diilip

“average electric field in a spherical control volume | 119 R θ x′ x Figure 5.9 Geometry used to evaluate the surface integral in (5.41). and hence ¿ SR dS |x − x | = żπ 0 (2πRsinθ)(cos θ x/ x )(R dθ) (Rcos θ − |x |)2 + (Rsinθ)2 = 2πR2 x |x | ż 1 −1 χ dχ R2 + |x | 2 − 2R|x |χ , (5.42) where χ = cos θ. The integral on the second line of (5.42) may now be evaluated using the indefinite integral ż χ dχ √a − bχ = 2 b2 a − bχ 3 − a a − bχ, and after a little work we obtain ¿ SR dS |x − x | = ⎧ ⎨ ⎩ 4π 3 x, x < R, (5.43a) 4π 3 R3 |x| 3 x, x > R. (5.43b) Thus our integral of E over VR becomes ż VR E(x)dx = VR 4πε0 ż |x|>R ρe(x) (−x) |x | 3 dx − 1 3ε0 ż VR x ρe(x )dx, (5.44) or equivalently ż VR E(x)dx = VREqout(0) − pqin 3ε0. (5.45) We have arrived back at (5.39), albeit after a great deal of integration. Although this particular derivation of (5.39) is rather long-winded, some ofthe results we have deduced on route, such as (5.43a, b), will prove useful when it comesto our discussion of magnetostatics.”
― Peter A. Davidson, An Introduction to Electrodynamics

“in tonight, do a special bulletin, get herself a nice scoop on the competition. “Yeah, yeah,” she called at the sound of the buzzer. “Just hang on.” She went to the door, looked through the security peep, saw a bit of profile and a big winter hat,”
― J.D. Robb, Obsession in Death

“Now, Clark’s Construction was officially open for business. He’d enjoyed his chat with the grocery store owner, Patty O’Neil, that first day. The older woman had eyed him up and down until finally she had smiled and slapped him on the shoulder and exclaimed that he’d fit right in.”
― Jill Sanders, A Dash of Love

“From over her shoulder, Dean took in the minimalist open space design. A large tarp covered a queen bed in the far-right corner. Sheets that were probably white under its layer of dust covered what appeared to be nightstands and lamps flanking the bed. There was a couch and an old tube tv that he doubted worked, a mini fridge, and a large bookcase overstuffed with books, old games, and knickknacks. Dusty plastic tubs of who knows what were stacked in the middle of the room. Garden tools leaned against the wall.”
― K.M. Fawcett, Wilde Christmas