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Chapter 33. The Magnetic Field Digital information is stored on a hard disk as microscopic patches of magnetism. Just what is magnetism? How are magnetic fields created? What are their properties? These are the questions we will address. Chapter Goal: To learn how to calculate and use the magnetic field.
Connections to current A magnetic field can be sensed with a magnetic material (compass) and is associated with a current. The earth’s field results from large scale internal currents. The field of a permanent magnet results from atomic scale currents.
The magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law:
where r is the distance from the charge and θ is the angle between v and r. (Valid if v<<c.) The Biot-Savart law can be written in terms of the cross product as
The average B field dB due to the moving charge in an element of circuit of vector length ds carrying current I follows from superposing the fields of the moving charges:
Magnetic field lines close upon themselves – they circulate rather them emanate from charges. Although a current loop can appear like a dipole pair of charges, there is no magnetic charge.
Magnetic field lines close upon themselves – they circulate rather them emanate from poles. The line integral of B around a closed loop is a measure of the strength in circulation.
Whenever total current Ithrough passes through an area bounded by a closed curve, the line integral of the magnetic field around the curve is given by Ampère’s law:
Motion in a uniform constant magnetic field The magnetic force on a moving charge q is perpendicular to B and to v and results in helical motion. (Circular motion if there is no velocity component along the field.)
Beam of electrons moving in a circle. Lighting is caused by excitation of atoms of gas in a bulb. http://en.wikipedia.org/wiki/Magnetic_field
Consider a segment of wire of length l carrying current I in the direction of the vector l. The wire exists in a constant magnetic field B. The magnetic force on the wire is
where α is the angle between the direction of the current and the magnetic field.
Interaction between electromagnet and a magnetic substance
An electromagnet can be used to pick up a ferromagnetic material. The field of the electromagnet induces an alignment of the atomic scale dipoles resulting in a net force of attraction.
What is the current direction in this loop? And which side of the loop is the north pole?
A. Current counterclockwise, north pole on bottom B. Current clockwise; north pole on bottom C. Current counterclockwise, north pole on top D. Current clockwise; north pole on top
A. Current counterclockwise, north pole on bottom B. Current clockwise; north pole on bottom C. Current counterclockwise, north pole on top D. Current clockwise; north pole on top
What is the current direction in this loop? And which side of the loop is the north pole?