midterm exam 1 solution

# Physics for Scientists and Engineers (3rd Edition)

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Unformatted text preview: Problems: 1) Four charges are arranged at equal distances ﬁ-om the origin of a coordinate system as shown in the diagram. The magnitude of each charge is q= 5x10'a C. The distance each charge has ﬁ‘omtheoriginisa= 3mm. a) What is the magnitude and direction of the electric ﬁeld at the point P? Show the direction by drawing an arrow onthediagram. _, .3 E .. .. E —0\ =) Camczf Ana .3 " t =-q : E7=q , .1— i. E “ 2" H176 -9 l/Vgﬁ 5x105” 212 E5]: —————g——- [02((0 antenna“? ‘lxlO M? C b) If an electron is placed at P, what will be the direction and the magnitude of the force on theelectron? _-. f: :3. 35—2 s) ﬂincﬁam 0%;- -u E7: LOX log/gx (.éox [0-m[=(l,éx [0 ﬂ// V— LITTEOq- 4:754 “2.76,... i=t I 5x (O’QZZé‘OZXVZ; =1 0.3xl0‘ Vi : 2:7; 9.?xl-xt0" sz3ar 60 M d) How much work does it take for an external force to bring the electron from inﬁnity to P? 0' ”C ) 2) An array of six capacitors is connected as shown in the diagram. 4 a) What is the equivalent capacitance of the array l 2 between the terminals A and B? C 4 ”3 => C = ‘F has A A‘s 4/4 2 [3% “‘0‘ ’43 ”gaff/"I C b) If the negative terminal of a 12 V battery is connected to A and the positive terminal is connected to B, how much charge will ﬂow out of the battery? la} C‘?V= LOX (OJ—S x’EI/= IREC) c) With the battery connected, what will be the potential at C if we take the potential at B as 12 Volts? -6 L v v- ——- VII-Jags am C:«/gucf+ow ‘i‘ 3) The Earth can be approximated as a uniformly charged conducting sphere. The average electric ﬁeld just above the surface of the Earth is about 150 NIC, directed downward a) What is the sign of the average charge on the surface of the Earth? Justify your answer. éMJJiqr/n «Uri-{act «.3 a {Vt/‘n I'M Hr aw'vl' in ﬁw‘i" 507 9!". A .3 . . E is 4...}?me {’0 M JW”7~CE‘ ,: " +'\'a( v A _ , *_"-52r-e _ a) ¢E,§5M—‘ES‘<0 .)_ b) Use Gauss’s Law to estimate the total charge on the surface of the Earth. The radius of the Earth is R = 6380 km. (Hint: Use an imaginary sphere with a radius just a little bit larger than the Earth’s radius and calculate the electric ﬂux through this surface.) 52:5 Eoﬁrésqm? " z :3 Q:— 977K (’in MAW [So/grQSon (03):} =5 "5 "5.8x MIC c) What is the net charge density directly at the Earth’s center? A Earn/(Q: is cameluc kind '5') E r: 0 who {/3 =3 Q: 0 in.) 1'04 4) Two wires of 100 in length are made out of 100 kg of Copper each. The ﬁrst wire has a cross sectional area shaped like a square with side length a. The second Wire’s cross sectional area is of circular shape with diameter d (The mass density of Copper is pa“ = 8.9 x 103 kg/m3, and the resistivity is p = 1.68 it 10‘s rim). a) What is the side length a of the wire with square cross section? c) What is the diameter d of the wire with circular cross section? 74 ii) p! (“N «A (1&1th [1‘1 ”97+ q). 4:T(§J?=>E:2f§=- d) What is the resistance of the “circular" wire? 72,3 f— ... 0.01512 (in/Ms) )- e) Explain in your own words why the resistances you have calculated for the two wires in questions b) and d) are the same or different. Jimq, f! [I ,4 are Mr sci-m {0/ £04 “/3445! [’01, an“; A Jew Maid+eme {(207 ...
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• Spring '04
• Rijssenbeek

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