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Q1. A single bead can slide with negligible friction on the stiff wire that has been bent into a circular loop of radius 12.4 cm, as in the figure below. The circle is always in a vertical plane and rotates gradually about its vertical diameter with a period of 0.445 s. The position of the bead is described by the angle θ that the radial line, from the center of the loop to bead, makes with the vertical.
Q2. The triangular loop of wire in the drawing carries a current of I= 6.91 A. A uniform magnetic field is directed parallel to the side AB of the triangle and has a magnitude of 2.77 T.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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