Consider a system of three point-like electric charges, with charges q; and positions ; (i 1,2,3), as follows: q₁ = +Q, 7₁ = (0, 0, d); q2 = +Q, F₂ = (d, 0, 0); 93 = -Q, 73 = (0,0,0). (a) Calculate the monopole moment of the given system of charges. (b) Calculate the dipole moment for m = 0.
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- For problem 4 part b in square centimeters using inner and outer radii of the spherical capacitor of a = 5.49 cm and b = 1.05 a, respectively. (Answer In 5 sig. figs.)A line charge of infinite length lies along the z axis and carries a uniform linear charge density of pe C/m. A perfectly conducting cylindrical shell, whose axis is the z axis, surrounds the line charge. The cylinder (of radius b), is at ground potential. Under these conditions, the potential function inside the cylinder (p b. (d) Find the stored energy in the electric field per unit length in the z direction within the volume defined by p> a, where a < b.The following sequence of problems guides you through the calculation of the total electrie field at a target point in space when there are two source partieles. We'll stick to two dimensions (get rid of the z-axis) just to reduce some of the arithmetic. The source partieles are both located on the z-axis with source 1 at z = 5 em and source 2 at zz = -5 cm. Source 1 has charge -5 uC while source 2's charge is 3 µC. 2. First, calculate the electric field vector due to source I at the target location, (5,6) em. [Enter your answer with the following format: X*i+Y*j. where you substitute the numerical values of the components along the z and y directions in place of the "X and "Y' in the expression. The letters i and j represent the unit vectors along different directions. Use the asterisks to denote multiplication. Make sure to convert your units to standard MKS base units and use two-decimal precision. Denote powers of ten with engineering notation, for example 1.23 x 10 should be…
- Consider a rod of length L carrying a charge of q distributed uniformly over its length. Where applicable, let V(r→∞)=0. a) What is the voltage V at point P (at distance a away from the near end of the rod) due to the charge over the length of the rod? Express your answer in terms of given parameters (L,q,a) and physical constants b) Calculate the electric field at point P by differentiating V with respect to a. Let positive sign of E indicate direction of electric field pointing away from the rod.Problem 1. Prove that for a vacuum-dielectric interface at glancing incidence ri→-1 (see Fig. 4.49 from textbook, also on slide 7 in Lecture 4). In the same figure, if a is the angle that the curve r(0.) makes with the vertical at 0; = 90°, then: Vn2 – 1 tana, 2 1.0 0.5 Op -0.5 56.3° -1.0 30 60 90 0; (degrees) Figure 4.49 The amplitude coefficients of reflection and transmission as a function of incident angle. These correspond to external reflection n; > n; at an air-glass interface (n = 1.5). Amplitude coefficients ofDetermine E at (2, 0, 2)m due to three standard charge distributions as follows: a uniform sheet at x = 0 m with ρs1=(13π)nCm2ρs1=(13π)nCm2, a uniform sheet at x = 4 m with ρs2=(−13π)nCm2,ρs2=(−13π)nCm2, and a uniform line at x = 6 m, y = 0 m with ρl=−2nCmρl=−2nCm.
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