A solenoid of 1.5 meter length and 4 cm diameter possesses 10 turn per cm. A current of 5 Amp i

step 1 In this problem first I am writing the given data. So n is given as 10 tons per centimeter which

A solenoid of 1.5 meter length and 4 cm diameter possesses...

A solenoid of $1.5$ meter length and $4 \mathrm{~cm}$ diameter possesses 10 turn per $\mathrm{cm}$. A current of $5 \mathrm{Amp}$ is flowing through it. The magnetic induction at axis inside the solenoid is (a) $2 \pi \times 10^{-3} \mathrm{~T}$ (b) $2 \pi \times 10^{-5} \mathrm{~T}$ (c) $2 \pi \times 10^{-2} \mathrm{G}$ (d) $2 \pi \times 10^{-5} \mathrm{G}$

A solenoid of $1.5$ meter length and $4 \mathrm{~cm}$ diameter possesses 10 turn per $\mathrm{cm}$. A current of $5 \mathrm{Amp}$ is flowing through it. The magnetic induction at axis inside the solenoid is
(a) $2 \pi \times 10^{-3} \mathrm{~T}$
(b) $2 \pi \times 10^{-5} \mathrm{~T}$
(c) $2 \pi \times 10^{-2} \mathrm{G}$
(d) $2 \pi \times 10^{-5} \mathrm{G}$

Key Concepts

Magnetic Permeability of Free Space

Magnetic permeability of free space, represented by ??, is a fundamental physical constant that quantifies the relationship between the magnetic field and the magnetic force in a vacuum. Its standard value is 4? × 10?? T·m/A, and it appears in the calculation of magnetic fields for current-carrying conductors, including solenoids.

Unit Conversion Between Tesla and Gauss

Understanding unit conversion is essential when interpreting magnetic field values. In the SI system, the magnetic field is commonly expressed in teslas (T), while in the CGS system it is expressed in gauss (G). The conversion factor is 1 T = 10,000 G, which allows one to convert between these units as needed.

Magnetic Field in a Solenoid

The magnetic field inside an ideal solenoid is calculated using the expression B = ?? * n * I, where ?? is the permeability of free space, n is the number of turns per unit length, and I is the current. This formula is derived from Ampère's Law and assumes that the solenoid is long enough so that edge effects are negligible, resulting in a uniform magnetic field along its axis.

Turn Density

Turn density, denoted by n, refers to the number of turns or coils per unit length of the solenoid. It is a critical parameter in determining the strength of the magnetic field generated inside the solenoid, with a higher turn density leading to a proportionally stronger field when other factors remain constant.

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