = 5.00×10−6 C/m2. (a) A small sphere of mass m = 8.00×10−6 kg and charge q is placed 3.00 cm above the sheet of charge and then released from rest. (b) What is q if the sphere is released 1.50 cm above the sheet?327views
Textbook QuestionA very large, horizontal, nonconducting sheet of charge has uniform charge per unit area σ = 5.00×10−6 C/m2. (a) A small sphere of mass m = 8.00×10−6 kg and charge q is placed 3.00 cm above the sheet of charge and then released from rest. (a) If the sphere is to remain motionless when it is released, what must be the value of q?922views
Textbook QuestionAn infinitely long cylindrical conductor has radius r and uniform surface charge density σ. (b) In terms of σ, what is the magnitude of the electric field produced by the charged cylinder at a distance r > R from its axis? (c) Express the result of part (b) in terms of λ and show that the electric field outside the cylinder is the same as if all the charge were on the axis.2500views1rank
Textbook QuestionAn infinitely long cylindrical conductor has radius r and uniform surface charge density σ. (a) In terms of σ and R, what is the charge per unit length λ for the cylinder?742views1rank
Textbook QuestionA 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. (a) Calculate the electric field in terms of α and the distance r from the axis of the tube for (i) r < a; (ii) a < r < b; (iii) r > b. Show your results in a graph of E as a function of R.779views1rank
Textbook QuestionA 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. (b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?1740views
Textbook Question"(II) Suppose the thick spherical shell of Problem 29 is a conductor. It carries a total net charge Q and at its center there is a point charge +q. What total charge is found on(b) the outer surface of the shell?"83views
Textbook Question(II) Suppose the thick spherical shell of Problem 29 is a conductor. It carries a total net charge Q and at its center there is a point charge +q. What total charge is found on(a) the inner surface of the shell and.88views
Textbook QuestionAn infinite cylinder of radius R has a linear charge density λ . The volume charge density (C/m³) within the cylinder (r ≤ R ) is p (r) = rp₀ / R, where p₀ is a constant to be determined. (b) The charge within a small volume dV is dq = p dV. The integral of p dV over a cylinder of length L is the total charge Q = λ L within the cylinder. Use this fact to show that p₀ = 3λ / 2πR² Hint: Let dV be a cylindrical shell of length L, radius r, and thickness dr. What is the volume of such a shell?264views
Textbook QuestionA 20-cm-radius ball is uniformly charged to 80 nC. (b) How much charge is enclosed by spheres of radii 5, 10, and 20 cm?272views
Textbook QuestionA proton orbits a long charged wire, making 1.0×10^6 revolutions per second. The radius of the orbit is 1.0 cm. What is the wire's linear charge density?265views
Textbook QuestionCALC A 12-cm-long thin rod has the nonuniform charge density λ(x)=(2.0 nC/cm)e−|x|/(6.0 cm) , where x is measured from the center of the rod. What is the total charge on the rod? Hint: This exercise requires an integration. Think about how to handle the absolute value sign.315views
Textbook QuestionCALC A rod of length L lies along the y-axis with its center at the origin. The rod has a nonuniform linear charge density λ=a|y|, where a is a constant with the units C/m^2. b. Determine the constant a in terms of L and the rod's total charge Q.362views
Textbook QuestionA thin rod of length L and total charge Q has the nonuniform linear charge distribution λ(x)=λ ₀x/L, where x is measured from the rod's left end. a. What is λ₀ in terms of Q and L?427views
Textbook QuestionThe electric field is constant over each face of the tetrahedron shown in FIGURE EX24.4. Does the box contain positive charge, negative charge, or no charge? Explain.112views
Textbook QuestionThe three parallel planes of charge shown in FIGURE P24.44 have surface charge densities ─ ½ η , η , and ─ ½ η. Find the electric fields EA (→ above E) to ED (→ above E) in regions A to D. The upward direction is the + y-direction.486views
Textbook QuestionCharges q₁ = -4Q and q2 = +2Q are located at 𝓍 = -a and 𝓍 = + a, respectively. What is the net electric flux through a sphere of radius 2a centered (a) at the origin and (b) at 𝓍 = 2a?252views
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