11.4 Magnetic Force on a Current-Carrying Conductor
3 min read•june 24, 2024
Current-carrying wires create magnetic fields, forming concentric circles around the wire. The field strength depends on current magnitude and distance. relates the around a closed loop to the electric current passing through it.
Magnetic forces on current-carrying wires in uniform fields are calculated using F = ILB sin θ. The determines force direction. Magnetic flux, , and dipole moments are key concepts in understanding magnetic properties and interactions.
Magnetic Fields and Forces
Magnetic fields from current-carrying wires
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Current flowing through a wire creates a magnetic field surrounding the wire
Magnetic field lines form concentric circles around the current-carrying wire (, )
determines the direction of the magnetic field
Point thumb in the current direction and fingers will curl in the magnetic field direction (, )
Magnetic field strength is affected by the current magnitude and distance from the wire
Directly proportional to the current: doubling the current doubles the magnetic field strength
Inversely proportional to the distance: magnetic field weakens as distance from the wire increases (, )
Ampère's law relates the magnetic field around a closed loop to the electric current passing through the loop
Force calculation for wires in magnetic fields
Magnetic force on a current-carrying wire in a uniform magnetic field is calculated using F=ILBsinθ
F: magnetic force measured in newtons (N)
I: current flowing through the wire in amperes (A) (circuit, appliance)
L: length of the wire segment in meters (m)
B: magnetic field strength in teslas (T) (, )
θ: angle between the current direction and the magnetic field
Maximum force occurs when the current is perpendicular to the magnetic field (θ=90∘)
sin90∘=1, simplifying the equation to F=ILB
No force is exerted when the current is parallel to the magnetic field (θ=0∘ or 180∘)
sin0∘=sin180∘=0, resulting in F=0 (, )
The describes the force experienced by a charged particle moving in a magnetic field
Right-hand rule for magnetic force direction
Right-hand rule determines the direction of the magnetic force on a current-carrying wire
Point fingers in the current direction
Orient palm to face the magnetic field direction
Thumb will point in the magnetic force direction (, )
Magnetic force is always perpendicular to both the current and the magnetic field
Force is a cross product of the current and magnetic field vectors (, )
Reversing either the current or magnetic field direction will reverse the force direction
Allows for precise control of magnetic forces in applications (, particle steering)
Magnetic Properties and Interactions
Magnetic flux represents the amount of magnetic field passing through a given area
Permeability is a measure of a material's ability to support the formation of a magnetic field within itself
The magnetic dipole moment characterizes the torque experienced by a magnet in an external magnetic field