Question

Figure P27.85 (0, L) (L, L (0, 0) (L, 0) 27.86 CALC Torque on a Current Loop in a Nonuniform Magnetic Field In Section 27.7 the expression for the torque on a current loop was derived assuming that the magnetic field B was uniform. But what if B is not uniform? Figure P27.85 shows a square loop of wire that lies in the y-plane. The loop has corners at (0, 0), (0, L), (L, 0), and (L, L) and carries a constant current lin the clockwise direction. The magnetic field has no z component but has both -r- and y-components: B (Boy/L)u (Bor/LN, where Bo is a positive constant. (a) Sketch the magnetic field lines in the xy-plane. (b) Find the magnitude and direction of the magnetic force exerted on each of the sides of the loop by integrating Eq. (27.20). (c) If the loop is free to rotate about the x-axis, find the magnitude and direction of the magnetic torque on the loop. (d) Repeat part (c) for the case in which the loop is free to rotate about the y-axis. (e) Is Eq. (27.26), T x B, an appropriate description of the torque on this loop? Why or why not?

Have to use $\overrightarrow{\tau} = \int \overrightarrow{R}\times \left ( I\overrightarrow{dl}\times \overrightarrow{B} \right )$ for parts c and d. Need help with c and d. please show all work for cross products and line integral of the cross products

Answer 1

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