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

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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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What will be needed in order to restore the balance if necessary?

scale1kgiceYou have a beam balance, the kind of scales that tips from one side to the other, depending on the weight on each side. On the left side lies a kilogram of ice. On the right side lies the standard kilogram. The pans are in balance.
After a while all the ice melted.
Does the balance tip to the right, to the left, or does it remain unchanged?
What will be needed in order to restore the balance if necessary?

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A solid sphere rolls down a roof

solid sphere rolls down a roofA solid sphere starts from rest and rolls without slipping a distance of 8 m down a roof that is inclined at 25˚. The roof’s edge is 5 m high from the ground. How far horizontally from the roof’s edge does the sphere hit the ground?

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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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How long would it take to fall through the center of the Earth?

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We have a hole that leads straight through the center of the Earth. We neglect air resistance and assume that the Earth has uniform density ρ. How long would it take to fall through the center of the Earth and reach the other side of the planet?

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A passenger is late for a train

mpzm6jA passenger is late for a train. He stood at a railway station while the accelerating train passed him car by car. The passenger noticed that the last train car passed him for 8 seconds and the previous train car for 10 seconds. How long was the passenger late for the train? You should consider that the train moved with uniform acceleration and the length of the train cars is the same.

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