Waiting
Login-Verarbeitung ...

Trial ends in Request Full Access Tell Your Colleague About Jove

29.14: Magnetic Vector Potential

TABLE OF
CONTENTS
JoVE Core
Physics

Ein Abonnement für JoVE ist erforderlich, um diesen Inhalt ansehen zu können. Melden Sie sich an oder starten Sie Ihre kostenlose Testversion.

Education
Magnetic Vector Potential
 
TRANSCRIPT

29.14: Magnetic Vector Potential

In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.

Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum permeability, the number of turns per unit length, and the current. Conversely, the magnetic field outside the solenoid is zero. Considering this, what is the vector potential for an ideal solenoid?

The magnetic flux through the solenoid is given by

Equation1

Since the magnetic field equals the curl of the vector potential, the magnetic flux can be rewritten in terms of the vector potential.

Equation2

Thus, the line integral of the magnetic vector potential equals the surface integral of the magnetic field.

Equation3

Now consider a circular Amperian loop of radius r inside the solenoid. The magnetic flux through this loop is given by

Equation4

Equating the magnetic flux to the line integral of the magnetic vector potential, the expression for the vector potential can be obtained.

Equation5

The vector potential mimics the magnetic field and acts along the circumference.


Suggested Reading

Tags

Magnetic Vector Potential Solenoid Magnetic Field Magnetic Flux Amperian Loop Electromagnetism

Get cutting-edge science videos from JoVE sent straight to your inbox every month.

Waiting X
Simple Hit Counter