Glossary
Charge carriers
The mobile particles, typically electrons in metals, that move to constitute an electric current within a conductor.
Example:
In a semiconductor, both electrons and holes can act as charge carriers, contributing to the flow of current.
Displacement vector of the conductor (d)
A tiny vector representing an infinitesimal segment of the conductor along which the current flows, used in the integral for calculating magnetic force.
Example:
When calculating the total magnetic force on a curved wire, you integrate over many small displacement vector of the conductor segments.
External magnetic field strength
The magnitude of the magnetic field present in the region surrounding the conductive loop, directly impacting the induced current and magnetic force.
Example:
Using a more powerful electromagnet increases the external magnetic field strength, leading to a stronger magnetic force on a current-carrying wire.
Free-body diagram
A visual representation of an object showing all external forces acting upon it, used to analyze its motion.
Example:
Drawing a free-body diagram for a current loop helps identify all forces, such as gravity and magnetic force, before applying Newton's second law.
Induced currents
Electric currents generated within a conductive loop due to a change in magnetic flux through the loop.
Example:
Moving a powerful magnet quickly through a coil of copper wire creates induced currents in the wire, which can light up a small LED.
Kinematic equations
A set of equations that describe the motion of objects with constant acceleration, relating displacement, initial velocity, final velocity, acceleration, and time.
Example:
After calculating the constant acceleration of a loop using Newton's second law, kinematic equations can predict its position and velocity at any future time.
Loop orientation
The angular position of the conductive loop relative to the magnetic field lines, which determines the amount of magnetic flux and the resulting induced current and force.
Example:
A motor's efficiency depends on the loop orientation within the magnetic field, as the torque is maximized when the loop's plane is parallel to the field lines.
Loop resistance
The opposition to the flow of induced current within a conductive loop, affecting the magnitude of the current.
Example:
A loop made of a highly conductive material like superconducting wire will have negligible loop resistance, allowing for very large induced currents.
Loop size and shape
The physical dimensions and configuration of a conductive loop, which influence the magnetic flux through it and the resulting induced current.
Example:
A larger loop size and shape will generally enclose more magnetic flux, leading to a greater induced current for the same change in magnetic field.
Loop velocity
The speed and direction at which a conductive loop moves relative to a magnetic field, influencing the rate of change of magnetic flux and thus induced current.
Example:
Increasing the loop velocity as it enters a magnetic field will increase the induced electromotive force and, consequently, the induced current.
Magnetic field vector (B)
A vector quantity representing the strength and direction of a magnetic field at a given point in space.
Example:
A compass needle aligns itself with the Earth's magnetic field vector, pointing towards magnetic north.
Magnetic flux
A measure of the total number of magnetic field lines passing through a given area, influencing the magnitude of induced current.
Example:
As a conducting loop moves out of a uniform magnetic field, the magnetic flux through it decreases, inducing a current.
Magnetic force vector (FB)
The vector quantity representing the force exerted by a magnetic field on a moving charge or current-carrying conductor.
Example:
A current-carrying wire placed in a uniform magnetic field experiences a magnetic force vector that can push it sideways, forming the basis of an electric motor.
Magnetic forces on conductors
Forces experienced by conductive loops when induced currents flow within them, interacting with pre-existing magnetic fields.
Example:
When a metal brake disc spins through a strong magnetic field, magnetic forces on conductors are generated, causing it to slow down due to eddy currents.
Newton's second law
A fundamental principle stating that the net force acting on an object is equal to the product of its mass and acceleration (F=ma).
Example:
To find the acceleration of a falling conducting loop in a magnetic field, one must apply Newton's second law by summing gravitational and magnetic forces.
Right-hand rule
A mnemonic rule used to determine the direction of vector quantities, such as magnetic force, given the directions of current and magnetic field.
Example:
Using the right-hand rule, you can quickly determine that a current flowing upwards in a wire within a magnetic field pointing right will experience an out-of-page force.
Rotational acceleration
The angular acceleration of an object that results in a change in its angular velocity, causing it to spin or rotate.
Example:
A current loop in a magnetic field can experience a torque, leading to rotational acceleration and causing it to spin like the rotor in an electric motor.
Terminal velocity
The constant velocity that a falling object eventually reaches when the opposing force (like magnetic force or air resistance) equals the gravitational force, resulting in zero net acceleration.
Example:
A conducting loop falling through a strong magnetic field will eventually reach a terminal velocity when the upward magnetic force perfectly balances the downward gravitational force.
Translational acceleration
The acceleration of an object that results in a change in its linear velocity, causing it to move in a straight line.
Example:
A conducting loop entering a magnetic field might experience translational acceleration, causing it to speed up or slow down as it moves.