Magnets and Magnetic Fields Magnets have two ends – poles – called north and south. Like poles repel; unlike poles attract.
Magnets and Magnetic Fields However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.
Magnets and Magnetic Fields Magnetic fields can be visualized using magnetic field lines, which are always closed loops.
Magnets and Magnetic Fields The Earth’s magnetic field is similar to that of a bar magnet. Note that the Earth’s “North Pole” is really a south magnetic pole
Electric Currents Produce Magnetic Fields an electric current produces a magnetic field.
Electric Currents Produce Magnetic Fields The direction of the field is given by a right-hand rule.
Magnetic Field Unit of B : tesla, T 1 T = 1 N / A · m
Force on Electric Charge Moving in a Magnetic Field If a charged particle is moving perpendicular to a uniform magnetic field, it experiences a force that is perpendicular to its velocity v Right hand rule; opposite for neg charge
Force between Two Parallel Wires If two wires carry currents I1 & I2 They experience a mutual force (per unit length of wire) r
Flux Magnetic flux: A = area of loop of wire. Unit of magnetic flux: 1 T · m 2
Induced EMF A voltage is induced (it’s called an ‘emf’, has symbol e) when the flux through a loop of wire varies with time
Transformers and Transmission of Power A transformer consists of two coils. A changing emf in one induces an emf in the other. The ratio of the emfs is equal to the ratio of the number of turns in each coil: (21-6)
Transformers This is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary:
Wave Motion Wave characteristics: Amplitude, A Wavelength, λ Frequency f and period T Wave velocity (11-12)
Types of Waves: Transverse and Longitudinal The motion of particles in a wave can either be perpendicular to the wave direction (transverse) or parallel to it (longitudinal).
Types of Waves: Transverse and Longitudinal Sound waves are longitudinal waves:
Interference The superposition principle says that when two waves pass through the same point, the displacement is the arithmetic sum of the individual displacements. In the figure below, (a) exhibits destructive interference and (b) exhibits constructive interference.
Interference These figures show the sum of two waves. In (a) they add constructively; in (b) they add destructively; and in (c) they add partially destructively.
Standing Waves Standing waves occur when both ends of a string are fixed. There are: nodes, where the amplitude is always zero, antinodes, where the amplitude varies from zero to the maximum value.
Standing Waves The frequencies of the standing waves on a particular string are called fundamental and harmonics.
Air Columns A tube open at both ends (most wind instruments) has antinodes, at the ends.
Air Columns A tube closed at one end (some organ pipes) has a node
Doppler Effect The Doppler effect occurs when a source of sound is moving with respect to an observer.
Doppler Effect As can be seen in the previous image: a source moving toward an observer has a higher frequency and shorter wavelength; the opposite is true when a source is moving away from an observer.
Visible light: 400 nm (violet) to 750 nm (red) 1 nm = 10 -9 m
Speed of light The wavelength and frequency of electromagnetic waves are related:
Double-Slit If light is a wave, there should be an interference pattern.
Double-Slit The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).
Double-Slit x d Diffraction pattern on screen has bright fringes separated by a distance
24.3 Interference – Young’s Double-Slit Experiment Between the maxima and the minima, the interference varies smoothly.
Diffraction by a Single Slit or Disk Light will diffract around a single slit (or around a circular obstacle). x d screen
Diffraction by a Single Slit or Disk The resulting pattern of light and dark stripes is called a diffraction pattern. y Position y of the first dark fringe, measured from the central bright spot