Ampère's law connects electric currents to the magnetic fields they create. It's a key principle in electromagnetism, showing that moving charges generate magnetic fields proportional to the current's strength.
For straight wires, the strength decreases as you move away. The helps visualize field direction: point your thumb along the current, and your curled fingers show the field's circulation.
Ampère's Law and Magnetic Fields
Ampère's law and magnetic fields
Top images from around the web for Ampère's law and magnetic fields
Electrodynamics/Ampere's Law - Wikibooks, open books for an open world View original
Is this image relevant?
Magnetic Fields Produced by Currents: Ampere’s Law – College Physics View original
Is this image relevant?
22.9 Magnetic Fields Produced by Currents: Ampere’s Law – College Physics View original
Is this image relevant?
Electrodynamics/Ampere's Law - Wikibooks, open books for an open world View original
Is this image relevant?
Magnetic Fields Produced by Currents: Ampere’s Law – College Physics View original
Is this image relevant?
1 of 3
Top images from around the web for Ampère's law and magnetic fields
Electrodynamics/Ampere's Law - Wikibooks, open books for an open world View original
Is this image relevant?
Magnetic Fields Produced by Currents: Ampere’s Law – College Physics View original
Is this image relevant?
22.9 Magnetic Fields Produced by Currents: Ampere’s Law – College Physics View original
Is this image relevant?
Electrodynamics/Ampere's Law - Wikibooks, open books for an open world View original
Is this image relevant?
Magnetic Fields Produced by Currents: Ampere’s Law – College Physics View original
Is this image relevant?
1 of 3
Ampère's law establishes a fundamental relationship between electric currents and the magnetic fields they generate
States the magnetic field around a is directly proportional to the total passing through the area enclosed by the loop
Mathematically expressed as ∮[B](https://www.fiveableKeyTerm:B)⋅dl=μ0Ienc
∮B⋅dl represents the of the magnetic field B along the closed loop
Ienc denotes the total current enclosed by the loop
μ0 is the , a constant equal to 4π×10−7 [T](https://www.fiveableKeyTerm:T)⋅[m/A](https://www.fiveableKeyTerm:m/A)
Demonstrates that electric currents (moving charges) serve as sources of magnetic fields
The strength of the generated magnetic field is directly proportional to the magnitude of the electric current
Ampère's law is a key principle in electromagnetism, alongside , , and the
Ampère's law is particularly useful in , where currents and magnetic fields are time-independent
Magnetic fields around straight wires
For an carrying a [I](https://www.fiveableKeyTerm:I), the magnetic field at a distance [r](https://www.fiveableKeyTerm:r) from the wire can be calculated using Ampère's law
The magnetic field magnitude is given by B=2πrμ0I
B represents the magnitude of the magnetic field
I is the current flowing through the wire
r is the perpendicular distance from the center of the wire to the point of interest
To derive this formula using Ampère's law:
Choose a of radius r centered on the wire as the path of integration
Due to the of the situation, the magnetic field is constant in magnitude along the loop
Simplify the line integral: ∮B⋅dl=B(2πr), where 2πr is the circumference of the loop
Apply Ampère's law: B(2πr)=μ0I, equating the line integral to the enclosed current
Solve for B to obtain the final expression: B=2πrμ0I
The magnetic field around a straight wire decreases inversely with increasing distance from the wire (falls off as 1/r)
This result is useful for calculating magnetic fields in situations involving long, straight current-carrying wires (power lines, electrical cables)
Right-hand rule for current direction
The is a convention used to determine the direction of the magnetic field circulation in relation to the current direction when applying Ampère's law
To use the right-hand rule:
Point your right thumb in the direction of the current flow
Your fingers will naturally in the direction of the magnetic field circulation
When applying Ampère's law, the direction of the line integral (circulation) must be consistent with the right-hand rule
If the current is pointing out of the loop (towards you), the circulation is counterclockwise
If the current is pointing into the loop (away from you), the circulation is clockwise
The right-hand rule ensures that the relationship between the current direction and the magnetic field circulation is consistent with Ampère's law
This convention is crucial for correctly determining the direction of the magnetic field when solving problems involving Ampère's law (solenoids, toroidal coils)
Ampère's Law and Maxwell's Equations
Ampère's law is one of , which collectively describe the behavior of electric and magnetic fields
The curl of the magnetic field is related to the current density and the time-varying electric field
Ampère's law in its original form applies to steady currents, but Maxwell's equations extend it to include time-varying fields
, as described by Faraday's law, is closely related to Ampère's law in Maxwell's equations