#### Question

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, `mu_0=4pixx10^-7 TmA^-1`

Magnetic field is given by the relation,

`B=mu_0nI`

`therefore nI=B/mu_0`

`=(100xx10^-4)/(4pix10^-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.