A point charge q is located at the origin. Consider the electric field flux through a circle a distance 3 μm from 9, subtending an angle 20, where 0 = 30°. The electric flux is equal to A. Find the proportionality constant A in the following cases: E0 a. Calculate the flux through the flat disk bounded by the circle. 0.66 X b. Calculate the flux through the spherical cap (with the sphere centered at the origin) bounded by the circle. 0.66 X
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- A point charge is located at the origin. Centered along the x axis is a cylindrical closed surface of radius 10 cm with one end surface located at x = 2 m and the other end surface ļocated at x = 2.5 m. If the magnitude of the electric flux through the surface at x = 2 m is 4 N.m/C, what is the magnitude of the electric flux through the surface at x = 2.5 m? Select one: 2. a. 1.8 N. m/C 2 b. 2.56 N. m /C C. 5.0 N. m /C d. 1.0 N. m/C e. 4.0 N. m /C O O Oa) Find the surface charge density σ2 of the cylindrical shell of radius R2. (Note the unit in the input box and the sign of charges.) Surface charge density σ2Give your answer up to at least three significance digits. b) Find an expression of electric field at rmm from the center where R1<r<R2. Assume the cylinder has a length L and L is very long so that electric field is uniform. Consider that the insulating material between the cylinders is air. (Hint : use Gauss's law and cylindrical Gaussian surface with radius r.) Magnitude of the electric field at r=0.76mm Give your answer up to at least three significance digits. c) Calculate absolute value of the potential difference between the wire and the cylinder. Absolute value of the potential difference Give your answer up to at least three significance digits. d) Calculate the capacitance C for this cylindrical system. Assume that the length of the cylinder is L=17cm. Capacitance C for this cylindrical system Give your…Positive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere. a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p. b) Determine the electric field, E(r), for r > R (outside the sphere). c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere (r = R)? d) What is the energy stored in this electric charge configuration?
- A cube has one corner at the origin and the opposite corner at the point (L,L,L). The sides of the cube are parallel to the coordinate planes. The electric field in and around the cube is given by E⃗=(a+bx)i^+cj^. Find the total electric flux ΦE through the surface of the cube. Express your answer in terms of a b c L What is the net charge qq inside the cube? Express your answer in terms of a b c L ϵ0Charge is distributed throughout a spherical volume of radius R with a density p = ar², where a is a constant (of unit C/m³, in case it matters). Determine the electric field due to the charge at points both inside and outside the sphere, following the next few steps outlined. Hint a. Determine the total amount of charge in the sphere. Hint for finding total charge Qencl = (Answer in terms of given quantities, a, R, and physical constants ke and/or Eg. Use underscore ("_") for subscripts, and spell out Greek letters.) b. What is the electric field outside the sphere? E(r> R) = c. What is the electric field inside the sphere? Hint for E within sphere #3 Question Help: Message instructor E(r < R) = Submit Question E с $ 4 R G Search or type URL % 5 T ^ MacBook Pro 6 Y & 7 U * 8 9 0 0An insulating sphere of radius a is placed at the center of a spherical conductor whose inner radius is b and outer radius is c (see figure). The +Q charge is uniformly distributed throughout the insulator sphere, while the spherical shell is -Q charged. Find the electric field strength E as a function of the radial distance r, d. outside the shell (r>c) e. How much charge on the inner surface of the spherical conductor (r= b), and how much on the outer surface of the spherical conductor (r = c)?
- An electric field has a uniform value (doesn't change with position) that can be described by the following equation: E = (Aĵ + B k) N/C where A and B are given by the values below. A = 1.35 B = 1.80 There is a flat circular surface that is in the x-y plane and centered at the origin point (0,0,0). This surface has a radius of 1.65 m. Calculate the magnitude of the electric flux through the surface due to the electric field described above. Your units should be Nm²/C.Q.1. Given a uniform electric field É = 5 × 10³ î N/C. Find the flux of this field through a square of side 10 cm on a side whose plane is parallel to the y-z plane. What would be the flux through the same square if the plane makes a 30° angle with the x-axis ?A non-conducting spherical shell has an inner radius & and an outer radius 28. There are no charges at r<& wherer is the distance from the center of the sphere. A total charge is distributed uniformly in the volume of the shell (between r=R and r=2R) Find the magnitude of the electric field at r=1718. Express your answer in units of using two decimal R² kQ places
- Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m² /C². Vacuum permitivity, eo = 8.854 x 10-12 F/m. Magnitude of the Charge of one electron, e = -1.60217662 x 10-19 C. Mass of one electron, me = 9.10938356 x 10 31 kg. Unless specified otherwise, each symbol carries their usual meaning. For example, uC means micro coulomb. Suppose you have q = 20 µC charge placed at the orign of your coordinate system.What would be the electric field for z0 << R and z0 >> R for the following integral? The integral is the answer to the following question: "A uniformly charged disk with charge Q and radius R sits in the xy-plane with its center at theorigin. Take z0 to be some point on the positive z-axis. What is the electric field at z0? Leave your answer in the form of a well-defined definite integral."A positively charged cylinder has a uniform volume charge density. Height l is larger than its radius a (1»a). a P a. When Point P is very close to the surface of the cylinder (1>r>a), the electric field there can be derived by treating the cylinder as an = Eŝ. infinitely long one. Suppose that we already measure the electric field at P as charge density in terms of E and a (ŝ is the radial unit vector in the cylindrical coordinate system as defined in the Equation: now use the Gauss's law to find the volume cos o â + sin ø ŷ, - sin ø Âx + cos ø ŷ, î. b. Now we move the detector from Point P to Point Q, which is so far away from the cylinder (R>l>a), that the cylinder can be treated as a point. Based on result in Part (a), find out the electric field at Q (Note that OQ is in the x direction.)