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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. - Physics

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Numerical

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.

Concept: Solenoid and the Toroid - the Solenoid
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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 4 Moving Charges and Magnetism
Q 15 | Page 170
NCERT Physics Part 1 and 2 Class 12
Chapter 4 Moving Charges and Magnetism
Exercise | Q 4.15 | Page 170

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