Q8 Which one of these electric fields is a possible E-field? k is some constant with appropriate units. (i) (ii) (iii) (iv) E = k(xy£ + 2yz ý+3xz 2) Ē = k[y²x + (2xy + z²) ŷ + 2yz 2] Ē = k[(xy + y²) x + (2yz + 2xy + z²) ŷ + (3xz + 2z) î] None of the above

5. The Poisson equation 8² + ax² ay² az² relates the electrostatic potential (r) = (x, y, z) to the charge distribution p(r) in vacuum. In partic- ular, when we are dealing with a point charge, we write this equation as 7²4 = | 8² əx² + 8² 8² əz² 2² + o(r) + G 5, 8) = - = 10² G(r, r') p(r) €0 -83) (r-r'), where r' = (x, y, z) is the position of the point charge, 63) (r - r') = 6(x − x')8(y - y')6(z - z') is the Dirac delta function in three-dimensional space. Solve for G(r, r') by performing a three-dimensional Fourier transform on the Poisson equation, followed by a three-dimensional inverse Fourier transform. You may use the result 00 sin id=

1. The magnitude of an electric field became 3.0 x 106 N/C or greater, so that electrical breakdown and thus sparking could occur. 2. The energy of a spark was 150 mJ or greater so that it could ignite the powder explosively. Let us check for the first condition in the powder flow through the plastic pipes. Suppose a stream of negatively charged powder was blown through a cylindrical pipe of radius R = 5.0 cm. Assume that the powder and its charge were spread uniformly through the pipe with a volume charge density p. a. Using Gauss' law, find an expression for the magnitude of the electric field E in the pipe as a function of radial distance r from the pipe center. b. Does E increase or decrease with increasing r? c. Is E directed radially inward or outward? d. For p = 1.1 x 10³ C/m³ (a typical value at the factory), find the maximum E and determine where that maximum field occurs. e. Could sparking occur, and if so, where? From the answer to part (a) of the problem, f. Find an…

Ē 4περτ2 This problem checks your understanding of the term in the equation for the electric field due to a point charge, Consider a charged particle at a point S whose coordinates are (10 m, 10 m, 7 m). We would like to find the electric field vector at a point P whose coordinates are (4 m, 5 m, 5 m). The term is the distance between point S and point P. What is its value, in meters? 1 Q ↑