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.

Solution

Given,
Magnetic field, $B = 100 G = 100 \times 10^{- 4} T = 10^{- 2} T$
Maximum current carrying capacity, I = 15 A
Number of turns per unit length, $n = 1000 m^{- 1}$

Magnetic field insie a solenoid is

$B = μ_{0} n l$
Therefore,
$nI = \frac{B}{μ_{0}} = \frac{10^{- 2}}{4 π \times 10^{- 7}} = \frac{10^{5}}{4 π} = 7961.5 ~ 8000$

We may have,

$I = 10 A and n = 800$ /m as per the requirement

The solenoid may have length 50 cm and cross section 5 x 10^–3 m² (five times given values) so as to avoid edge effects etc.

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

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Moving Charges And Magnetism

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