Sources of the magnetic field

A very long straight wire carries the current $I=8.0\mathrm{A}$. Compute the magnitude of the magnetic field $4.0\mathrm{cm}$ from the wire and the distance at which the field equals $1.0\cdot 10^{-5}\mathrm{T}$.

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A right circular cone has a base of radius $4.0\mathrm{cm}$ and is placed in a uniform magnetic field of magnitude $0.30\mathrm{T}$, parallel to the axis of the cone and directed from the vertex toward the base. Compute the flux of the field through the lateral surface of the cone, oriented with the outward normal.

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A flat coil consists of $200$ circular turns of radius $8.0\mathrm{cm}$, carrying the current $0.50\mathrm{A}$. Compute the magnitude of the magnetic field at the center of the coil.

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Two infinite parallel straight wires are $6.0\mathrm{cm}$ apart and carry the current $12\mathrm{A}$ in opposite senses. Compute the magnitude of the magnetic field at the midpoint of the segment perpendicular to the wires that joins them.

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Two straight parallel conducting bars, $2.0\mathrm{m}$ long, are $8.0\mathrm{mm}$ apart and carry the currents $40\mathrm{A}$ and $25\mathrm{A}$ in the same sense. Treating the bars as infinite wires, compute the force between them and state whether it is attractive or repulsive.

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A circuit consists of a circular arc of radius $3.0\mathrm{cm}$ and angle $90^{\circ }$ and of the two radii joining its endpoints to the center $C$. The circuit carries the current $9.0\mathrm{A}$. Compute the magnitude of the magnetic field at $C$.

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A circular loop has radius $R=3.0\mathrm{cm}$. Find at what distance from the center, along the axis, the magnetic field is one eighth of the field at the center.

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A long straight wire of radius $R=3.0\mathrm{mm}$ carries the current $45\mathrm{A}$, distributed uniformly over the cross section. Compute the maximum magnetic field and the distances from the axis at which the field is half the maximum value.

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We want to build a solenoid $50\mathrm{cm}$ long that produces inside a magnetic field of $0.020\mathrm{T}$ with a current of $5.0\mathrm{A}$. Compute the number of turns per unit length and the total number of turns needed.

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A toroid of $1000$ turns, carrying the current $1.2\mathrm{A}$, has inner radius $20\mathrm{cm}$ and outer radius $25\mathrm{cm}$. Compute the maximum value and the minimum value of the magnetic field inside the ring.

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A square loop of side $20\mathrm{cm}$ is in a uniform magnetic field of $0.50\mathrm{T}$, which forms an angle of $30^{\circ }$ with the plane of the loop. Compute the flux of the field through the loop.

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A coaxial cable has an inner conductor of radius $0.50\mathrm{mm}$ and an outer conductor with radii $3.0\mathrm{mm}$ and $3.5\mathrm{mm}$; the two conductors carry the current $10\mathrm{A}$ in opposite senses. Compute the magnitude of the magnetic field at $1.0\mathrm{mm}$ and at $4.0\mathrm{mm}$ from the axis.

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A proton moves with velocity $3.0\cdot 10^{5}m/s$ parallel to an infinite straight wire, $2.0\mathrm{cm}$ from the wire, in the same sense as the current $25\mathrm{A}$ in the wire. Compute the magnitude of the magnetic force on the proton and state whether it points toward the wire or away from it.

Solution available to those who have unlocked the subject.