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.

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Solution

Magnetic field is given by the relation,
$B = μ_{o} n I$
$\Rightarrow n I = B / μ_{o} = 100 \times 10^{- 4} / 4 π 10^{- 7} \approx 8000 A / m$
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.

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