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Magnetism cases

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1. Imagine a small cylindrical permanent magnet floating above a superconducting tin disk bathed in liquid helium at around 1.2 K. The magnet was placed on the disk, and the latter was cooled below its transition temperature, at which point the magnet spontaneously jumped into the air. Explain what happened. This same kind of magnet levitation is being applied via high-temperature superconductors to produce frictionless magnetic bearings for gyroscopes, computer disk drives and the like.

2. A coaxial cable (like those used in cable TV installatins and with VCR's) consist of central conducting wire imbedded in a cylindrical insulating core which is then surrounded by another outer conducting cylinder usually made of wrapped aluminum foil or copper braid. Suppose such a cable carries a current of 2.00 A flowing in the opposite direction along the wire and 2.00 A flowing in the opposite direction along the foil. Use Ampere's Law to find the magnitude of the magnetic field at at radial distance
r = 1.5 mm tht is between conductor's?

3. Use Ampere's Law to find the magnitude of the magnetic field outside the coaxial cable in the previous problem.

4. A proton travels downward in the vertical x-z plane at an angle -40 deg with respect to the x-axis. It passes through a uniform horizontal B-field directed in the +y-direction. In what direction is the resulting magnetic force?

5. A negatively charged particle traveling in the positive y-direction enters a region of space pervaded by a 1.0-T uniform magnetic field directed in the negative y-direction. Determine the direction of the magnetic force acting on the particle.

6. Determine the magnetic force acting on a tiny sphere carrying a charge of 2.00nC and traveling at a speed of 500 m/s perpendicular to a 2.00-T B-field.

7. A proton moving at 3.00X 10^6 m/s through a uniform magnetic field experience a maximum force of
5.2 x 10^-12 N, straight upward when it's traveling due east. Determine B.

8. Consider a tiny 1.00 x 10^-6 kg sphere carrying a charge of 2.5 nC. The sphere is moving at 3.00 x 10^6 m/s in the positive x-direction. Given that it enters a region occupied by a uniform 0.300-T field making an angle of 30.0 deg to the x-axis, determine the magnitude of the spere's acceleration.

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