$l$

Definition

$l$ is a variable that represents length, a fundamental physical quantity that describes the one-dimensional extent of an object. In the context of 13.3 Motional Emf, $l$ is a key parameter that describes the length of a conductor moving through a magnetic field, which is a crucial factor in determining the induced electromotive force (emf) in the conductor.

5 Must Know Facts For Your Next Test

1. The length $l$ of a conductor moving through a magnetic field is a key factor in determining the magnitude of the induced emf, as described by Faraday's law of electromagnetic induction.
2. The induced emf in a conductor is proportional to the length $l$ of the conductor, the velocity $v$ of the conductor, and the strength of the magnetic field $B$.
3. The direction of the induced emf is determined by the relative orientation of the conductor, the magnetic field, and the motion of the conductor, as described by Lenz's law.
4. The length $l$ of the conductor, along with its velocity $v$ and the magnetic field strength $B$, determines the rate of change of magnetic flux through the conductor, which is the underlying cause of the induced emf.
5. Understanding the role of $l$ in the context of motional emf is crucial for analyzing and solving problems related to electromagnetic induction in moving conductors.

Review Questions

• Explain how the length $l$ of a conductor moving through a magnetic field affects the induced electromotive force (emf).
  • The length $l$ of a conductor moving through a magnetic field is a key factor in determining the magnitude of the induced emf, as described by Faraday's law of electromagnetic induction. The induced emf is proportional to the length $l$ of the conductor, the velocity $v$ of the conductor, and the strength of the magnetic field $B$. Specifically, the induced emf is given by the equation '$\varepsilon = -Blv$,' where '$\varepsilon$' represents the induced emf. Therefore, a longer conductor will experience a greater induced emf, all else being equal, due to the increased length over which the magnetic flux is changing.
• Describe how the relative orientation of the conductor, the magnetic field, and the motion of the conductor affects the direction of the induced emf, as related to the variable $l$.
  • The direction of the induced emf is determined by the relative orientation of the conductor, the magnetic field, and the motion of the conductor, as described by Lenz's law. Specifically, the induced emf will oppose the change in magnetic flux through the conductor, which is determined by the length $l$ of the conductor, its velocity $v$, and the strength of the magnetic field $B$. The direction of the induced emf can be determined using the right-hand rule, where the thumb points in the direction of the conductor's motion, the index finger points in the direction of the magnetic field, and the middle finger points in the direction of the induced emf. The length $l$ of the conductor is a key factor in this determination, as it defines the orientation of the conductor relative to the magnetic field and the direction of motion.
• Analyze how changes in the length $l$ of a conductor moving through a magnetic field would affect the rate of change of magnetic flux, and consequently, the induced emf.
  • The length $l$ of a conductor moving through a magnetic field is directly proportional to the rate of change of magnetic flux through the conductor, which is the underlying cause of the induced emf. According to Faraday's law of electromagnetic induction, the induced emf is equal to the negative rate of change of magnetic flux. Specifically, the induced emf is given by the equation '$\varepsilon = -N\frac{d\phi}{dt}$,' where '$N$' is the number of turns in the conductor and '$\frac{d\phi}{dt}$' is the rate of change of magnetic flux. As the length $l$ of the conductor increases, the area over which the magnetic flux is changing also increases, leading to a greater rate of change of magnetic flux and, consequently, a larger induced emf. Therefore, the length $l$ of the conductor is a critical parameter in determining the magnitude of the induced emf in the context of motional emf.

Related terms

Magnetic Flux: The measure of the strength of a magnetic field over a given area, often denoted by the Greek letter '$\phi$.'

Velocity: The rate of change of an object's position with respect to time, often denoted by the variable '$v$.'

Magnetic Field: A region in space where a magnetic force can be exerted on a moving electric charge or a magnetic material, typically represented by the variable '$B$.'