Month: May 2014

036 Line Emission Spectral

The light from the Sun, a filament lamp, a candle flame, produces a continuous spectrum. The light from a gas discharge lamp however produces a discrete line spectrum.  For example, the hydrogen gas atoms emit visible light of wavelength 656.3 nm, 486.1 nm, 434.0 nm, 410.2 nm, 397.0 nm, 365 nm (called the Balmer series), and nothing in between. Why?

hydrogen_spectrum

It turns out that the electrons in a gas atom can only exist at certain energy levels. As a result, when the gas atom is excited (by the high voltage in the gas discharge tube), an electron in the atom can only be excited occupy not just any energy level, but only certain allowed energy levels. Subsequently, when the electron de-excites from a higher energy level to a lower energy level, a photon is emitted. And the energy of the photon is equal to the difference in the energy levels.

Since the energy levels are discrete, the electrons cannot de-excite from any energy level to any energy level. They can only de-excite from one of the allowed energy levels, to another of the allowed energy levels. As a result, only photons of certain energy levels, are emitted. Since E=hf, it follows that only light of only certain frequency and wavelength (E=hf), are emitted.

035 What makes the heart spin?

A current carrying conductor placed (perpendicularly) in a magnetic field will experience a magnetic force. (F=BIL)

Capture

Most of the action is taking place at the bottom of the heart near the magnet. The right half of the heart experiences a magnetic force into the screen, whereas the left half of the heart experiences a magnetic force out of the screen. These two forces form a couple which rotates the heart in an anti-clockwise direction (seen from the top).

034 Why did bulb Y become dimmer?

For simplicity, let’s assume that the resistances of the bulbs are constant.

Picture1

In the original arrangement, by the potential divider principle, VAB = VBC = 2 V. So bulbs X and Y were equally bright.

Picture2

When bulb Z was added in parallel to bulb Y, the effective resistance between nodes B and C was halved. By the potential divider principle, the potential difference across bulb X has increased to 2/3 of 4 V = 2.67 V, whereas the pd across bulb Y (and bulb Z) has dropped to 1.33 V. This explains why bulb X now shines brighter than before, whereas bulb Y dims compared to before.

033 Anti-Gravity Biscuit Tin

We expect the biscuit tin to roll downslope. Why?

Picture1

We assume that the biscuit tin has its center of mass (C.M.) at the center of the tin. If so, when the tin roll downward, the C.M. goes lower. So the tin loses GPE to gain KE. Everything makes sense.

Picture2

The biscuit tin in the video however has a C.M. that is off centre (because of the mass of the magnets). If the C.M. is positioned on the uphill side, the tin rolls upward, but the C.M. actually goes lower. So again, the tin loses GPE to gain KE. There is nothing “anti-gravity” about the tin’s motion.

Picture3It is even possible for the tin to rest on the slope. This occurs when the C.M. of the tin is vertically above the contact point. The allows the contact force FC  to balances the weight of the tin, and yet does not exert any moment about the C.M. of the tin.

032 Eddy Current

Picture1The moving magnet produces a changing magnetic field, which induces an electric field. Since the aluminium ring is conductive, an induced current is produced.

Picture3Again, Lenz’s Law dictates that the direction of induced emf and current is to oppose the change that caused the induced emf. So it is no surprise that the resulting magnetic force experienced by the ring due to the induced current, is such that the ring “chases” after the magnet (in an attempt to reduce the relative motion).

The path around the ring offers the lowest electrical resistance and thus results in the largest induced current. This is why the magnetic effect is most obvious when the magnet is moving just above the one arm of the ring. (Remember that the moving magnet is producing a double loop kind of emf.)

031 Lenz’s Law

Picture1

Say the north pole of the magnet is facing the ring. Note that the magnetic flux of the magnet is captured by the aluminum ring.

Picture2

When the magnet is lifted away from the ring, the magnetic flux density at the ring decreases. An emf is induced around the ring since the ring experiences a change in flux linkage (Faraday’s Law, ε=-dΦ/dt). The direction of the induced emf (and current) should be such as to produce an effect to oppose the change that resulted in the induced emf in the first place (Lenz’s Law). Since the ring experiences a decreasing downward magnetic flux, the direction of induced current must be to produce a downward magnetic flux as well (in an attempt to arrest the decreasing magnetic flux). Since the magnetic field of the magnet and the ring are in the same direction, the ring experiences an attractive magnetic force that lifted the ring off the table.

030 Eddy Current

Suppose the north pole of the magnet is facing downward into the plate.

Picture1

The aluminum plate is non-ferromagnetic. So it is not surprising that it was not attracted to a stationary, (and a very slowly moving) magnet.

However, when the magnet was moved quickly rightward, a changing magnetic field is produced. The resulting changing magnetic flux linkage induces circular EMFs in the plate. (Faraday’s Law ε=-dΦ/dt)

The part of the plate ahead of the magnet experiences an increasing flux linkage. To oppose the change which is an increasing flux linkage, the induced emf and current must produce magnetic flux that is opposite in direction (Lenz’s Law). So the induced current is an anti-clockwise one.

The part of the plate behind the magnet experiences an decreasing flux linkage. To oppose the change which is an decreasing flux linkage, the induced emf and current must produce magnetic flux that is in the same direction (Lenz’s Law). So the induced current is a clockwise one.

Picture4

We now have electric current in the plate that is flowing perpendicularly to the magnetic field of the magnet. A current-carrying conductor in a magnetic field experiences a magnetic force (F=BIL). Using Fleming’s Left Hand Rule, one can confirm that the plate experiences a rightward magnetic force.

This result is not surprising. Since the cause of electromagnetic induction is the relative motion between the magnet and the plate, the direction of the induced emf (and current) must be an attempt to oppose or reduce the relative motion (Lenz’ Law). So the direction of the induced emf (and current) must be to produce a magnetic force on the plate that is in the same direction as the motion of the moving magnet.