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A cylindrical solenoid 40cm long with a radius of 5 mm has 300 tightly wound turns uniformly distributed along its length. Around the middle of the solenoid is a two-turn rectangular loop 3 cm by 2 cm made of resistive wire having a resistance of 150 ohms. One microsecond after connecting the loose wire to the battery to form a series circuit with the battery and a 20-ohm resistor, what is the magnitude of the current in the rectangular loop and its direction (clockwise or counterclockwise in the diagram) ? Can you please solve the problem explaining the steps.
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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