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Exercise 1 5 points X O -l/2 l/2 Figure 1: Configuration comprising a current-carrying wire along the x-axis. Consider the configuration in Fig. 1 comprising a wire of negligible cross-section and length that is located along the x-axis and symmetrically with respect to the x = 0 plane. The wire carries the current I, flowing in the x-direction. The configuration is in free space, the permeability being po. y²+2 (a vector quantity is a) Calculate the magnetic field B(r) at points (0, y, z) with r = requested). (2 points) b) Assume that the magnitude of the magnetic field B(r) calculated at subpoint (a) is B(r) μοι l 2πr √²-4r.2 = i.e., Eq. (20.10) in the textbook Prove that when /r> 1 this expression results into B(r) that was derived for an infinite, straight wire. (1 point) HOT 2πr

Now consider the configuration in Fig. 2 comprising a contour in the z = 0 plane and consisting of 6 straight segments of wires of negligible cross-section and equal lengths . The contour carries the current I and is immersed in a uniform magnetic field B = -Bâ. The configuration is in free space, the permeability being po. c) Calculate the total magnetic force Ftot exerted on the wire contour (a vector quantity is re- quested). (2 points) P4 /45° P₂ B 45% O X P₁ Po Figure 2: Configuration comprising a current-carrying wire contour in the z = 0 plane. 45° P3 Y P6