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A very long coaxial cable consists of a solid cylindrical inner conductor of radius 4mm , surrounded by an outer cylindrical conductor with inner radius 7mm , and outer radius 9.5mm . The region between the two conductors is filled with a waxlike insulating material to keep the conductors from touching each other. The inner conductor carries a current 2.55A , into the page, while the outer conductor carries a current 2.05A , out of the page.
A) Use Ampère's law to derive an expression for the magnetic field as a function of r (the distance from the central axis) at points between the two conductors (R1<r<R2i). Use this expression to find the magnetic field at 4.1mm .
B) Use Ampère's law to derive an expression for the magnetic field as a function of r (the distance from the central axis) at points inside the outer conductor (R2i<r<R2o). Use this expression to find the magnetic field at 7.4mm .
C) Use Ampère's law to derive an expression for the magnetic field as a function of r (the distance from the central axis) at points outside the outer conductor (r>R2o ). Use this expression to find the magnetic field at 14.9mm .
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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