and torques on are key concepts in electromagnetism. They explain how electric currents interact with magnetic fields, creating forces and rotational effects that are crucial in many applications.
Understanding these interactions helps us grasp the behavior of electric , generators, and other electromagnetic devices. The interplay between current loops and magnetic fields forms the basis for converting electrical energy into mechanical motion and vice versa.
Magnetic Forces and Torques on Current Loops
Net force on current loops
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Top images from around the web for Net force on current loops
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Sum of forces acting on each segment of the loop in an external magnetic field
Force on each segment given by : F=IL×B
I represents current in the loop
L represents vector for length and direction of the segment
B represents external magnetic field
with sides of length a and b in a uniform magnetic field has zero net force
Forces on opposite sides of the loop cancel each other out (top and bottom, left and right)
may result in non-zero net force on the loop
Force depends on across the loop (change in field strength from one side to another)
Torque on current loops
Current loop in a magnetic field experiences a torque that aligns the loop with the field
Torque on a current loop given by: τ=m×B
m represents of the loop
B represents external magnetic field
Magnitude of the torque given by: τ=mBsinθ
θ represents angle between moment and magnetic field
Direction of torque is perpendicular to both magnetic dipole moment and magnetic field (determined by right-hand rule)
Maximum torque when loop is perpendicular to magnetic field (θ=90°)
Zero torque when loop is parallel to field (θ=0° or 180°)
Magnetic dipole moment concept
Vector quantity m characterizes magnetic properties of a current loop
Magnitude of magnetic dipole moment given by: m=IA
I represents current in the loop
A represents area enclosed by the loop
Direction of magnetic dipole moment is perpendicular to plane of the loop (determined by right-hand rule)
If fingers of right hand curl in direction of current, thumb points in direction of magnetic dipole moment
Analogous to electric dipole moment, but for magnetic fields instead of electric fields
Interaction between current loop's magnetic dipole moment and external magnetic field responsible for torque experienced by the loop
Potential energy of a magnetic dipole in a magnetic field given by: U=−m⋅B
Minus sign indicates dipole tends to align itself with the field to minimize potential energy (stable equilibrium position)
Magnetic Field Sources and Interactions
relates the magnetic field around a closed loop to the electric current passing through the loop
is a long coil of wire that generates a uniform magnetic field inside when current flows through it
Magnetic flux is a measure of the total magnetic field passing through a given area
describes how easily a material can be magnetized in response to an external magnetic field
is the precession of the magnetic moments of electrons, atoms, or nuclei around the direction of an external magnetic field