Phys 0175 - Worksheet _9 Solution

# Phys 0175 - Worksheet _9 Solution - PHYS 0175 S rin 2008...

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Unformatted text preview: PHYS 0175 S rin 2008 — Worksheet Problem Set #9 Part A Your Name: (P ' h if r TA: Score: The diagram below shows a long, straight wire, carrying a current of i=200 A, that runs through a cubical wooden box, entering and leaving through holes in the centers of two opposite faces. The box has side length 5 = 0.200 m. Consider an element (1! of the wire that is 5.00x10‘3 m long, centered at the center of the box, and points in the same direction as the current ﬂow. Determine the magnitude and direction of dB, the magnetic ﬁeld produced by this element at points a, b, c, d, and e. Point a is at the center of the top face of the cube, point c is at the center of the front face, and point d is at the center of the right face; point b is at the midpoint of the top right edge; and point e is at a corner. (Assume that dl is small in comparison to the distances from the current element to the points where the magnetic ﬁeld is to be calculated.) (1) What is the defining equation for calculating the :?7127'1L~ Swami—f («4447" magnetic ﬁeld dB produced by an element (ll of a u -> A conductor? Write it down in vector form. _ Q __ /U«c Z ’T (42 B _ L ‘fo’ If (2) Choose a coordinate system whose origin is at the center of the cube and whose axes point as follows: the positive x-axis passes through point c, the positive y-axis passes through point d, and the positive z—axis passes through point a. Using unit vector notation, express d! and the unit vector f for point a; ﬁnd the magnitude of rfor point a; then use these results and the defining equation above to ﬁnd the magnitude and direction of dB at point a. (Describe the direction of dB in terms of unit vectors in the above coordinate system.) § /( A (k 9. “mm « “ ewmi (W) v J w(.§r(f70x(0 («l d Aﬁa A .k A 3, 1;, : K b} I“ A ‘psm—v ﬂ . 72:0..mm am; LOCK“; ( 2 (3) Repeat this procedure for points c, d, b, and e. (Use the back of this sheet or attach an additional sheet to give yourself adequate space to work out the answers.) My answers are: [cl «6 7/ = S J /“0 V N .w, I. «W b (001 tktH‘l‘lJ S X (m) .119) 3:93) a 0 0 Carpet) 0 0,100 O ‘00 (l1) amp 0 0 Q” _. OM50 0,5175) —- 0400 PHYS 0175 S rin 2008 —Worksheet Problem Set #9 PartB Your Name: 6 ("l 1 € r ' Score: The long, straight wire AB shown in the diagram below carries a current IW=14.0A. The rectangular loop whose long sides are parallel to the long wire carries a current |L=5.00A. Determine the magnitude and direction of the net force exerted on the loop by the magnetic ﬁeld produced by the wire. (1) What is the equation that relates the magnitude of ~—‘ the magnetic ﬁeld produced by a long, straight : 411]“ r + W (at ,1 V / conductorto the distance from the conductor? What LA AT 31 7/” 0 p ' u “p is the direction of the magnetic ﬁeld produced by the long wire in the plane of the rectangular loop? (2) First, consider the magnetic forces acting on the two short legs of the loop: based on the equation you found above, will the forces vary over the lengths of the short legs? How do their magnitudes and directions compare? { E ‘ l; 'r’ A :1 chltawk Cut/1 :l:+yp :’- 'boﬁowl [QCzutSJZ C‘U'Vr‘e/LLi S lr/vt 49//Z/‘S41( {{th .» HLLV‘VL g mfg? Lg T (K LE/L/L1 ., (3) Now consider the magnetic forces acting on the two long legs of the loop: will th forces vary overthe lengths of the long legs? How do their magnitudes and directions compare? \ﬁ "4‘ 4 (m baa/c151; RR>RL a 0W1 E Met a, gmgmi we KI L 1441(th EL a £04265 ,6»: Q 3me 01K; Lk é/Ccoaq . ‘h, Cut/U (“Mod *0 ti“! "ELM; 71R wﬂrm'w‘l to ﬂu "Mgld‘. (4) Now you are ready to determine the magnitude and direction of the net force on the >oop. [34: => ,fcl=(ig‘b3c’w MG):(ZV('LD(’U°) : [0047er N ( RP o . 1L0 HAL “ 9 g/L’EQ L’ 26570240- NI igﬁ ' 20 RK _§; (‘7‘ (v0 My answers are: ...
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