solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius bb and outer radius cc ((figure 1)). the central conductor and tube carry currents i1i1 and i2i2 correspondingly in the same direction. the currents are distributed uniformly over the cross sections of each conductor. derive an expression for the magnitude of the magnetic field

The magnetic influence on moving charges, electric currents, as well as magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is moving through a magnetic field. The magnetic field of a permanent magnet pulls on ferromagnetic substances like iron and attracts and repels other magnets. Para magnetism, diamagnetism, as well as antiferromagnetic are three additional magnetic effects that a nonuniform magnetic field can have on "nonmagnetic" materials, though these forces are typically so minute that they can only be discovered by laboratory equipment. Electric currents, like those used in electromagnets, as well as electric fields that change in time produce magnetic fields that surround magnetised materials.

Where μ_0 is the permeability of free space, i1 is the current in the central conductor, r is the radius of the central conductor, b is the inner radius of the conducting tube, and c is the outer radius of the conducting tube.

How to derive magnitude?

B = (4π*10-7 N/A2)*30 A/(2π*0.01 m)

= 1.2*10-5/*0.02 = N/(As) = 6*10-4 T.

Near the center of the solenoid B = μ0nI

= 4π10-7(1000/0.4)*I T, with I in units of Ampere.

With B = 10-4 T, we need I = 10-4A/(4π*10-7 2500) A = 31.8 mA.

For comparison, near Knoxville, TN,

the strength of the Earth magnetic field is ~ 53 microT = 5.3*10-5 T.

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