Ph272- General Physics II (Electricity and
Magnetsism)
Lecture 15: Ch. 29 - Source of magnetic field
Key Topics
Overview
- Source of magnetic field: In the last lecture, we
see that a current loop acts like a magnet. In fact, all magnetic
fields are generated by currents (i.e. moving charges). Inside
a bar magnet, the magnetic field is generated by "current"
inside the atoms (see Ch. 27 for more details)
- Biot-Savart Law: Tells you the magnetic field due
a segment of a current (analogous to Coulomb's Law tells you
the E-field due to a small volume of charge).
- Ampere's Law: Relates the magnetic circulation to
the enclosed current (analogous to Gauss's Law). Ampere's Law
can be used to calculate the magnetic field due to symmetrical
current distribution such as current flowing down an infinite
cylinder and an infinite "selenoid".
Biot-Savart Law
- A moving point charge produces a magnetic field. If
the charge moves at a constant velocity, it produces a
magnetic field given by Eq. 25-1 (analogous to the E-field of
a point charge).
- Biot-Savart Law: In most cases, we are dealing with
many moving charges or currents. The Biot-Savart Law states the
magnetic field due to a segment of a current (Eq. 25-4). The
total magnetic field is obtained by summing up the contribution
from all the segments (i.e. integration). The math is often tedious
because of the vector cross product. We will use straight current
segments to illustrate the equation.
Ampere's Law
- New term: Magnetic Circulation= line integral of B
. dl (Here, it is the tangential component of B-field that contributes
to the integral. This is different from electric flux which is
a surface integral of the normal component of E-field)
- Ampere's Law: The magnetic circulation is proportional
to the current enclosed, Eq. 25-15.
- Use Ampere's Law to find B-field due to symmetrical current
distribution: such as current flowing down an infinite cylinder
and an infinite "selenoid".
Review
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