Alpha particles travel in a vacuum at speed v and enter an area where there is a uniform magnetic field of flux density B. In this area, it begins to move in a circular trajectory.
(a)
Show that the momentum of a single alpha particle is given by:
where e is the elementary charge and r is the orbital radius.
An alpha particle moves across the Earth's equator towards the east. At this point, the Earth's magnetic field has a direction due north and is parallel to the surface.
(b)
Deduce the direction of the force acting on the alpha particle at this instant.
Charged particles from the sun, carried by the 'solar wind', may become trapped in the Earth's magnetic field near its poles, causing the sky to glow. Some of these charged particles travel in a circle of radius 45 km in a region where the flux density is 6.0 × 10–5 T.
(c)
Show that these charged particles cannot be electrons.
A cylindrical aluminium bar XY of mass 6.0 g rests on two horizontal aluminium rails, separated by 5.0 cm.
The rails are connected via a switch to a cell that can drive a current of 4.5 A through XY. A magnetic field of flux density 0.20 T acts into the screen.
(c)
Calculate the angle to the horizontal to which the rails must be tilted in order to keep XY stationary.
A beam of electrons, each travelling at various speeds, passes through a hole in plate P1. P2 is parallel to P1, also with a hole in it. The region between the plates contains a uniform electric field and a uniform magnetic field. Both the electric field strength E and the magnetic flux density B are adjustable.
Electrons that are undeviated travel with a particular speed v along the straight line joining the holes in P1 and P2.
(a)
Deduce the direction of the electric field between the plates.
The equipment is adjusted such that a single electron is shot with kinetic energy K through the hole in P1. The distance between the plates d is fixed, and electric field is switched off, such that the electron is incident in a region of uniform magnetic flux density B only.
(c)
Show that the maximum magnetic flux density Bmax that ensures the electron reaches P2 is given by:
where me is the rest mass of the electron and e is its charge.
Very small cracks in some metals can be detected by a method which includes the use of magnetism. In a particular method for steel pipes, a coil of wire is wrapped around it, and a current passed through the coil. This magnetises the pipe and cracks in the direction shown in the image can be found by sprinkling iron filings on the pipe.
Cracks along or parallel to the length of the pipe do not show up.
(a)
Deduce why this method cannot be used for copper pipes.
[2]
Question 4b
Marks: 2
(b)
Explain why iron filings cluster around the crack shown in the image in part (a).
[2]
Question 4c
Marks: 3
The crack only shows up if it is across the direction of the field.
(c)
Describe and explain how the coil in the image in part (a) should be arranged so that the magnetic field it produces will show cracks cracks that are along the pipe.
[3]
Question 5a
Marks: 2
The image shows the main features of a loudspeaker L. A current-carrying coil is positioned within the magnetic field provided by a permanent magnet, and the current directions in the coil at a particular instant is shown.
The dust cap D prevents dust from blocking the gap between the cardboard tube and the south pole of the magnet.
(a)
Identify, on the diagram, the direction of the force on the coil at this particular instant with the current directions shown.
The coil consists of 200 turns, each of average diameter 2.0 cm. The magnetic flux density created by the permanent magnet is 0.40 mT. The peak current in the coil is 0.48 mA.