Magnetic field due to a straight infinite current-carrying wire
Apply Ampere's Circuital Law to calculate the magnetic field produced by a long, straight, current-carrying wire.
What is Magnetic field due to a straight infinite current-carrying wire?
A physical constant that describes the ° of magnetization that a vacuum can support. Its value is $4\π \× 10-7 T m/A$.
Key formula / rule: Magnetic field due to an infinite straight wire
Key points
- To derive the magnetic field due to an infinite straight current-carrying wire using Ampere's Law.
- To apply the derived formula to solve problems.
- To determine the direction of the magnetic field using the right-hand rule.
Common exam trap
Confusing the formula with that of a magnetic dipole or solenoid.
Definitions
- Term
Permeability of free space (\μ0)
- Meaning
A physical constant that describes the ° of magnetization that a vacuum can support. Its value is $4\π \× 10-7 T m/A$.
- Term
Amperian Loop
- Meaning
An imaginary closed loop used in Ampere's Circuital Law to calculate the magnetic field. For a straight wire, a circular loop concentric with the wire is chosen.
Learning objectives
To derive the magnetic field due to an infinite straight current-carrying wire using Ampere's Law.
To apply the derived formula to solve problems.
To determine the direction of the magnetic field using the right-hand rule.
Formulae
- Name
Magnetic field due to an infinite straight wire
- Note
Where B is the magnetic field strength, \μ0 is the permeability of free space, I is the current, and r is the perpendicular distance from the wire.
- Expression
B = \frac{\μ0 I}{2\π r}
Prerequisites
Understanding of electric current.
Concept of magnetic field lines.
Ampere's Circuital Law.
Vector dot product.
Common mistakes
Confusing the formula with that of a magnetic dipole or solenoid.
Incorrectly applying the right-hand rule to find the direction.
Using the diameter instead of the radius in the formula.
Keywords
Magnetic field
Straight wire
Current
Ampere's Law
Permeability
Right-hand rule
Concentric circles
Practice preview
A long straight wire carries a current of 5 A. If the wire is bent into a single circular loop, what is the magnetic field at the center of the loop, assuming the radius of the loop is 10 cm?…
medium
A long straight wire carries a current of 10 A. What is the magnetic field at a distance of 5 cm from the wire?…
easy
A long straight wire carries a current I. If the current is doubled and the distance from the wire is also doubled, how does the magnetic field strength change?…
medium