CONGRATULATIONS TO THE CLASS OF 2012!

The Class of 2012 is now done, and my heartfelt congratulations to all of you! This is a tremendous group of young women and men who are set to take on the top colleges in the country, and make their mark on the world! I am truly proud to have worked with each and every one of these students.

If you want a 3-D simulation that will allow you to view electric fields for a wide variety of charged systems, check out this Falstad simulation site. It is really a useful visual display!

Charged Particles in B-fields

Here's a case of charged particle flying through magnetic fields, and what happens to those particles. We know that fundamentally magnetism is formed by moving charges. So the moving charged particle has its own magnetic field. This field interacts with any external magnetic field, thus creating a magnetic force. We know this goes as F = qv x B. It is a cross product. But this then means the force is perpendicular to the motion of the particle. The consequence of this condition is circular motion, or mv^2/R = qvB. This video will show ActivPhysics simulations to get a sense of the 3-D nature of this motion. If the particle comes in 90-degrees to the magnetic field, we get a circular orbit. If the particle comes in at any angle other than 90-degrees or 0-degrees (parallel) to the field, then there is a component of motion perpendicular to the field (circular motion), as well as a component parallel to the field, which means no force and it keeps moving in that direction. A spiral/helix/corkscrew results! I also show a simulation of a mass spectrometer, where we use the circular motion to measure the mass of particles or ions. Check it out.

Check out Rotating Pulleys

Check out how to find the TWO tensions in the same rope for a real, spinning pulley problem. The video is here. Also, check out small oscillations (like a pendulum) here, or a more complicated one here.

Rotating Conducting Rod in B-field

The previous post outlined how to find the induced voltage across a moving metal rod in a B-field. Because of qv x B, we found the rod polarizes and therefore has an E-field and voltage difference because of a separation of charge. Here is a different situation. Suppose instead of moving linearly through the B-field, the metal rod is nailed down on one side, and rotates in the magnetic field?! It is a moving conductor, so we would still expect it to polarize, and therefore have a voltage difference across the rod. The trouble is, different points of the rod will have a different speed! How do we handle this situation? Check this out...

Moving a Conducting Rod through a B-field

Here's a case where by simply moving a metal stick through a magnetic field, the stick acts like a battery. The idea is that because it is a conductor, the rod has free electrons. By moving it in a B-field, we will have F = qv x B kick in. This causes the rod to become polarized, with one end positive and one end negative. But think about what else is set up if one separates charge on an object - you would have a voltage difference between the two ends. And if there is a voltage difference across a conductor, E = -dV/dr tells use there is an E-field running through the rod. This E-field produces an electric force on those same delocalized electrons. So a magnetic force points one way, and an electric force points in the opposite direction. At some point the electric force will balance the magnetic force, as long as the speed of the rod remains constant: qE = qvb.

I need student feedback.  For the how-to videos, is there a topic or problem that should have a video but does not?  Thanks for letting me know.

How to do LC Circuits - like Simple Harmonic Motion!

Here is an example of an LC circuit, where a charged capacitor is connected to an inductor.  The beauty of this circuit is that one can start an oscillating current (AC current).  This is the same as 'shaking' electrons, and this means electromagnetic waves are produced in the E-and B-fields.  These waves travel at the speed of light.  We will see that the math produces the same second-order differential equation we have in simple harmonic motion of oscillating springs!  So sines and cosines are the solutions to this equation.  Check it out!

SHM of Oscillating Stick due to Spring

Simple Harmonic Motion (SHM) is a periodic motion of some object caused by a restoring force that is proportional to the displacement, such as a spring.  Here is a different type of setup where a stick is lying on a frictionless table, with one end nailed to the table (which serves as the axis of rotation) and a spring attached near the other end of the stick.  If the stick is stretched slightly, so the stick forms a small angle relative to the vertical axis it had prior to stretching the spring, we can use the small angle approximation.  This says that for a small angle, the angle in radians is approximately equal to the sine of the angle.  Also, cosine of that small angle approaches 1.  We need both these approximations to solve this one!  Check it out.

A Very Cool Way of Looking at the Size Scales of the Universe

Check out this site, which is a very neat way of checking out the size scale of objects in the universe. It is similar to the classic Powers of Ten videos, but has better graphics. Enjoy!