The divergence theorem explains that the total outward flux of a vector field A through a closed surface S is the same as the volume integral for the divergence of A. What does a closed surface mean in this theorem? Explain.
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The divergence theorem explains that the total outward flux of a vector field A through a closed surface S is the same as the volume integral for the divergence of A. What does a closed surface mean in this theorem? Explain.
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- Use Gauss's Law in to solve problems 1 to 3, showing and justifying your steps and using related conceptual diagrams and mathematical formula as needed. (1) Find the Electric Field outside an infinitely long slab with uniform charge density sigma. (2): Find the Electric Field (a) outside and (b) inside a non-conducting solid sphere with uniformly distributed charge Q. (3) Find the Electric Field outside an infinitely long rod with uniform charge density lambda.Problem An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as DE - dÃ= Q piR2L We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain E A = qenc / epsilon0 (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: qenc = Qr2/R2 On the other hand, the Gaussian surface inside the wire is given by A = 2pirL Using Equation 1, the electric field in simplified form is E = Qr / 2piR2Lepsilono Case 2: Outside the wire Since, r falls outside the wire, then, all the charge must be enclosed, thus qenc = On the other hand, the Gaussian surface…A nonconducting, thin plane sheet of charge carries a uniform charge per unit area of 6.25 pC/m2 as in the figure below. Gaussian sur face E for0 Gaussian surface (a) Find the electric field at a distance of 9.12 cm from the plate. Your response differs from the correct answer by more than 10%. Double check your calculations (b) Explain whether your result changes as the distance from the sheet is varied.
- If possible please box each corresponding answer. Thanks.Consider an infinitely long cylinder with radius R. The cylinder is an insulator and it is positively charged, the charge per unit of length is A. (Hint: because it is an insulator you should assume that the charge is spread uniformly across its entire volume). By reflecting on the symmetry of the charge distribution of the system, determine what a) the E-field lines look like around the cylinder. Describe the E-field in words and with a simple sketch. In order to give a complete description of the E-field lines make two sketches: i) one with a side view of the cylinder, ii) one with a cross-sectional view of the cylinder. Make sure to also show the direction of the E-field lines. b) (-- . the figure. Your goal for this part is to properly use Gauss' law to calculate the electric field at point P. Follow the 5 steps below. Consider a point P outside the cylinder, at a distance d from its axis, d > R, as shown inUse gauss' law to explain
- If the electric field is not collinear with the normal unit vector of the surface, which of the following trigonometric functions is associated to the smallest angle between the electric field and the normal unit vector? O cosecant O cosine; O the answer cannot be found on the other choices; O cotangent;A Gaussian surface is a closed surface in three-dimensional space through which the electric flux is calculated.Given a spherical Gaussian surface that has a radius of 0.5 meters and encloses 30 electrons. A.Find the value of the electric flux through this surface B.From the calculated value of the electric flux,determine the value of the electric field at a distance equal to 0.6 meters from the center of the surface. Please answer all my queries.Thank you in advance.God bless!Find the electric field a distance z over the center of a charged disk. List the first four steps to solve this problem! Use metacognition, i.e. validate your result