(I) How many turns of wire would be required to make 130 -mH inductance out of a 30.0 - cm-long

step 1 Okay, so we want to find out how many turns of wire it would take to make a 130 micro henry Indu

(I) How many turns of wire would be required to make 130 -mH...

Key Concepts

Geometrical Parameters in Coil Design

The physical dimensions of a coil, such as its length and cross-sectional area, are critical factors in determining its inductance. The cross-sectional area is usually calculated for a circular coil using the formula A = ?r², where r is the radius. These geometrical considerations are important for optimizing the design of inductors to meet specific inductance requirements.

Inductance of a Solenoid

The inductance of a solenoid is determined by its geometry and the number of turns in the coil. The formula L = ?? N²A / l relates the inductance (L) to the permeability of free space (??), the number of turns (N), the cross-sectional area of the coil (A), and the length of the coil (l). This relationship shows that the inductance increases with the square of the number of turns and depends directly on the coil’s area.

Magnetic Permeability

Magnetic permeability, specifically the permeability of free space (denoted as ??), is a fundamental constant that represents how a magnetic field propagates through vacuum. It is essential in calculating magnetic fields in solenoid inductors and appears in many electromagnetic formulas.

Algebraic Manipulation of Formulae

Solving for an unknown such as the number of turns in a coil involves algebraic manipulation of the physical formulas. Isolating the variable from the inductance formula (L = ?? N²A / l) requires rearranging the equation and taking square roots, which is a fundamental mathematical skill in physics and engineering.

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