Category: 16 Electromagnetic Induction

161 Magnet and Coil

The easiest way to make sense of the induced voltages is to first figure out the how the magnetic flux linkage (of the coil) varies with time. Obviously, the flux linkage is strongest when the magnet is centred with the coil.

1 Fall Through

(a) magnet approaching coil
(b) magnet is centred with coil
(c) magnet left coil

2 Bungee Dip

(a) magnet at the top
(b) magnet at the bottom
(c) magnet at the top

3 Aligned

(a) magnet at the top
(b) magnet centred with the coil
(c) magnet at the bottom
(d) magnet centred with the coil
(e) magnet at the top

4 Cross-over

(a) magnet at the top
(b) magnet centred with coil
(c) magnet at the bottom
(d) magnet centred with coil
(e) magnet at the top

153 Non Conservative Field

The following diagrams summarise some interesting measurements, the outcome of which will probably surprise many people. (the red circle represents the region of alternating magnetic field)

nonConservative1

Note that the voltmeters give different readings even though they are connected across the same two points.

nonConservative2

This is due to the fact that the electric field generated by a changing magnetic field is fundamentally different from the so-called coulomb fields. In an non-coulomb field, where the field is not set up by electrical charges, the field is non-conservative. So moving a charge round one complete circuit actually does not return the charge to the original potential.

It is also useful to note that the “surprising” readings all have the voltmeter forming a loop that encloses the changing magnetic field itself.

130 Damped Oscillation

This video demonstrates both EMI and Oscillations.

Electromagnetic Induction

The oscillating aluminium plate experiences a damping force which is EMI in nature. The aluminium plate cuts the magnetic flux (originating from the neodymium magnets). The induced emf results in induced eddy current in the plate. The induced current interacts with the magnetic field of the neodymium magnets, resulting in F=BIL magnetic forces. The direction of the magnetic forces are always opposite in direction to the (current) velocity of the oscillating plate. How do we know that? Lenz’s Law!

Oscillations

The G-clamp provides a convenient mechanism to gradually increase the amount of damping, thus showing the behaviour of underdamped, critically damped and overdamped oscillations.

An underdamped oscillation always overshoots the equilibrium position and comes to rest only after a number of oscillations.

Critical damping returns the pendulum to rest at the equilibrium position in the shortest amount of time possible, without overshooting the equilibrium position.

An overdamped oscillation does not overshoot the equilibrium position, but takes a longer time before coming to rest at the equilibrium position (compared to critical damping).

098 Electromagnetic Induction: Race to the Bottom

Since the rods experience a changing magnetic flux as the magnets make their descent, emf is induced in the rods. The resulting eddy current creates a magnetic field that opposes the descent of the magnets, resulting in a retardation force on the magnets.

Assuming all four magnets are identical, then the induced emf in all the four rods should be exactly the same. However, the induced current is different due to the different resistivities of the four rods. Copper, with the lowest resistivity, has the largest induced current and thus experiences the largest retardation force. Plastic is basically an insulator and has zero induced current (despite the same induced emf). It thus suffers practically no retardation force.

073 Electromagnetic Induction: Self Steering Magnets

As the magnet rolled down the slope, the aluminium underneath the magnet experiences experiences first an increasing and then a decreasing flux linkage, resulting in induced emf. (E=/dt)

Since aluminium is an electrical conductor, (eddy) currents formed in the block near the magnet.

The direction of the induced current must produce a magnetic field that results in a retarding magnetic force on the rolling magnet. (Lenz’s Law).

Picture1

When the magnet is near the edge of the block, the retardation force is weaker on the side of the magnet nearer the edge, for the simple reason that there is less (or no) metal there for eddy current to form. The retardation forces thus exerts a turning moment on the magnet, which rotates it back to the block.

071 Magnetic Braking: Whack the Pig

As the magnet swings over the aluminium block, the aluminium underneath the magnet experiences experiences first an increasing and then a decreasing flux linkage, resulting in induced emf. (E=/dt)

Since aluminium is an electrical conductor, (eddy) currents formed in the block, producing their own magnetic field.

The polarity of the induced emf must be such as to produce a induced current and magnetic field that opposes the change that caused the induction in the first place. (Lenz’s Law). This predicts a retarding magnetic force on the approaching magnet, bringing the magnet to rest.

068 Oscillations: Critical Damping

 

Critical Damping

Damped oscillations must return to the equilibrium position eventually as the damping force saps energy continously from the oscillation. However, the manner in which the oscillations cease depends on the degree of damping.

oscda8

In the video, critical damping was achieved when the aluminium block was 2.0 cm from the magnets (1:46). Under critical damping, the pendulum returned immediately to the equilibrium position in the shortest amount of time possible, without overshooting the equilibrium position.

With less damping than critical (underdamping or light damping), the pendulum overshoots the equilibrium position and oscillates around it. The amplitude of oscillation decays exponentially as the damping force withdraws energy from the pendulum.

With more damping than critical (overdamping or heavy damping), the pendulum also does not overshoot the equilibrium position, but returns to the equilibrium position more slowly.

The collage at the end of the video shows very clearly that critical damping brings the oscillator to rest in the shortest time.

Why is there a damping force?

As the magnet swings, the aluminium along side the magnet experiences first an increasing and then a decreasing flux linkage, resulting in induced emf. (E=/dt)

Since aluminium blocks are conductors, (eddy) currents formed in the blocks, producing their own magnetic field.

The polarity of the induced emf must be such as to produce a induced current and magnetic field that opposes the change that caused the induction in the first place. (Lenz’s Law). This predicts a retarding magnetic force on the pendulum that is always in opposite direction to the velocity of the pendulum, hence a damping force.

How is the degree of damping varied?

By moving the block closer to the magnets, the rate of change of magnetic flux linkage is increased, resulting in a larger induced emf, current and thus damping force.

062 Eddy Current: “Magnetic Parachute”

As the magnet descended, the aluminium beside the descending magnet experiences first an increasing and then a decreasing flux linkage, resulting in induced emf. (E=/dt)

Since aluminium is conductive, (eddy) currents formed in the blocks, producing their own magnetic field.

The polarity of the induced emf must be such as to produce a induced current and magnetic field that opposes the change that caused the induction in the first place. (Lenz’s Law). This predicts a retarding magnetic force on the descending magnet, bringing it to a (surreally) low terminal velocity.

046 Lenz’s Law Jumping Ring

When the solenoid was energized, it produces a magnetic field. The ring thus experienced an increase in magnetic flux linkage. This results in an induced emf around the ring. (Faraday’s Law: emf=dΦ/dt)

The magnetic flux captured by all three rings are exactly the same. (It’s is the same solenoid, so B is the same. The rings have the same circular area, so A is the same. And Φ=BA) Clearly, all three rings experienced the same change in magnetic flux linkage. This leads to the conclusion that the induced emf in all three rings are exactly the same!

So why do they jump to different heights?

Firstly, they jump because the induced current (caused by the induced emf) produces its own magnetic field. The interaction of the magnetic field of the ring and the magnetic field of the solenoid leads to a mutually repulsive force. (This outcome is predicted by Lenz’s Law). Note that the effect of the induced emf is felt only when it results in an induced current.

The solid ring presents the largest cross sectional area, and thus smallest resistance to the induced emf. (R=ρL/A) The induced current is the largest, hence it jumped the highest. The holes in the second ring confines the current to the edges of the ring. With a larger resistance, the induced current is less (despite the same induced emf), hence it jumped less high. As for the broken ring, there was practically zero induced current (despite the same induced emf) thanks to the infinite resistance presented by the air gaps.