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Electromagnetic induction is a fundamental principle in physics that describes how a changing magnetic field can create an electric current. This section focuses on understanding the relative directions of the magnetic force on a moving charge, the magnetic field, and the induced current.
When a charged particle moves within a magnetic field, it experiences a magnetic force. The direction of this force is perpendicular to both the velocity of the charge and the magnetic field.
The magnetic force ($F$) on a charged particle with charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by:
$$ \vec{F} = q (\vec{v} \times \vec{B}) $$
The direction of the force is determined by the right-hand rule. If the fingers of your right hand point in the direction of $\vec{v}$, and your thumb points in the direction of $\vec{B}$, then your palm points in the direction of $\vec{F}$.
A magnetic field is a region around a magnet or a current-carrying conductor where a magnetic force can be detected. Magnetic fields are represented by magnetic field lines.
The direction of a magnetic field is defined as the direction in which a north-seeking pole of a small magnet would point. Magnetic field lines emerge from the north pole and enter the south pole of a magnet.
A changing magnetic field can induce an electric current in a conductor. This phenomenon is known as electromagnetic induction. The induced current flows in a direction that opposes the change in the magnetic flux.
Faraday's Law of Induction quantifies the magnitude of the induced electromotive force (EMF) or voltage:
$$ \mathcal{E} = - \frac{\Delta \Phi}{ \Delta t} $$
Where:
The direction of the induced current is given by Lenz's Law, which states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.
Lenz's Law provides the direction of the induced current:
The induced current creates a magnetic field that opposes the change in the original magnetic flux.
| Quantity | Direction | Rule |
|---|---|---|
| Magnetic Force on a Moving Charge | Perpendicular to both the velocity of the charge and the magnetic field | Right-hand rule: Fingers point in the direction of $\vec{v}$, thumb points in the direction of $\vec{B}$, palm points in the direction of $\vec{F}$ |
| Magnetic Field Direction | From North to South pole of a magnet | Magnetic field lines emerge from the North pole and enter the South pole. |
| Induced Current Direction (Lenz's Law) | Opposes the change in magnetic flux that produced it | The induced current creates a magnetic field that opposes the change in the original magnetic flux. |