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.

Answer 1

Magnetic field is given by the relation,

$B={\mu }_{o}nI$

$\Rightarrow nI=B/{\mu }_o=100\times {10}^{-4}/4\pi {10}^{-7}\approx 8000A/m$

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.