Consider a cube of length of one side 2 m is place in a uniform electric filed 60 V/m i is shown below. Rank the electric flux through the surfaces 1,2, and 3 in ascending order. 1 (a) 1=2=3 (b) 1=2<3 (c) 2=3<1 (d) 1=3<2 3 ËÎ X
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- A large hollow sphere is composed of a uniformaly positive charge gel. The hollow cavity has a radius of R and the outer radius of the sphere has radius 4R. What is the total electric field energy within the entire sphere computed by using electric fields?A charge distribution has the charge density given by p =Q{s(x– x,)- 8(x+ x, } . For this charge distribution the electric field at (2x,,0,0)A dielectric rod with cross-section area of A and polarization of Px = ax² + b is extended from x = 0 to x = L. (a) Calculate the bound volume charge density and bound surface charge density. b) Determine the total bound charge.
- A charge distribution creates the following electric field throughout all space: E(r, 0, q) = (3/r) (r hat) + 2 sin cos sin 0(theta hat) + sin cos p (phi hat). Given this electric field, calculate the charge density at location (r, 0, p) = (ab.c).The electric flux density of a charge distribution with spherical symmetry is given by (a³po -âr, r2 a 3r2 rpo D = r a C-A very large nonconducting plate lying in the xy-plane carries a charge per unit area of 3?. A second such plate located at z = 2.40 cm and oriented parallel to the xy-plane carries a charge per unit area of −2?. Find the electric field for the following. (a) when z<0 (b) when 0 < z < 2.40 cm (c) when z > 2.40 cm
- When you polarize a neutral dielectric, charge moves a bit, but the total charge remains zero. This fact should be reflected in the bound charges σ and ρ. Prove from σb = P. n and Pb = −√. P that the total bound charge vanishes.A ring and a disk both are centered at (0, 6, 3) and are both lying on the plane y = 6. The ring has a radius of 7 m, while the disk has a radius of 9 m, so that the ring is around the disk. Determine the magnitude of the electric field in kV/m at point (0, -9, 3) if the ring has a total charge of -8 mC and the disk has a total charge of 6 mC. All coordinates are measured in meters.Ra1 +9 -9 Rea Consider two concentric spherical conductors, separated by an isolating material with (absolute) permittivity e. The two conductors have radius R1 and R2, they are put on a potential V and V2, which leads to a charge +q and –q sitting on them, respectively. By the problem's spherical symmetry, we see that the charge on each conductor is distributed uniformly, and that, in spherical coordinates, the electric field between the two conductors is of the form E(r) = -E(r) er. Determine the capacity C using the following steps: 1. Use Gauss's Law in integral form, with N a ball of radius r (R2 < r < R1), to find an expression for E(r) in terms of q. 2. Calculate AV = Vị – V2 using the formula - E•dr Δν and with C the black line segment indicated on the drawing (parallel with e,). 3. The capacity now follows from C = q/AV.
- Figure 22-40 shows an electric dipole. What are the (a) magni- tude and (b) direction (rèlative to the positive direction of the x axis) of the dipole's electric field at point P, located at distance r> d? +q d/2 d/2 Fig. 22-40 Problem 19.Any net charge on a conductor resides on its surface even if the the conductor is NOT in electrostatic equilibrium. O True O False(1 )Region one z>0 consist of dielectric medium (er=4) (2)Region two z<0 consist of perfect conductor. Determine D&E at point (3,2,-3) and point (2,-1,3), if the surface charge on the conductor is equal to 8nc/m?