4.15) A magnetic field of 100 G ( 1G = 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.

Answers (1)
S Sayak

Strength of the magnetic field required is  100 G ( 1G = 10 ^{-4}) T

B=\mu _{o}nI

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

nI\\=\frac{100\times 10^{-4}}{4\pi \times 10^{-7}}\\ \\=7957.74 \approx 8000

Therefore keeping the number of turns per unit length and the value of current within the prescribed limits such that their product is approximately 8000 we can produce the required magnetic field. 

e.g. n=800 and I=10 A.

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