A solenoid 1.30 m long and 2.60 cm in diameter carries a current of 18.0 A. The magnetic field i

step 1 We can find the total length of a wire that forms a solenoid. By first finding n is the number o

A solenoid 1.30 m long and 2.60 cm in diameter carries a...

A solenoid 1.30 $\mathrm{m}$ long and 2.60 $\mathrm{cm}$ in diameter carries a current of 18.0 A. The magnetic field inside the solenoid is 23.0 $\mathrm{mT}$ .
Find the length of the wire forming the solenoid.

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Key Concepts

Solenoid

A solenoid is a long coil of wire that produces a nearly uniform magnetic field inside when an electric current passes through it. It is an important component in electromagnetism, used to convert electrical energy into magnetic energy.

Magnetic Field Inside a Solenoid

The magnetic field inside a solenoid is calculated 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 is fundamental in understanding how current and coil density affect the magnetic field strength.

Turn Density (Number of Turns per Unit Length)

Turn density, defined as the number of turns per unit length of the solenoid, is a key parameter that influences the magnetic field generated inside the coil. It is used in the formula for the magnetic field and is essential for determining the overall coil design.

Geometry and Length of Wire

The total length of the wire used to form a solenoid is obtained by calculating the number of turns in the solenoid and multiplying it by the circumference of one turn. The circumference, which depends on the solenoid's diameter, directly affects the total length of wire, linking the geometrical dimensions to the electrical and magnetic properties.

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