Magnetic field due to a solenoid
Understand the concept of a solenoid and use Ampere's Circuital Law to determine the magnetic field inside and outside an ideal solenoid.
What is Magnetic field due to a solenoid?
A long coil of insulated wire wound in a helical shape, used to produce a uniform magnetic field when current flows through it.
Key formula / rule: Magnetic field inside an ideal solenoid
Key points
- Define a solenoid and its properties.
- Apply Ampere's Circuital Law to find the magnetic field inside an ideal solenoid.
- Explain why the magnetic field outside an ideal solenoid is zero.
- Calculate the magnetic field strength inside a solenoid.
Common exam trap
Forgetting that the formula B = μ₀nI is for an ideal solenoid.
Definitions
- Term
Solenoid
- Meaning
A long coil of insulated wire wound in a helical shape, used to produce a uniform magnetic field when current flows through it.
- Term
Ampere's Circuital Law
- Meaning
States that the line integral of the magnetic field around any closed loop is equal to μ₀ × the total current enclosed by the loop (∮ B ⋅ dl = μ₀Ienc).
- Term
Permeability of free space (μ₀)
- Meaning
A fundamental physical constant representing the measure of the ability of a vacuum to support the formation of a magnetic field.
Learning objectives
Define a solenoid and its properties.
Apply Ampere's Circuital Law to find the magnetic field inside an ideal solenoid.
Explain why the magnetic field outside an ideal solenoid is zero.
Calculate the magnetic field strength inside a solenoid.
Formulae
- Name
Magnetic field inside an ideal solenoid
- Note
where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current.
- Expression
B = μ₀nI
- Name
Number of turns per unit length
- Note
where N is the total number of turns and L is the length of the solenoid.
- Expression
n = N/L
Prerequisites
Understanding of electric current and magnetic fields.
Knowledge of Ampere's Circuital Law.
Vector calculus basics (line integral).
Common mistakes
Forgetting that the formula B = μ₀nI is for an ideal solenoid.
Assuming the magnetic field outside a real solenoid is exactly zero.
Incorrectly applying Ampere's Circuital Law, especially in choosing the Amperian loop.
Confusing turns per unit length (n) with the total number of turns (N).
Keywords
Solenoid
Magnetic field
Ampere's Circuital Law
Uniform field
Ideal solenoid
μ₀
Turns per unit length
Practice preview
What is the magnetic field inside an ideal solenoid?…
easy
An ideal solenoid has n turns per unit length and carries a current I. What is the magnitude of the magnetic field inside the solenoid?…
easy
Consider a long solenoid. If the current flowing through the solenoid is doubled and the number of turns per unit length is halved, how does the magnetic field inside the solenoid change?…
medium