Suppose a thin disk of dielectric with polarization P=Kz 2, radius a, and height h« a...
Eo z-h/2 The cylinder in the figure has radius a, height h and lies along the z axis with the origin in the middle. The cylinder is made by a perfect dielectric material and is polarized. The polarization vector is P Poay with (a) Find the density of all polarization charge distributions that may exist within or on t he cylinder. [4 points] (b) Without doing calculations, determine the direction of the electric field E at the origin. Briefly justify...
Question 1 2 έρ The cylinder in the figure has radius α, height and lies along the z axis with the origin in the middle. The cylinder is made by a perfect dielectric material and is polarized. The polarization vector is P -Poa with Po > 0 (a) Find the density of all polarization charge distributions that may exist within or on the cylinder. [4 points] (b) Without doing calculations, determine the direction of the electric field E at the...
A dielectric sphere of radius a has a polarization P Kr2f. Find the electric field and electric displacement at distance r from center, a) for r < a (inside the sphere), and b) for r>a (outside the sphere)
Given a circular disk of charge with surface charge density ρs and radius a in the xy plane with the center located at the origin, see figure. Find the vector electric field at a point P (0,0,h) induced by the circular disk. Evaluate the vector electric field at P when a→∞
A conducting disk of a radius a and a small height h is made of a material of a finite conductivity σ and a permeability o μ . It is placed on the xyplane in the presence of a uniform, time-varying, magnetic flux density B = azBo cos ωt as shown in Fig. 6.14. Ignoring time-delay of emf at different points on the disk, and neglecting the magnetic field induced by the current in the disk, compute (a) induced emf...
A dielectric sphere of radius a has a ”frozen in” polarization given by P (r) = krrˆ in standard spherical coordinates, with the origin of the coordinate system at the center of the sphere. (A) The sphere is surrounded by a conducting shell of inner radius a and outer radius b > a. The total charge on the conducting shell is zero. Is there an induced charge on the inner and outer surfaces of the conducting shell? If so, what...
A thin disk with a circular hole at its center, called an annulus, has inner radius R1 and outer radius R2. The disk has a uniform positive surface charge density σ on its surface. (Figure 1) A)The annulus lies in the yz-plane, with its center at the origin. For an arbitrary point on the x-axis (the axis of the annulus), find the magnitude of the electric field E⃗ . Consider points above the annulus in the figure. Express your answer...
Starting from Coulomb’s Law, calculate the electric field at a height of z = h below the center of a charged disk which lies in the x-y plane with radius a and surface charge density of σ.
A uniformly charged disk with radius R = 25.0 cm and uniform charge density σ 7.60 x 10-3 C/m2 lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z 5.00 cm MN/C (b) z 10.0 cm MN/C (c) z-50.0 cm MN/C (d) z 200 cm MN/C
3. A circular disk of radius 2 cm slides at a speed 10 cm/sec in the direction of (t) (3, 4). As it slides it spins counterclockwise at 3 revolutions per second. Initially (ie, t = 0), the center of the disk is at the origin, O- (0,0). Find parametric equations for the trajectory of the point P on the edge of the disk, which is initially at (2,0). (Hint: Split the motion into sliding(i.e. translation) of the center and...