5.4 Magnetic Effects of Electric Currents

An electron is incident normally into a region of uniform magnetic flux density 0.50 T at a speed of 1.3 × 10⁷ m s^–1. 

Two electrons, X and Y, travel in a uniform magnetic field. X has kinetic energy E_X and Y has kinetic energy E_Y. 

Calculate the ratio if X is incident at 30° to the field but Y is incident normally to it. 

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. 

A similar metal rod is suspended in a magnetic field by two identical, vertical springs. The cell and the rod have negligible internal resistance. 

When the switch S is closed, the metal rod is displaced a distance x from its starting point. 

Show that, when both the spring constant and electrical resistance of each spring is doubled, closing S would cause the rod to be displaced by . 

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. 

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. 

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. 

The crack only shows up if it is across the direction of the field. 

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. 

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.