Physics

Physics · electromagnetism

Problem

iii. Consider another tube, identical and parallel to the first one. <image_3> The second tube has the same magnetic field but in the opposite direction and its centre is placed at y=l,x=z=0y=l, x=z=0 (so that the tubes form opposite sides of a square). Determine the magnetic interaction force FF between the two tubes. Given constants: Part C. Magnetic straws Consider a cylindrical tube made of a superconducting material. The length of the tube is ll and the inner radius is rr with l≫rl \gg r. The centre of the tube coincides with the origin, and its axis coincides with the zz-axis. <image_1> There is a magnetic flux Φ\Phi through the central cross-section of the tube, z=0,x2+y2<r2z=0, x^{2}+y^{2}<r^{2}. A superconductor is a material which expels any magnetic field (the field is zero inside the material). Context question: i. Sketch five such magnetic field lines, which pass through the five red dots marked on the axial cross-section of the tube, on the designated diagram on the answer sheet. Context answer: <image_2> Context question: ii. Find the tension force TT along the zz-axis in the middle of the tube (i.e. the force by which two halves of the tube, z>0z>0 and z<0z<0, interact with each other). Context answer: T=Φ22μ0πr2T=\frac{\Phi^{2}}{2 \mu_{0} \pi r^{2}}

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