(a) What would have to be the self-inductance of a solenoid...

Name: Problem 49, Chapter 30: University Physics with Modern Physics
Uploaded: 2019-08-17T08:27:13-08:00
Duration: 3 min 37 s
Channel: Abhishek Jana
Description: (a) What would have to be the self-inductance of a solenoid for it to store 10.0 J of energy when a 2.00-A current runs through it? (b) If this solenoid's cross-sectional diameter is 4.00 cm, and if you could wrap its coils to a density of 10 coils/mm, how long would the solenoid be? (See Exercise 30.15.) Is this a realistic length for ordinary laboratory use?

(a) What would have to be the self-inductance of a solenoid for it to store 10.0 J of energy when a 2.00-A current runs through it? (b) If this solenoid's cross-sectional diameter is 4.00 cm, and if you could wrap its coils to a density of 10 coils/mm, how long would the solenoid be? (See Exercise 30.15.) Is this a realistic length for ordinary laboratory use?

Key Concepts

Self-Inductance

Self-inductance is a property of an electrical circuit, especially coils like solenoids, where a change in the current flowing through the circuit induces an electromotive force (EMF) in the circuit itself. This concept is central to understanding how magnetic energy is stored and how circuits oppose changes in current. It is quantified by the constant L, which relates the induced voltage to the rate of change of the current via Faraday's law.

Energy Stored in an Inductor

The energy stored in an inductor, such as a solenoid, is given by the expression (1/2)LI², where L is the self-inductance and I is the current. This energy is stored in the magnetic field generated by the current flowing through the coil, and the formula reflects how both the inductor’s properties and the current's magnitude contribute to the energy storage. Understanding this relation is key in designing circuits that efficiently store and release magnetic energy.

Solenoid Geometry

A solenoid is a coil of wire designed to generate a uniform magnetic field in its interior when an electric current passes through it. Its geometry, including its length, cross-sectional area, and number of turns, directly influences its inductance and the strength and distribution of the magnetic field. Analyzing these geometrical factors is important when calculating inductance and energy storage for practical applications.

Coil Density

Coil density refers to the number of turns or coils per unit length of the solenoid. It is a critical parameter because it determines the total number of loops in the coil, which in turn affects the solenoid's self-inductance. A higher turn density typically increases the inductance, assuming other geometrical parameters remain constant, and it is used in designing solenoids to meet specific inductance requirements.

Practical Considerations in Laboratory Design

When designing laboratory equipment such as solenoids, it is important to consider not only the theoretical calculations for inductance and energy storage but also the practical feasibility of the physical dimensions. Assessing whether the required dimensions, such as the solenoid’s length, are realistic for typical lab setups is essential in bridging the gap between theoretical designs and experimental implementations.

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