An infinite, uniformly charged sheet with surface charge density o cuts through a spherical Gaussian surface of radius R at a distance.x from its center, as shown in the figure below. The electric flux D through the Gaussian [B.H.U-2012] surface is 27 Ro (b) z (R² – x² )o (d) (c)
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- A thin, circular plate of radius B, uniform surface charge density, and total charge Q, is centered on the origin and lies in the x-y plane. What is the electric flux ΦE through a sphere of radius r, also centered on the origin, as a function of r? Consider both (a.) r > B and (b.) r < B:Solve the following:a. Find the flux through a spherical Gaussian surface of radius a= 1 m surrounding a charge of 8.85 pC.b. Find the value of the electric field at a distance r= 10 cm fromthe center of a non-conducting sphere of radius R= 1 cm whichhas an extra positive charge equal to 7 C uniformly distributedwithin the volume of the sphere.A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.
- calculate the flux of the vector field through the given surface. ~F = z ~k through a square of side length 5 in the plane z = 2. The square is centered on the z-axis, has sides parallel to the axes, and is oriented in the positive z-direction.Consider an infinitesimal segment located at an angular position θ on the semicircle, measured from the lower right corner of the semicircle at x=a, y=0. (Thus θ=π2 at x=0, y=a and θ=π at x=−a, y=0.) What are the x- and y- components of the electric field at point P (dEx and dEy) produced by just this segment? Express your answers separated by a comma in terms of some, all, or none of the variables Q, a, θ, dθ, and the constants k and π.Consider two concentric insulating cylinders of infinite length. The inner cylinder is solid with radius R, while the outer cylinder is a hollow shell with inner radius a and outer radius b. Both cylinders have the same volume charge density of +ρ. Using Gauss’s Law, find the electric field as a function of r (where r= 0 at the central axis) in the interval a≤r < b. Note: Your final equation should be in terms of given parameters of ρ,a,b,R, and r.
- For problem 7, calculate the total flux through the one side of the cube in kNm2/C for a particle with a charge 3.39 uC at the center of the cube.(5 sig. figs.)A thin straight infinitely long conducting wire having charge density X is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.In free space, let D = 8xyz4ax + 4x2z4ay + 16x2yz3 az pC/m2.Find the total electric flux passing through the rectangularsurface z = 2, 0 < x < 2, 1 < y < 3, in the az direction. Find Eat P(2, −1, 3).
- Consider the three-dimensional conductor in the figure, that has a hole in the center. The conductor has an excess charge 7.2 μC on it. What is the electric flux (in N⋅m2/C) through the Gaussian surface S1 shown in the figure? Now put a point of charge 27.4 μC inside the cavity of the conductor. What is the flux (in N⋅m2/C) through the Gaussian surface S1? Now consider the Gaussian surface S2. With the charge still inside the cavity, what is the flux (in Nm2/C) through this surface?Prove that the polarization flux through a closed surface is directly proportional to the enclosed bound chargeAn infinitely long cylindrical shell, with uniform charge density p, has an inner radius of X and an outer radius of Y. An infinitely long line consisting of uniform charge density L is located right at the axis of the cylindrical shell. A. With the help of a diagram of a Gaussian surface, find the equation for the electric feild strength in a region where r>X and r<Y. B. With the help of a diagram of a Gaussian surface, find the equation for the electric feild strength in a region where r<X C. A charge, Q, with a mass of M is released at rest. The charge is released at a radius of 10Y. Derive an equation for the direction and magnitude of the initial acceleration of the charge