A solenoid has diameter 2.5 cm, length 30 cm, and inductance 1.34 mH. (a) How many turns of wi

step 1 This question belongs to the electromagnetic induction in which we have a solenoid having diamet

A solenoid has diameter 2.5 cm, length 30 cm, and...

A solenoid has diameter $2.5 \mathrm{~cm}$, length $30 \mathrm{~cm}$, and inductance $1.34 \mathrm{mH}$. (a) How many turns of wire does it have?
(b) What's the energy stored in the solenoid when it carries a 6.0 - A current?

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Key Concepts

Inductance of a Solenoid

This concept involves calculating the inductance of a solenoid using its physical dimensions and number of turns. The inductance is given by the formula L = ?? N² A / ?, where ?? is the permeability of free space, N is the number of turns, A is the cross-sectional area (typically a function of the solenoid's diameter), and ? is the length of the solenoid. Understanding this relationship is crucial for relating the geometric properties of the solenoid to its ability to store magnetic energy.

Energy Storage in an Inductor

This concept pertains to the energy stored in a current-carrying inductor, expressed by the formula U = ½ L I², where L is the inductance and I is the current. This formula captures the work done in establishing the magnetic field within the inductor and is fundamental in the study of circuits and electromagnetic energy conversion.

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