For a Certain surface ‘S’, if polarization vector ‘P’ is equal to 2× 10-16 C/m2is inclined at an angle of 60 degrees normal to that surface what is the value of bound surface charge density ‘σ’ of that surface?
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For a Certain surface ‘S’, if polarization vector ‘P’ is equal to 2× 10-16 C/m2is inclined at an angle of 60 degrees normal to that surface what is the value of bound surface charge density ‘σ’ of that surface?
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- A sphere of radius R carries a static radial polarization density P(r) = kr, r< R where k is a constant and r is the radial vector from the center of the sphere. (a) What are the dimensional units of the constant k? (b) Calculate the surface areal bound charge density o(R, 0, 0) and the volume bound charge density p(r). (c) Find the electric field inside and outside the sphere.A quarter-disc in the first quadrant has a surface charge density given by K cos φ C/m2. If the radius of the discis b, calculate the electric field at a point P(0, 0, −hAn infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as given by the following expression where pa, and are positive consta axis of the cylinder p-p(0-1) Use Gauss's law to determine the magnitude of the electric field at the following radial distances. (Use the following as necessary: Po, b, c, and R.) (a) R EM Po x 2R (-36) 200 x
- A circular surface charge with density ps, radius ra and with its axis is coinciding with the z axis is said to be located on the z = zo plane. Assume that zo is greater than zero. By using appropriate law obtain the electric field intensity induced by this structure at a point of (0, 0, h) where h is greater than zo.R OI A very thin spherical plastic shell of radius R = 18 cm carries a uniformly distributed negative charge of Q = -8 nC on its outer surface. An uncharged solid metal block is placed nearby. The block is w = 9 cm thick and is 9 cm away from the surface of the sphere. Calculate the magnitude of the elec- tric field at the exact center of the conductor generated only by the polarization of the con- ductor. In other words, do not include the electric field generated by the sphere. Answer in units of N/C.A cylinder of radius a and height L is centered about the z -axis and has a uniform polarization alongits axis, P = P_0 z-hat. (P is a vector in the z direction).Find the electric field and electric displacement everywhere on its axis.
- A point charge Q is located at (x, y, z) quadrant r > 0, y > 0 is bounded by two grounded conducting planes defined separately by y = 0 and x = 0. Solve for V(x > 0, y 2 0, z) using the method of image charges. (a) The (x > 0, y > 0, z) can be obtained by in- cluding image charges qa (x, y, z) = at (-a, -b, 0). Demonstrate by explicit calcula- tion of V(r, y, z) that the boundary conditions V (0, y > 0, 2) = 0 and V(x > 0,0, z) = 0 are satisfied if qa = q6 = -Q and qab = +Q (a, b, 0), as shown in the drawing. The %3D %3D potential in the physical region at coordinates y vx x plane (-a, b, 0), qb at (a, -b, 0) and qab (a,b) (a,b) (-a,-b) (a,-b) (b) What is the surface charge density on the grounded plane at (x, y, z) = (a, 0, 0)?On the line described by x = 2 m and y = – 4 m, there is a uniform line charge distribution of density ρL = 20 nC/m. Determine the electric field at (–2, –1, 4) m.What is the scalar electric field strength 12 mm away perpendicularly from the center of a ring of charge with 15mm radius and has a total charge of +750 uC. note: Answer in GN/C and 3 decimal places
- A sphere of dielectric material, with radius a, is electrically polarized, with polarization P = Pâ. 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.If the electric flux density is given by C D = x²a, + y²z a, determine the volume charge density at the point P(1,2,3).The surface charge density of a charged thin circular disc of radius R is n(r ) = Ar,where A is a constant and r is the position vector of a point of the thin disc from the center ofthe disc. Calculate the electric field at any point on the axis of the disc.