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 m² . 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.

Magnetic field strength, B = 100 G = 100 x 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, μ0 = 4π x 10^-7 T m A^-1

Magnetic field is given by the relation,

B = μ0 nl

=>nl =B/μ0 = (100 x 10⁻⁴ )/(4π x 10^-7 )

= 7957.74  ≈ 8000 Am⁻¹

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.