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A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression ρ = Ar2, where A is a constant and r < R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r > R) the sphere is E = AR5/5ϵ0r2. (b) Show that the magnitude of the electric field inside (r < R) the sphere is E = Ar3/5ϵ0. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr.
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Chapter 23 Solutions
Physics for Scientists and Engineers with Modern Physics
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- I need help with part B. I cant seem to get the correct answer. Please walk me through what youre doing to get to the answer and what that could bearrow_forwardQuestion 6: Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl₂ gas is 8.70 L at 895 torr and 24°C. (a) How many grams of Cl₂ are in the sample? ⚫ Atomic mass of CI = 35.453 g/mol • Molar mass of Cl₂ = 2 x 35.453 = 70.906 g/mol Solution: Use the Ideal Gas Law: Step 1: Convert Given Values • Pressure: P = 895 torr → atm PV= = nRT 1 P = 895 × = 1.1789 atm 760 • Temperature: Convert to Kelvin: T24273.15 = 297.15 K • Gas constant: R = 0.0821 L atm/mol. K Volume: V = 8.70 L Step 2: Solve for n . PV n = RT n = (1.1789)(8.70) (0.0821)(297.15) 10.25 n = = 0.420 mol 24.405 Step 3: Calculate Mass of Cl₂ Final Answer: 29.78 g of Cl₂. mass nx M mass= (0.420)(70.906) mass= 29.78 garrow_forwardE1 R₁ w 0.50 20 Ω 12 R₁₂ ww ΒΩ R₂ 60 E3 C RA w 15 Ω E2 0.25 E4 0.75 Ω 0.5 Ωarrow_forward
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