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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.
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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, μ0 = 4π × 10−7 T mA−1
Magnetic field is given by the relation,
`"B" = mu_0"nI"`
∴ `"nI" = "B"/mu_0`
= `(100 xx 10^-4)/(4pi xx 10^-7)`
= 7957.74
`≈ 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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