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NCERT Class XII Chapter
Moving Charges and Magnetism
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Question : 15 of 28
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A magnetic field of 100 G (1G = 10−410^{-4} T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10−3m210^{-3}\text{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\text{m}^{-1}. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.
Solution:  
The magnetic field required is 100 G in a length of 10 cm. So, the solenoid should have a length larger than 10 cm. The maximum current capacity of wire is 15 A, so less than 15 A should flow in wire. Now using
B = μ0Nl\mu_0 \frac{N}{l} I or 10 × 10−410^{-4} = 4π × 10−7Nl10^{-7} \frac{N}{l} I
Nl\frac{N}{l} I = 7961.8
Now we can think of a possible combination with I = 10 A and total length of solenoid l = 50 cm
N50×10−2\frac{N}{50 \times 10^{-2}} × 10 = 7961.8 or N = 398.09 turns.
So, one combination for the desired 100 G magnetic field in a length 10 cm can be a total length of solenoid of 50 cm and current in the solenoid of 10 A and total turns nearly 400.
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