1. Suppose that you place an uncharged, infinitely long metal cylinder of radius a in ain initial...
An infinitely long solid insulating cylinder of radius a = 5.5 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density rho = 25 mu C/m^3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 14.4 cm, and outer radius c = 17.4 cm. The conducting shell has a linear charge density lambda = -0.42 mu C/m. 1) What is E_y(R), the y-component of...
If you can draw a FBD as well 70. When an uncharged conducting sphere of radius a is placed at the origin of an xyz coordinate system that lies in an initially uniform electric field E = E, Î, the resulting electric potential is V(x, y, z) = V, for points inside the sphere and E, az V(x, y, z) = V. – Eoz + (x2 + y2 + z2)3/2 for points outside the sphere, where V, is the (constant)...
Electrostatics problem 2. An infinitely long circular cylinder of radius a and dielectric constant E is placed with its axis along the z-axis and is put in an electric field which would have been uniform in the absence of the cylinder, pointing along the x-axis (see figure). Find the total electric field at all points outside and inside the cylinder. Find the bound surface charge density.
An infinitely long cylinder with axis aloong the z-direction and radius R has a hole of radius a bored parallel to and centered a distance b from the cylinder axis (a+b<R). The charge density is uniform and total charge/length is placed on the cylinder. Find the magnitude and direction of the electric field in the hole.
Please help with finding the potential using cylindrical coordinates. Please use detail and clear writing. thank you very much. Will UpVote for great detail. 3. Consider an infinitely long quarter cylinder whose apex lies along the z-axis. The curved surface of the quarter cylinder is kept at potential Ф V, and its plane sides at potential Ф 0, Figure 2.. Find the potential inside the quarter cylinder. (5.0 points) 3. Consider an infinitely long quarter cylinder whose apex lies along...
ery long dielectric cylinder of radius a and dielectric constant er is placed in a field Eo perpendicular to its A v axis. The electric potential inside the cylinder is r in and the electric potential outside the cylinder is The electric field inside of the cylinder is and the electric field outside the cylinder is n11 out-_E Find the surface charge density and take the cylinder axis to be the z-axis and take Eo - Eo ery long dielectric...
5. An infinitely long cylinder of radius R carries a frozen-in" magietization parallel to z-axis and is given by M = ksi, where k is a constant and s is the distance from the axis. There is no free current anywhere. Find the magnetic field inside and outside the cylinder.
Suppose that you have a very long cylinder (treat it as infinitely long) with a uniform charge density p (coulombs per cubic metre). The cylinder has a radius a. Let the axis of the cylinder be the 2- axis. The cylinder is rotating about this axis with a constant angular speed w in a counterclockwise direction. @=w2 a. [5 points] What is the current density ✓ at a general point in the cylinder, at a distance r from the ĉ-axis,...
One surface of an infinitely large ideal conductor plate is at the planex -0 of the Cartesian coordinate system, with the x-y plane being the plane of the paper and the z axis represented by the dot, as shown in the figure. The conductor plate is grounded (i.e. at a potential 0). A positive point charge O is located at (d, 0, 0). Assuming free space (i.e. vacuum, with permittivity &o). find the following: (1) The electric field and potential...
An infinitely long cylindrical conductor with radius R has a uniform surface charge density ơ on its surface. From symmetry, we know that the electric field is pointing radially outward: E-EO)r. where r is the distance to the central axis of the cylinder, and f is the unit vector pointing radially outward from the central axis of the cylinder. 3. (10 points) (10 points) (a) Apply Gauss's law to find E(r) (b) Show that at r-R+ δ with δ σ/a)....