Download AP Physics Chapter 29-30 Key Equations and Ideas Magnetic Fields

AP Physics Chapter 29-30 Key Equations and Ideas
Magnetic Fields

 
E
For crossed E & B: v 
F  qv x B
B
Circulating charge: qvB 

 
F  IL x B
mv 2
r
 r

  I ds x r̂
o
Biot Savart Law: dB 
4 r2
mv
qB
 T 
2r 2m

v
qB
Long straight wire: B 
oI
2r
 LI I
oI
Two parallel wires: F  o 1 2 parallel currents attract

2d
4r
 
 IN
Solenoid: B = oIn Toroid: B  o
 B  ds   o Ienc
2r
Center of arc: B 
Ampere’s Law:
Key Ideas:

A permanent magnet or moving charge (i.e. current) produces a magnetic field.

The magnetic force acting on a charged particle moving through a magnetic field is always
perpendicular to the velocity vector and the magnetic field vector. The direction of the
force is determined by the right hand rule.

The magnetic field points out of north magnetic poles and into south magnetic poles.

Opposite magnetic poles attract each other and like magnetic poles repel.

In a conductor, the velocity of the charged particles is the drift velocity.

A particle whose velocity is perpendicular to a uniform magnetic field will move in uniform
circular motion. The magnetic force is the centripetal force keeping the particle moving in
a circle. If there is a component of the velocity parallel to the magnetic field, the particle
will move in a helical path.

The magnetic force acting on a current carrying wire in a magnetic field is always
perpendicular to the current and the magnetic field vector. The direction of the force is
determined by the right hand rule.

Two parallel wires with current flowing in the same direction will attract one another. If
the current is flowing in opposite directions, the wires will repel one another.

Biot-Savart Law (rhymes with “Leo” and “bazaar”) is used to calculate the magnetic field at
a point in space. In many cases, symmetry and simplifications are used to solve problems.

Current-Magnetic Field Right Hand Rule: Imagine grasping the current-carrying wire in
your right hand with your thumb extended and pointing in the direction of the current.
Your fingers will then naturally curl around in the direction of the magnetic field. This is
a different right hand rule than the one used for vector cross products.

The magnetic field due to a current moving through a long straight wire is proportional to
1/R, where R is the perpendicular distance from the wire.

To find the force on a current-carrying wire due to a second current-carrying wire, first
find the magnetic field from the second wire at a point on the first wire. Then find the
force on the first wire using the current in the first wire and the magnetic field from the
second wire.

Ampere’s Law can be used to find the magnetic field in problems with a certain degree of
symmetry. This is analogous to finding the electric field using Gauss’s Law. With Ampere’s
Law, you integrate around a closed loop called an Amperian loop, while with Gauss’s Law, you
integrate over a closed surface called a Gaussian surface.

The permeability constant, 0, is the magnetic analog of the electric permittivity constant,
0.

Curl your right hand around the Amperian loop, with your fingers pointing in the direction
of integration. A current passing through the interior of the loop in the direction of your
outstretched thumb is considered to be positive, while a current in the opposite direction
is considered to be negative.

The magnetic field inside or outside a current-carrying wire can be found using Ampere’s
Law.

The magnetic field inside an ideal solenoid is proportional to the current and is constant
everywhere inside the solenoid. The magnetic field inside a toroid is proportional to the
current and inversely proportional to the distance from the center of the toroid.