A magnetic field of `100G(1G=10^-4T)` is required which is uniform in a region of linear dimension about `10cm` and area of crossection about `10^-3m^2`. The maximum current carrying capacity of a given coil of wire is `15A` and the number of turns per unit length that can be wound round a core is at most `1000turns m^-1`. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

Explanation

Magnetic field strength, `B = 100 G = 100 xx 10^(-4)T`
Number of turns per unit length, `n = 1000 "turns" m^(-1)`
Current flowing in the coil, `I = 15A`
Permeability of free space, `mu_(0) = 4pi xx 10^(-7)TmA^(-1)`
Magnetic field is given by the relation,
`B = mu_(0)nI`
`:. nI =(B)/(mu_(0))`
`=(100 xx 10^(-4))/(4pi xx 10^(-7)) = 7957.74`
`~~ 8000 A//m`
If the length of the coil is taken as 50 cm, radius 4cm, number of turns 400, and current 10A, then these values are not unique for the given purpose. There is always a possibility of some adjustments with limits.