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The Solenoid

The Solenoid

Content Standards

Students will

  • Understand magnetic field due to current-carrying conductors.
  • Use Biot–Savart law and Ampere’s law in symmetric situations.
  • Analyze magnetic field distribution inside and outside a solenoid.
  • Interpret diagrams that show field line behavior and Amperian loops.

Performance Standards

Students will be able to:

  • Correctly deriving and explaining, B=μ₀nI, using Ampere’s circuital law.
  • Accurately drawing and labelling magnetic field line diagrams for finite and long solenoids.
  • Solving numerical problems involving turns per unit length, current, and magnetic field.
  • Verbally describing why, the magnetic field outside a long solenoid approaches zero.

Alignment Standards

Reference: NCERT Book Alignment 

The lesson is aligned with the NCERT Grade 12 Physics Textbook, Chapter 4: Moving Charges and Magnetism, Section 7 –The Solenoid.

Learning Objectives

By the end of the lesson, students will be able to:

  • Define a solenoid and distinguish between finite and ideal long solenoids.
  • Explain how magnetic fields due to individual turns combine to produce a uniform field.
  • Apply Ampere’s circuital law to derive the magnetic field inside a long solenoid.
  • Interpret magnetic field line diagrams of solenoids (finite vs long.
  • Calculate magnetic field inside a solenoid using B=μ₀nI
  • Differentiate between fields at interior and exterior points using textbook reasoning.
  • Relate the solenoid to practical applications (electromagnets, induction coils, MRI systems).

Prerequisites (Prior Knowledge)

  • Magnetic field due to a straight conductor and circular loop.
  • Right-hand thumb rule and direction of magnetic field.
  • Ampere’s circuital law: ∮B⋅dl=μ₀I
  • Basic vector concepts and symmetry considerations.

Introduction

Solenoids are one of the most important devices in electromagnetism. It consists of a long, tightly wound helical coil of wire which produces a magnetic field when an electric current passes through it. According to Ampere’s circuital law, the magnetic field inside a long solenoid is uniform, strong and directed along its axis, whereas the field outside is negligibly small.

In this lesson, students explore how the magnetic fields due to individual circular loops combine, how the field between neighboring turns cancels, and how the idealized long solenoid leads to the expression

B=μ₀nI

where n is the number of turns per unit length. This understanding is foundational for later concepts like electromagnetic induction, magnetic materials, and electromagnets.

Timeline (40 Minutes)

TitleApproximate DurationProcedureReference Material
Engage6

Show students a bar magnet and a current-carrying coil and ask:

 

Display NCERT Fig. 4.15(b) showing the finite solenoid’s field pattern and ask students to observe differences from a bar magnet.

Slides

Explore10

Explore VR lab for Solenoid.

Slides + Virtual Lab

Explain10
  • Explain how circular field loops between neighboring turns cancel, as shown in Fig. 4.15(a) 
  • Discuss the finite solenoid field pattern, distinguishing the strong uniform field at point P and weak field at Q.
  • Introduce the ideal long solenoid model (Fig. 4.16) and derive using Ampere’s law:

B=μ₀nI

  • Identify why field outside approaches zero: the Amperian loop contributions in exterior segments vanish.

Slides

Evaluate10

Students will attempt the Self Evaluation task on LMS.

Virtual Lab

Extend5

Challenge students:
“How does inserting a soft iron core modify the field inside the solenoid?”

Slides

The Solenoid

Introduction

A solenoid is a long, cylindrical coil made by winding many turns of insulated wire closely together. When an electric current passes through it, the solenoid produces a magnetic field like that of a bar magnet. The field inside an ideal long solenoid is uniform, strong, and directed along its axis, making it extremely useful in devices like electromagnets, inductors, and MRI machines. Understanding the formation and properties of this magnetic field is crucial for mastering electromagnetism

Theory

A solenoid generates a magnetic field because each circular loop of current produces its own magnetic field. When many such loops are wound close together, the magnetic fields of individual turns add up inside the solenoid and cancel out outside. This leads to a strong, uniform field inside and a very weak or negligible field outside.

Magnetic Field Inside the Solenoid:
Inside a long solenoid, magnetic field lines are nearly parallel, equally spaced, and strong. This uniformity arises from the superposition of fields from many tightly packed loops.
Using Ampere’s circuital law, the magnetic field inside a long solenoid is derived as:

B= μ₀nI

Where,

  • B is the magnetic field inside the solenoid,
  • μ₀ is the permeability of free space,
  • n is the number of turns per unit length,
  • I is the current flowing through the solenoid.

This formula applies well to a solenoid whose length is much greater than its radius (ideal long solenoid).

Derivation:

We consider a rectangular Amperian loop abcd to determine the field.  If solenoid is made longer it appears like a long cylindrical metal sheet. The field outside the solenoid approaches zero. We shall assume that the field outside is zero. 

The field inside becomes everywhere parallel to the axis. Along cd the field is zero as argued above. Along transverse sections bc and ad, the field component is zero. Thus, these two sections make no contribution. 

Let the field along ab be B. Thus, the relevant length of the Amperian loop is, L = h. Let n be the number of turns per unit length, then the total number of turns is nh.

 The enclosed current is, Ie = I (n h), where I is the current in the solenoid. 

From Ampere’s circuital law BL = μ₀ I ,

 B h = μ₀ I (n h) 

B = μ₀ n I 

The direction of the field is given by the right-hand rule. The solenoid is commonly used to obtain a uniform magnetic field.
Magnetic Field Outside the Solenoid:
The field outside an ideal long solenoid is extremely small. This happens because the circular magnetic fields generated by neighboring turns cancel one another in the outward direction.

Finite vs Long Solenoid
In a finite solenoid, the field near the centre behaves almost like that of a long solenoid—uniform and strong. Near the ends, the field becomes less uniform and spreads out.

Applications of Solenoids:
Solenoids are used in:

  • Electromagnets
  • Relays and inductors
  • Magnetic levitation systems
  • Particle accelerators
  • MRI systems

Their ability to create a controlled, uniform magnetic field makes them essential in modern electrical and electronic systems.

Vocabulary

This is the list of vocabulary terms used throughout the lesson.

  • Solenoid: A long, tightly wound helical coil that produces a magnetic field when current flows through it.
  • Turns per unit length (n): Number of coil turns present per meter of the solenoid.
  • Magnetic field (B): The region around a current or magnet where magnetic effects can be experienced.
  • Ampere’s circuital law: A law stating that the line integral of magnetic field around a closed loop equals 0times enclosed current.
  • Uniform magnetic field: A magnetic field with constant magnitude and direction at every point.
  • Permeability of free space (μ₀): A constant that measures the ability of vacuum to support magnetic fields.
  • Electromagnet: A magnet formed when current flows through a coil, often strengthened with an iron core.
  • Superposition of fields: The principle that total magnetic field is the vector sum of fields produced by individual turns.
  • Ideal long solenoid: A solenoid whose length is much greater than its diameter, giving a perfectly uniform interior magnetic field.
  • Soft iron core: A material inserted inside a solenoid to increase its magnetic field strength due to high permeability.

The Solenoid

Category

Introduction

This Virtual Reality (VR) Lab is designed to help you explore how magnetic fields are produced by electric current. You will move through a series of immersive scenes that progress from basic magnetic field concepts to the magnetic field of a solenoid. Each scene visualises magnetic field lines clearly so you can observe patterns, directions, and strengths of fields that are otherwise invisible. The final scene includes interactive sliders that allow you to change the current and number of turns to see how the magnetic field inside a solenoid varies. This lab will strengthen your understanding of NCERT Class 12 Physics, Chapter 4 – Moving Charges and Magnetism.

Key Features

  • Immersive 3D Environment: Visualize magnetic field lines around different conductors and magnets.
  •  Field Visualization Mode: See dynamic animations of field lines forming concentric circles or bar magnet patterns.
  • Real-time Field Simulation: Dynamic field lines update instantly with changes in current or turns.
  • Learning Checkpoints: Interactive questions at the end to reinforce concepts.
  • Sequential Concept Learning: Each scene builds on the previous one, matching the NCERT logical flow of electromagnetism topics.

Step-by-Step Procedure for VR Experience

 Step 1: Introduction – Bar Magnet and Magnetic Field

  • Enter the VR environment and observe the 3D model of a bar magnet.
  • Note how field lines are dense near the poles and spread out away from them.
  • View magnetic field lines emerging from the North pole and entering the South pole.

 Step 2: Magnetic Field Lines through a Current-Carrying Straight Conductor

  • Observe circular magnetic field lines forming concentric circles around the wire.

Step 3:  Magnetic Field Through a Loop

  • Approach the circular current loop displayed in 3D.
  • Watch how magnetic field lines emerge from one face of the loop and converge at the other, resembling a small bar magnet.
  • Observe how the field becomes stronger and more concentrated at the centre of the loop.

Step 4: Magnetic Field Lines of a Solenoid 

  • Study how fields from each loop combine:
  • inside → fields add up (strong & uniform)
  • outside → fields cancel (very weak)

Step 5: Magnetic Field Lines of a Solenoid 

  • Interact with the  sliders for current (I) and number of turns per unit length (n).
  • Adjust the sliders slowly to see real-time changes in the magnetic field magnitude.
  • Observe the relation: B=μ₀ nI
  • Try increasing the current first, then the number of turns, and compare how the field strength changes.
  • Complete the activity by noting how uniform the field remains even as parameters change.

Step 6: Evaluation

  • After interaction, students proceed to the quiz:
    • 2  MCQs
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