As a new electrical technician, you are designing a large...

As a new electrical technician, you are designing a large solenoid to produce a uniform 0.150 T magnetic field near the center of the solenoid. You have enough wire for 4000 circular turns. This solenoid must be $55.0 \mathrm{~cm}$ long and $2.80 \mathrm{~cm}$ in diameter. What current will you need to produce the necessary field?

Key Concepts

Electric Current

Electric current, measured in amperes, is the flow of electric charge. In the context of a solenoid, the current is directly responsible for generating the magnetic field, and adjusting the current allows control over the field strength produced inside the solenoid.

Unit Conversion

In electromagnetic calculations, it is essential to ensure that all measurements are in consistent SI units. Conversions, such as from centimeters to meters, must be carefully performed to correctly apply the formulas and obtain accurate results.

Solenoid

A solenoid is a coiled wire designed to create a uniform magnetic field when an electric current passes through it. Its design parameters, such as length, number of turns, and diameter, directly influence the characteristics of the produced magnetic field.

Magnetic Field in a Solenoid

The magnetic field inside an ideal solenoid is uniform and calculated using the formula B = ?0 * n * I, where B is the magnetic field, ?0 is the permeability of free space, n is the number of turns per unit length, and I is the electric current. This relationship shows how the solenoid's design and the current determine the magnetic field strength.

Turn Density

Turn density refers to the number of coil turns per unit length (n = total turns/length). It is a critical factor in determining the field strength, as a higher density of turns increases the magnetic field produced for a given current.

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