Ncert Exercises & Solutions

4.15 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.

Magnetic field strength,

B = 100 G = 100 \times 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,

μ_{0} = 4 π \times 10^{- 7} T m A^{- 1}

Magnetic field is given by the relation,

B = μ_{0} nI

\Rightarrow nI = \frac{B}{μ_{0}} = \frac{100 \times 10^{- 4}}{4 π \times 10^{- 7}} = 7957.74 \approx 8000 {Am}^{- 1}

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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