20 sin 0 If V : - V in free space, find: (a) py at P(r = 2,0 = 30°, Ø = 0);
Q: ) Let F = ai + bj – ck where a, b, and c are positive constants. nd the flux of F through a square…
A: Given: F→=ai^+bj^-ck^ The normal on the plane is ∇.→x+y+z=i^+j^-k^
Q: 1. Consider an infinitely deep rectangular slot with boundary conditions (x, 0) = Vx(L — x), þ(0, y)…
A: GivenConsider an infinitely deep rectangular slot with boundary conditions phi(x, 0) , and phi(x,…
Q: Consider two uniform electric fields with magnitudes E1=200 N/C and E2=600 N/C which both exist…
A:
Q: (a) Determine the electric field intensity E caused by a spherical cloud of electrons in free space…
A:
Q: An electric dipole located at the origin in free space has a moment p = 3āx 2āy + āz nC.m, find (a)…
A: Given data, Electric dipole, p→=3i^-2j^+k^ nC.m therefor, its magnitude p=3i^-2j^+k^×10-9…
Q: Given a non-uniform VOLUME charge density p = ko r. z cos p, ko = constant, r, p, z are cylindrical…
A: hey dear this question is from electrostatics I solved it with diagram
Q: charge distribution in free space has volume charge density r (4 cos2 θ) nC/m3 for [5] 0 ≤ r ≤ 20 m…
A: Gauss Law relates the charge distribution to resulting electric field, according to which electric…
Q: The electric Charge uniformly distríbuted on the surface of an infinitely long cylinder of Radius…
A: Electric field outside the cylinder Electric field inside the cylinder is zero because there are no…
Q: I need help with this question: Assume that a stationary electron is a point of charge. What is the…
A: Energy density is u Radial distance is denoted as r
Q: Two concentric spheres of radii R and R, are charged with surface charge densities o1 and 2, as…
A:
Q: The electric field has been measured to be horizontal and to the right everywhere on the closed box…
A:
Q: 12. A uniform volume charge density, p, = 60p C/m³, lies within the cylinder p = 1 m, and P, = 0…
A: Gauss law states that the net flux through a closed surface enclosing a volume equals the…
Q: A force F of magnitude 920 lb is applied to point C of the bar AB as shown. Determine both the x-y…
A: A force F of magnitude 920 lb is applied to point C of the bar AB as shown in the figure. We need to…
Q: On a cylindrical surface of radius R(10cm) and length I (I>>R) s some charge is uniformly…
A:
Q: Consider a circular region of radius R = 6.00 cm in which there is an electric flux directed out of…
A:
Q: A uniform electric field, E = 275 N/C, that points straight upward passes through a rectangular ramp…
A: Electric flux is given as dot product of electric field vector and area vector ds is E.ds . For…


Step by step
Solved in 2 steps with 1 images

- pls answer number 1 and pls show a clear solution ty.An infinite cylinder of radius R has a charge density given by p(r) = ar", where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aR E(r) 7€or satisfies V ·Ē = 0 for r > R. Explain briefly why this condition must be obeyed.An 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
- An uncharged, infinitely long conducting cylinder of radius a is placed in an initially uniform clectric ficld E = Eoi, such that the cylinder's axis lics along the z axis. The resulting clectrostatic potential is V (x, y, z) = Vo for points inside the cylinder, and Ega?x x² + y? V (r, y, z) = Vo – Egx + for points outside the cylinder, where Vo is the (constant) clectrostatic potential on the conductor. Usc this expression to determine the resulting clectric ficld, E.(Pr. 4) If a soft material has a dielectric response characterized by a single relaxation time t, then the polarization - [P(t)- XoE (t)], where X is the static electric susceptibility. obeys the equation: dP dt T (a) Under an applied sinusoidal field given, in complex notation, by E(t) = Ege-iw verify by direct substitution that P = XEE e-i satisfies the equation dP(t) = − ² [P(t) = x₂ €₁E (t)]. Show that the complex - dt hence calculate the real and imaginary parts of the complex Xs 1-iw susceptibility obeys the Debye law x = susceptibility, and sketch what they look like. (c) Apply this model to the case of water at room temperature, for which Xs≈ 80 and t = 9.4 ps. Compute the frequency in Hz at which the imaginary part of the susceptibility is maximum. What is the real part of the susceptibility of water for quasistatic fields (low frequency)? And for high frequency? When is water more polarizable by the electric field, and why? Is water a Newtonian liquid at low frequency? And at…A thin conducting cylindrical shell of radius a, carries a surface charge density o> 0 (the thick- ness of the shell can be neglected). Based on Gauss Law the electric field due to this cylinder is given by SE b) Inside the cylinder r a Determine the corresponding electric potential V(r) as a function of r and relative to a fixed arbitrary reference point A (i.e. rA) for a) Outside the cylinder, at a particular distance r, r > a.
- The electric field in a region of space near the origin is given by E(z, y, :) – E, (*) yî+ xî a (a) Evaluate the curl Vx E(x, y, z) (b) Setting V(0, 0, 0) = 0, select a path from (0,0, 0) to (x, y, 0) and compute V (r, y,0). (c) Sketch the four distinct equipotential lines that pass through the four points (a, a), (-a, a), (-a, -a), and (a, -a). Label each line by the value of V.Find the flux of F = xi - 2yj + zk across the portion of cylinder x² + z² = 9 in the first and forth octants. (3,-3,0) n X (0,0,3) (3,0,0) (0,3,0) yGgg