Compass Needle in Uniform and Rotating Magnetic Fields

view

experiment

time t

50.

ℐ

2.33

f

2.87

ℳ

2.76

B

1

1.54

B

2

1.9

ω

0

1.

θ

0

0.49



θ

0

-0.53

A compass needle undergoes forced oscillations under the influence of a uniform magnetic field

B

1

and a rotating magnetic field

B

2

with angular velocity

ω

0

(black arrow). The compass needle has a moment of inertia

ℐ

, a friction constant

f

, and a magnetic moment ℳ. This is a simple example of a system that shows chaotic motion. In a real experiment it is impossible to repeat a particular motion from initial conditions

θ

0

and



θ

0

because the system is chaotic.

Details

The differential equation to solve is

ℐ

..

θ

+f



θ

+ℳ

B

1

sin(θ)+ℳ

B

2

sin(θ-

ω

0

t)=0

.

External Links

Angular Velocity (ScienceWorld)

Moment of Inertia (ScienceWorld)

Magnetic Field (ScienceWorld)

Magnetic Torque (ScienceWorld)

Phase Space Trajectory (ScienceWorld)

Chaos (Wolfram MathWorld)

Poincaré Map (Wolfram MathWorld)

Permanent Citation

Enrique Zeleny

"Compass Needle in Uniform and Rotating Magnetic Fields"
http://demonstrations.wolfram.com/CompassNeedleInUniformAndRotatingMagneticFields/
Wolfram Demonstrations Project
Published: July 30, 2010