Glossary
Charge Carriers
Particles, typically electrons in metals, that move within a conductor to constitute an electric current.
Example:
In a copper wire, free electrons act as charge carriers, moving collectively to transmit electrical signals.
Faraday's Law
A law of electromagnetism stating that the magnitude of the induced electromotive force (EMF) in a circuit is proportional to the rate of change of magnetic flux through the circuit.
Example:
Generators operate based on Faraday's Law, converting mechanical energy into electrical energy by changing magnetic flux.
Induced Current ($I$)
The magnitude of the current produced in a conductor due to electromagnetic induction.
Example:
Spinning a coil rapidly near a magnet generates a larger induced current, which can light up a small LED.
Induced Currents
Electric currents generated within a conductor due to a changing magnetic flux through the conductor's loop or area.
Example:
When you swipe a credit card, the changing magnetic field from the card's strip creates induced currents in the reader's coil, allowing data to be read.
Induced EMF ($\epsilon$)
The electromotive force (voltage) generated in a conductor due to a changing magnetic flux, which drives the induced current.
Example:
When a metal detector coil passes over a metal object, the changing magnetic field creates an induced EMF in the coil, signaling the object's presence.
Infinitesimal Displacement Vector ($\vec{dl}$)
A small vector element representing a segment of a current-carrying wire, used in integral calculations for magnetic force.
Example:
To calculate the total force on a curved wire, we sum the forces on many tiny infinitesimal displacement vectors along its length.
Kinematics Equations
A set of mathematical equations that describe the motion of objects with constant acceleration, relating displacement, velocity, acceleration, and time.
Example:
After calculating the acceleration of a loop using Newton's Second Law, we can use kinematics equations to find its final velocity or position.
Loop Size and Shape
The physical dimensions and configuration of a conducting loop, which determine the area through which magnetic flux can pass.
Example:
A larger loop size and shape will generally enclose more magnetic flux, leading to a greater induced current for a given magnetic field change.
Magnetic Field
A region around a magnetic material or a moving electric charge where a force of magnetism is exerted on other magnetic materials or moving charges.
Example:
The Earth's magnetic field protects us from harmful solar radiation by deflecting charged particles.
Magnetic Field Vector ($\vec{B}$)
A vector quantity that describes the strength and direction of a magnetic field at a given point in space.
Example:
A compass needle aligns itself with the local magnetic field vector, pointing towards magnetic north.
Magnetic Flux
A measure of the total number of magnetic field lines passing through a given area, indicating the strength of the magnetic field over that area.
Example:
Changing the magnetic flux through a coil by moving a magnet near it is how a generator produces electricity.
Magnetic Force Vector ($\vec{F}_{B}$)
The vector quantity representing the force exerted by a magnetic field on a moving charge or a current-carrying conductor, determined by the cross product of current element and magnetic field.
Example:
When a current flows through a wire in a strong magnet, the resulting magnetic force vector can cause the wire to jump.
Magnetic Forces on Conductors
Forces experienced by current-carrying wires or loops when placed within an external magnetic field, resulting from the interaction between the moving charge carriers and the field.
Example:
A speaker uses the magnetic forces on conductors to make a coil vibrate, pushing air and creating sound waves.
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 ($\vec{F} = m\vec{a}$).
Example:
To predict how a conducting loop will move in a magnetic field, we apply Newton's Second Law by summing all forces acting on it.
Ohm's Law
A fundamental law stating that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them ($V=IR$).
Example:
Once the induced EMF is known, Ohm's Law can be used to calculate the magnitude of the induced current in a loop with a given resistance.
Orientation of the Loop
The angle or alignment of the conducting loop's plane relative to the magnetic field lines, which affects the amount of magnetic flux passing through it.
Example:
When the orientation of the loop is perpendicular to the magnetic field, the induced current and force are maximized.
Resistance of the Loop Material
A material's opposition to the flow of electric current, which affects the magnitude of the induced current in a conducting loop.
Example:
A loop made of copper has a low resistance of the loop material, allowing for a larger induced current compared to a loop made of nichrome.
Right-Hand Rule
A mnemonic used to determine the direction of magnetic force, magnetic field, or current, typically involving the thumb, fingers, and palm of the right hand.
Example:
To find the direction a current-carrying wire will be pushed in a magnetic field, students often use the Right-Hand Rule.
Rotational Acceleration
The rate of change of an object's angular velocity, causing it to spin or rotate.
Example:
The motor in an electric fan uses magnetic forces to create rotational acceleration in its blades, making them spin.
Strength of the External Magnetic Field
The magnitude of the magnetic field applied from an external source, directly impacting the induced current and the resulting magnetic force.
Example:
Using a stronger magnet increases the strength of the external magnetic field, leading to a more powerful magnetic force on a current-carrying wire.
Translational Acceleration
The rate of change of an object's linear velocity, causing it to move in a straight line.
Example:
A conducting loop experiencing a net magnetic force in one direction will undergo translational acceleration, speeding up as it moves.
Velocity of the Loop
The speed and direction at which a conducting loop moves relative to a magnetic field, influencing the rate of change of magnetic flux.
Example:
Increasing the velocity of the loop as it enters a magnetic field will increase the induced current and thus the magnetic force.