Homework 3-solutions - soto (rrs946) – Homework 3 –...

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Unformatted text preview: soto (rrs946) – Homework 3 – Hoffmann – (56605) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points In a particular region of the earth’s atmo- sphere, the electric field above the earth’s surface has been measured to be 152 . 5 N / C downward at an altitude of 270 m and 173 N / C downward at an altitude of 413 m. The permittivity of free space is 8 . 85 × 10 − 12 C 2 / N · m 2 . Neglecting the curvature of the earth, cal- culate the volume charge density of the at- mosphere assuming it to be uniform between 270 m and 413 m. Correct answer:- 1 . 26871 × 10 − 12 C / m 3 . Explanation: Let : ℓ 1 = 270 m , ℓ 2 = 413 m , E l 1 = 152 . 5 N / C , E l 2 = 173 N / C , and ǫ = 8 . 85 × 10 − 12 C 2 / N · m 2 . Choose a closed cylinderical surface for this portion of the atmosphere. The total flux is integraldisplay S E n dA = Q net ǫ ( E l 1- E l 2 ) A = Q net ǫ Q net = ( E l 1- E l 2 ) A ǫ . Thus the volume charge density is ρ = Q net V = ( E l 1- E l 2 ) A ǫ A l 1 = ( E l 1- E l 2 ) ǫ ℓ 2- ℓ 1 = 152 . 5 N / C- 173 N / C 413 m- 270 m × (8 . 85 × 10 − 12 C 2 / N · m 2 ) =- 1 . 26871 × 10 − 12 C / m 3 . The curvature of the earth can be neglected because the maximum helight is < . 01% of the radius of the earth. 002 10.0 points A charge of 5 . 6 μ C is 20 cm above the center of a square of side length 40 cm. The permittivity of free space is 8 . 85 × 10 − 12 C 2 / N · m 2 . Find the flux through the square. Correct answer: 1 . 05461 × 10 5 N · m 2 / C. Explanation: Let : q = 5 . 6 μ C = 5 . 6 × 10 − 6 C , ℓ = 20 cm = 0 . 2 m , s = 40 cm = 0 . 4 m , and ǫ = 8 . 85 × 10 − 12 C 2 / N · m 2 . The point charge is at the center of the cube. Applying Gauss’ law, the flux through one face of the square is Φ square = 1 6 Φ total = 1 6 q inside ǫ = 1 6 parenleftbigg 5 . 6 × 10 − 6 C 8 . 85 × 10 − 12 C 2 / N · m 2 parenrightbigg = 1 . 05461 × 10 5 N · m 2 / C ....
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This note was uploaded on 11/10/2011 for the course PHYSICS 303L taught by Professor Hoffman during the Fall '11 term at University of Texas.

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Homework 3-solutions - soto (rrs946) – Homework 3 –...

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