The toroid of is a coil of wire wrapped around a doughnut-shaped ring (a torus). Toroidal magnetic fields are used to confine fusion plasmas.
a. From symmetry, what must be the shape of the magnetic field in this toroid? Explain.
b. Consider a toroid with N closely spaced turns carrying current I. Use Ampère’s law to find an expression for the magnetic field strength at a point inside the torus at distance r from the axis.
c. Is a toroidal magnetic field a uniform field? Explain.
a. The shape of the magnetic field in this toroid, from symmetry is direction is counterclockwise.
b. An expression for the magnetic field strength at a point inside the torus at distance from the axis is .
c. The toroidal magnetic field a uniform field is Non- Uniform.
We need to find the shape of the magnetic field in this toroid, from symmetry.
The entry of the current is from the bottom side and out of the top side. Therefore we apply the right-hand rule, we can also find the magnetic field inside the toroid.
Counterclockwise, the magnetic field is distributed within the toroid and the space region enclosed by the toroid.
We need to find an expression for the magnetic field strength at a point inside the torus at a distance from the axis.
This magnetic field tangent to circular path inside the toroid.
Out of the toroid, this field is zero because the current inside the coil is opposite to that outside the coil. therefore, the magnetic field is only in the space region inside the toroid. The turns of the coil, the net current is .
Solving equation () for B to get the magnetic field.
We need to find the toroid magnetic field as a Uniform field.
The magnetic field of the toroid depends on the geometry of the toroid, it is non-uniform because changes and changes.
The element niobium, which is a metal, is a superconductor (i.e., no electrical resistance) at temperatures below . However, the superconductivity is destroyed if the magnetic field at the surface of the metal reaches or exceeds . What is the maximum current in a straight, diameter superconducting niobium wire?
An antiproton is identical to a proton except it has the opposite charge, -e. To study antiprotons, they must be confined in an ultrahigh vacuum because they will annihilate—producing gamma rays—if they come into contact with the protons of ordinary matter. One way of confining antiprotons is to keep them in a magnetic field. Suppose that antiprotons are created with a speed of and then trapped in a magnetic field. What minimum diameter must the vacuum chamber have to allow these antiprotons to circulate without touching the walls?
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