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1. Consider a solid ball of radius R centered at the origin carrying a charge density $\rho(r) = 1 + k\frac{r^2}{R^2}$ for $0 \le r \le R$, where k is a constant. (a) Using Gauss's law, find the electric field inside and outside the ball. (b) Find the electric potential inside and outside the ball, taking infinity as the reference point. (c) Calculate the work required to assemble this charge distribution in two different ways: i. Using $W = \frac{\epsilon_0}{2} \int_{\text{all space}} E^2 d\tau$. ii. Using $W = \frac{1}{2} \int_D \rho V d\tau$.

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The central carbon of the tert-butyl carbocation, ($CH_3$)$_3C^+$, is A sp3 hybridized with a 0 formal charge. B sp3 hybridized with a +1 formal charge. C sp2 hybridized with a +1 formal charge. D sp2 hybridized with a 0 formal charge.

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How many kJ of hear will it take to heat 76 grams of butter from freezer tempurature (0 degrees celsius) to right below its boiling point (100 degrees celsius)? Include correct units for all values and round you results to the correct number of significant digits.

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In terms of application, the views of a rule-deontologist are closest to those of an egoist. True False

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Suppose that the government decides to impose a rent control of $1,900 per month on rental apartments in New York City. On the following grap use the green point (triangle symbol) to shade the area representing consumers' surplus in the presence of rent control. Use the purple point (diamond symbol) to shade the area representing producers' surplus after the rent control. Then use the grey point (star symbol) to shade the ar representing deadweight loss resulting from the rent control. MONTHLY RENT (Dollars per apartment) 2600 Demand 2400 2200 2000 Rent Ceiling 1800 Supply 1600 0 0.8 1.6 2.4 3.2 4.0 QUANTITY OF APARTMENTS (Millions per month) ? CS w/ Rent Control ? PS w/ Rent Control ? Deadweight Loss

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4. A particle has a total energy E of 5 GeV and a momentum p of 3 GeV/c (i.e., cp, which has dimensions of energy, is equal to 3 GeV). Calculate the following: A). The rest mass of the particle in kg. B). The velocity of the particle in m/s. C). The kinetic energy of the particle in MeV.

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My friend is not answering his phone. Either he is busy or there is something wrong. My friend always texts me when he will be busy and is not able to talk for a period of time. I didn't get a text from him, so there must be something wrong. Which of the following is the best statement of the flaw in the argument above? 1. I always receive a text from my friend when he is busy 2. Something is wrong because I didn't get a text from my friend. 3. My friend must be busy if he didn't send a text

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QUESTION 9 George Black is single and files Form 1040 for the current year. He received the following income: Fully taxable pension $18,600 Wages from part-time job 9,400 Interest income 990 Total $28,990 George also received Social Security benefits of $5,980. How much of George's Social Security is taxable? $0 $4,700 $2,990 $5,980

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The Fig. P1.1 shows a cross-section of the magnetic structure of a four-pole DC machine. On each of the four stator poles, there is a coil with equal turns. The four coils are connected in series and carry the same current. The stator poles and yoke are made of laminations of cast steel sheets, while the rotor yoke is made up of silicon steel. The B-H curves for cast steel and silicon steel are shown in Fig. P1.2. The DC machine has the following dimensions: Each pole (cast steel): magnetic length = 10 cm; cross-section = 400 cm^2 Each air gap: length = 0.1 cm; cross-section = 400 cm^2 Rotor Yoke (silicon steel): average length = 20 cm; average cross-section = 400 cm^2 Stator Yoke (cast steel): mean circumference = 160 cm; average cross-section = 200 cm^2 The flux supplied by each pole is the same (quarter of the exciting ampere-turns are placed on each of the four poles). (a) Draw the magnetic equivalent circuit in terms of the N, I, ip, ig, ip, and is. Label and show all the flux directions in all sections. The s are reluctances. (b) Determine the mmf produced per pole required to produce a flux density of 1.1 T in the magnetic circuit (c) Determine the rotor flux.

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Question 3: Find Derivative and Show all steps/necessary rules beside steps. [3 Marks] $2x(\cos 4x)^2$

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leah s.