Magnetic field due to a toroid
Understand the concept of a toroid and apply Ampere's Circuital Law to calculate the magnetic field inside and outside a toroid.
What is Magnetic field due to a toroid?
A toroidal coil is a doughnut-shaped coil formed by winding a wire around a circular core.
Key formula / rule: Magnetic field inside a toroid
Key points
- Define a toroid.
- Apply Ampere's Circuital Law to a toroid.
- Calculate the magnetic field inside a toroid.
- Determine the magnetic field outside a toroid.
Common exam trap
Assuming a magnetic field exists outside the toroid.
Definitions
- Term
Toroid
- Meaning
A toroidal coil is a doughnut-shaped coil formed by winding a wire around a circular core.
- Term
Amperian Loop
- Meaning
An imaginary closed loop used in Ampere's Circuital Law to calculate the magnetic field.
Learning objectives
Define a toroid.
Apply Ampere's Circuital Law to a toroid.
Calculate the magnetic field inside a toroid.
Determine the magnetic field outside a toroid.
Formulae
- Name
Magnetic field inside a toroid
- Note
where \μ0 is the permeability of free space, N is the total number of turns, I is the current through the wire, and r is the radius of the Amperian loop inside the toroid.
- Expression
B = \frac{\μ0 NI}{2\π r}
- Name
Magnetic field inside a toroid (alternative form)
- Note
where n = N/(2\π r) is the number of turns per unit length along the circumference of the toroid.
- Expression
B = \μ0 nI
Prerequisites
Understanding of magnetic fields.
Knowledge of solenoids.
Concept of current carrying wires.
Ampere's Circuital Law.
Common mistakes
Assuming a magnetic field exists outside the toroid.
Incorrectly calculating the enclosed current for the Amperian loop.
Confusing the toroid with a straight solenoid.
Keywords
Toroid
Magnetic Field
Ampere's Law
Solenoid
Inductor
μ₀
N
I
r
Practice preview
What is the magnetic field inside a toroid?…
easy
Consider a toroid with N turns, mean radius R, and carrying a current I. Which of the following statements is TRUE?…
hard
What is the magnetic field outside a toroid?…
easy