Question

A long, straight wire of radius a = 2.0 cm is located along the z-axis and carries a current I1 = 2.1 A in the negative 2-direction. A cylindrical conducting shell of inner radius b= 4.0 cm and outer radius c = 5.7 cm coaxial with the wire carries a uniformly distributed current 12 = 7.1 A in the positive z-direction as shown. Figure 1: (a) What are the r- and y-components of the magnetic field at point A located a distance d=27 cm from the origin along the c-axis as shown? (3pt) (b) What are the r- and y-components of the magnetic field at point B located at 2, y) = (d/v2.d/V2) as shown? (3pt) (c) What are the r- and y-components of the magnetic field at point D located at 1, y) = (-4.6.0) cm as shown? (3pt) (d) What are the r- and y-components of the magnetic field at point E located at 2,y) = (-1.0, 1.0) cm as shown? (3pt) (e) What is the value of the line integral Bds along the dashed path ABC in the figure above: first from point A to point B at 1, y) = (d/2,d/V2), and then to point C at (x,y) = (0.6d, 0.6d)? (3pt) (f) What is the value of the line integral [ B. ds along the straight line path from point C to point A as shown? (3pt) (Hint: What is the value of the line integral of B along the closed loop ABC A?] (g) Suppose the magnitude of current I, is doubled. How does the magnitude of the magnetic field at I, y) = (2,0) cm change? Explain. (2pt)

Answer 1

a) Net current through ακρογ tou see Ο radius d= 0.27 m. is 2 = 12-1, = 71-211=5A Hence magnetic field at point AO is givenas, 13. lol. Ho 5 2nd 2080.27 Amperion loop BA= 307 xlobT and its direction is in the y konce Bar = 3.7 xlő6 T S BAX=0 6) The distance of point is from origin is %= d. hence B = 307 8106 T Bay Z Here x-componant Box 18 12 BEARBY _ IS 07 Boy - 3.78156 T2 = -2.62 X 100 T 12 Box and ISBY = 2062x10 T Boy = 2 Now c) Here current through amperiau loop of radius I r=4.6cm =0.046m is givenas I (0.046) = (0.042 X7.17–2.1 = 0.1217 A = 0.057) = (0.0012 - Mol 2x0.1217 *107 -5.38167 How B = 26.046 = 0.046 oooub Box =0 and Boy = -5034107T D Here curreut through amuportandose de 1 = 1947) XI = 3 x2.1 = tor 1.05 Now Belo I. chis = 28.14,05 = 148.5X107T or BE = 1.5x10ST and Bex = 1.5xto = 1.05810T and BEY=1005x105T