**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 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

**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, $\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}$

Magnetic field is given by the relation,

$B=\mu_{0} n I$

$\therefore n I=\frac{B}{\mu_{0}}$

$=\frac{100 \times 10^{-4}}{4 \pi \times 10^{-7}}=7957.74$

$\approx 8000 \mathrm{~A} / \mathrm{m}$

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.