Magnetic field due to a current in a straight wire

BiotSavartImg1A corner point makes angles θ1 and θ2 with the ends of a straight wire carrying current I. The distance of the point from the wire is a. What is the
magnetic field at the point?

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The boat is pulled to the shore


A boy stands on a shore and pulls a rope connected to a boat. The velocity of the rope vr is constant. Prove that the closer the boat to the shore, the faster it moves.

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The force required to hold a water hose

Calculate the force required to hold a water hose of radius 0.04 m when it emits a jet of water at a speed of 20 m/s.

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The stones in the container

smallStonesA vertical container (right rectangular prism) with base area measuring 0.15 m by 0.2 m is being filled with identical small stones, each with a volume of 2*10-8 m3 and a mass of 0.05*10-3 kg. Assume that the volume of the empty spaces between the stones is negligible. If the height of the stones in the container increases at the rate of 3*10-3 m/s, at what rate does the mass of the stones in the container increase?

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