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

#### Solution

Magnetic field strength, B = 100 G = 100 × 10^{−4 }T

Number of turns per unit length, n = 1000 turns m^{−1}

Current flowing in the coil, I = 15 A

Permeability of free space, μ_{0} = 4π × 10^{−7} T mA^{−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 4 cm, number of turns 400, and current 10 A, then these values are not unique for the given purpose. There is always a possibility of some adjustments with limits.