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A horizontal, 30-cm-long conducting rod is rolling along two conducting rails that are parallel to the x-axis. The rod is parallel to the y-axis, but moves in the +x direction with a speed of 6.5 m/s . The rails are electrically connected by a second conducting rod attached to the rails at an x-coordinate smaller than that of the rod. The entire assembly is immersed in a uniform magnetic field of 0.45 T in the +z direction (up). An emf is developed by the moving conductor. The moving rod has a resistance of 8.7 ohms, while the resistance of the circuit-closing rod and rails in series with the rod is 95 ohms. The emf drives a current around the circuit. Neglecting friction, what force (in Newtons) is needed to keep the rod moving at a constant speed?
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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