A sphere of dielectric material, with radius a, is electrically polarized, with polarization P = P2. P is a constant. Calculate the total polarization charge (bound charge) on the hemisphere located on the positive z-axis and on the entire sphere.
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- dx P. ++ + + + + + dq L Evaluate an expression for the electric field at point P of a uniformly charged rod with linear charge density, 2 [C/m²], as shown above. Hint: The integral will be of the form: E (P) = [ k dq , where dq = 1 dx x2 1A square metal plate of edge length 7.3 cm and negligible thickness has a total charge of 5.4 × 10-6 C. (a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.55 mm from the center) by assuming that the charge is spread uniformly over the two faces of the plate. (b) Estimate E at a distance of 29 m (large relative to the plate size) by assuming that the plate is a charged particle.A square metal plate of edge length 9.9 cm and negligible thickness has a total charge of 5.8 x 10-6 C. (a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.75 mm from the center) by assuming that the charge is spread uniformly over the two faces of the plate. (b) Estimate E at a distance of 45 m (large relative to the plate size) by assuming that the plate is a charged particle. (a) Number Units (b) Number Units
- We have calculated the electric field due to a uniformly charged disk of radius R, along its axis. Note that the final result does not contain the integration variable r: R. Q/A 2€0 Edisk (x² +R*)* Edisk perpendicular to the center of the disk Uniform Q over area A (A=RR²) Show that at a perpendicular distance R from the center of a uniformly negatively charged disk of CA and is directed toward the disk: Q/A radius R, the electric field is 0.3- 2€0 4.4.1bA charge of 7.60 pC is spread uniformly throughout the volume of a sphere of radiusr= 4.15 cm. What is the magnitude of the %3D electric field at a radial distance of (a)6.29 cm and (b)3.23 cm?Calculate the electric field at the center of a dielectric cylinder of circular cross-section of height h and radius a with a permanent uniform polarization P0 perpendicular to its circular faces.