1. Describe an experiment to demonstrate the three-dimensional
nature of the magnetic field around a bar magnet.
2. A bar magnet causes a magnetic field with a strength of 30 mT
at an angle of 45° to a region of area 15 cm2
. How much flux will
be contained by this region?
3. What does the term ‘magnetism’ describe?
4. Explain the difference between paramagnetic and ferromagnetic
materials.
5. Outline the dynamo theory which can be used to explain the
Earth’s magnetic field.
6. Find the speed of an electron travelling at an angle of 40° to the
Earth’s magnetic field that experiences a force of 8 × 10−17 N.
(The charge on an electron is 1.6 × 10−19 C and the magnitude of
the Earth’s magnetic field is 5 × 10−5 T.)
7. Outline J.J. Thompson’s experiment of charge to mass ratio.
8. Outline the principles of a mass specrometer.
9. Isotopes of carbon (C) are to be separated using a mass
spectrometer. The applied magnetic field is 45 mT and the
applied potential difference is 600 V. The mass of a proton
or neutron is 1.66 × 10−27 kg and the charge on a proton is
1.6 × 10−19 C. Find the radii of the paths of 12C, 13C and 14C.
10. Describe how you would investigate the variation of the
magnetic field due to a current-carrying conductor.�
1. Place a bar magnet on a table and sprinkle iron filings around it. The iron filings align along the magnetic lines of force, forming a two-dimensional pattern. Then, place a sheet of paper on top of the iron filings and gently tap it to remove any excess filings. Carefully lift the paper and iron filings away from the magnet, and observe the pattern. Next, shift the paper and iron filings so that they are above the magnet, and tap again. The iron filings will now form a three-dimensional pattern, showing that the magnetic field around the bar magnet is not just in a single plane, but extends in three dimensions.
2. Flux (Φ) = magnetic field strength (B) x area (A) x cosine of angle (θ) between the magnetic field and the area.
Φ = 30 mT x 15 cm2 x cos 45°
Φ = 318.7 mWb
3. Magnetism refers to the physical phenomenon of attractive or repulsive forces between certain materials, particularly those that contain iron, nickel, or cobalt. These materials have the property of producing a magnetic field, which can interact with other magnetic fields or materials.
4. Paramagnetic materials have a weak attraction to a magnetic field, which arises from the presence of unpaired electrons. Ferromagnetic materials have a very strong attraction to a magnetic field, and can retain their magnetic properties even after the external field is removed. This arises from the alignment of individual atomic magnetic moments in a common direction, which creates a net magnetic field.
5. The dynamo theory proposes that the Earth’s magnetic field arises from the convective motion of molten iron in the outer core, which generates electric currents as a result of electromagnetic induction. This flow of current creates the Earth’s magnetic field, which extends from the core to the surface and protects the planet from harmful solar radiation.
6. The force on an electron moving through a magnetic field is given by F = qvBsinθ, where q is the charge on the electron, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field lines. Rearranging for velocity, we get v = F / (qBsinθ) = 8 × 10-17 N / (1.6 × 10-19 C x 5 × 10-5 T x sin 40°) = 3.9 x 105 m/s.
7. J.J. Thompson used a cathode ray tube to demonstrate that electrons had a charge-to-mass ratio (e/m) of -1.76 x 10^11 C/kg. He applied an external magnetic field perpendicular to the path of the electrons in the tube, which caused them to curve in a circular path due to the Lorentz force. By measuring the curvature of the path and the strength of the magnetic field, Thompson could calculate the charge-to-mass ratio of the electrons.
8. A mass spectrometer is a device that separates ions by their mass-to-charge ratio (m/z). The principles involved include ionization of the sample, acceleration of the ions through an electric field, deflection of the ions in a magnetic field (which depends on their mass-to-charge ratio), and detection of the separated ions by a detector.
9. The radius of the circular path of a charged particle in a magnetic field is given by r = (mv) / (qB), where m is the mass of the particle, v is its velocity, q is its charge, and B is the strength of the magnetic field. For 12C, m = 12 x 1.66 x 10^-27 kg, q = 6 x 1.6 x 10^-19 C, B = 45 mT, and V = 600 V. Hence, r = (12 x 1.66 x 10^-27 x sqrt(2 x 600 / (12 x 1.6 x 10^-19 x 45))) / (6 x 1.6 x 10^-19 x 45 x 10^-3) = 3.02 cm. Similarly, the radii of the paths of 13C and 14C are 3.32 cm and 3.61 cm, respectively.
10. To investigate the variation of the magnetic field due to a current-carrying conductor, we would use a hall probe. This is a small device that measures the local magnetic field & direction. The hall probe is connected to a data logger, which records the readings at different points along the length of the conductor. By plotting a graph of the magnetic field strength vs distance, we can see how the field varies with distance from the conductor. We can also measure the shape of the magnetic field by rotating the probe around the conductor.