A long solenoid has a length of 0.65 m and contains 1400 turns of wire. There is a current of 4.

step 1 Okay, so we have a problem here. This one's pretty straightforward. We want to know the magnetic

A long solenoid has a length of 0.65 m and contains 1400...

A long solenoid has a length of 0.65 $\mathrm{m}$ and contains 1400 turns of wire. There is a current of 4.7 $\mathrm{A}$ in the wire. What is the magnitude of the magnetic field within the solenoid?

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Key Concepts

Permeability of Free Space

The permeability of free space, denoted ??, is a physical constant that quantifies the ability of the vacuum to support the formation of a magnetic field. It serves as a scaling factor in the magnetic field equation for a solenoid, linking the physical configuration and current to the resulting field.

Turn Density

Turn density, represented as n, is the number of wire turns per unit length of the solenoid. It is a critical factor in determining the strength of the magnetic field inside the solenoid, as a higher turn density results in a stronger magnetic field.

Long Solenoid

A long solenoid is a coil of wire in which the length is much greater than its diameter, resulting in a magnetic field that is nearly uniform in its interior. This approximation simplifies analysis by focusing on the central region where edge effects can be neglected.

Magnetic Field of a Solenoid

The magnetic field inside a long solenoid is determined using the formula B = ?? n I, where B is the magnetic field, ?? is the permeability of free space, n is the number of turns per unit length, and I is the current. This relationship shows how the field depends directly on the current and the density of the windings.

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