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. 

Show that the percentage reduction in the magnetic force exerted on the electron is 50% when the electron is incident at an angle of 30°. 

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. 

Calculate the angle to the horizontal to which the rails must be tilted in order to keep XY stationary. 

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. 

Deduce the direction of the electric field between the plates.

Mark with an X a position on P₂ that would indicate where electrons with a speed greater than v may strike 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. 

Show that the maximum magnetic flux density B_max that ensures the electron reaches P₂ is given by:

where m_e 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. 

Deduce why this method cannot be used for copper pipes. 

Explain why iron filings cluster around the crack shown in the image in part (a). 

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

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. 

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. 

Identify, on the diagram, the direction of the force on the coil at this particular instant with the current directions shown. 

Describe how the magnitude and direction of the force on the coil varies over a complete cycle. 

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.

Calculate the maximum magnetic force on the coil. 

The diagram shows a charged particle entering a region of magnetic field that is directed into the page.

The path of the particle is a quarter circle. 

Justify why the particle is positive.

The proton enters the region with a speed of 5.4 × 10⁶ ms^–1. The magnetic flux density of the field is 0.35 T. 

Calculate the radius of the protons circular path.

Calculate the time the proton spends in the region of the magnetic field.

The diagram shows the path of a charged particle passing through a thin metallic foil.

State and explain the direction of motion of the particle and the sign of its charge.

Positive charges are seen passing through different magnetic fields. 

Determine the direction of the missing quantity between B, v and F for each:

The diagram shows two parallel plates. The electric field between them is directed from top to bottom and has a magnitude 2.6 × 10³ N C^–1. The shaded region is a region of magnetic field normal to the page.

Deduce the magnetic field magnitude and direction so that an electron experiences zero net force when travelling through the plates with a speed of 3.0 × 10⁵ ms^–1.

Suggest and give a reason whether a proton shot with the same speed through the plates experiences zero net force.

The electron’s speed is halved. 

Suggest whether the electron would still be undeflected for the same magnetic field found in (b).

In the national grid electricity is generated by current carrying wires within a magnetic field. 

There are two wires carrying equal currents into the page.

Determine the direction of the magnetic field at point X.    

Use a diagram to help you with your answer.

A bar magnet is placed in a uniform magnetic field as shown in the diagram.

Suggest whether there is a net force on the bar magnet, causing it to move to a different position. Explain your answer.

The bar magnet does move in a specific type of motion. Determine how it will move.

A taut electrical wire carries electricity between a generator and the step-up transformer. The current is 2000 A and the magnetic field of the Earth at the position of the wire is 4.50 × 10^–5 T and makes an angle of 45⁰ below the horizontal. 

Calculate the force experienced by a 25.0 m length of this wire.

A current I passes through a conductor. The electrons move with a drift speed v. A magnetic field B at right angles to the direction of motion of the electrons is also present in the conductor.  

Draw the arrows to indicate the directions of the: 

(i)   Conventional current in the conductor

(ii)   Magnetic force on the electron

A is the cross-sectional area of the conductor, q is the charge of one electron, n is the number of electrons per unit volume and v is the drift speed of the electrons. 

Show that the current on the conductor is given by I = qnAv.

The number density of the electrons is 3.5 × 10²⁸ m^–3. The current in the wire is 0.30 A and its cross-sectional area is 4.4 × 10^–6 m². 

Hence, calculate the drift velocity of the electrons moving in the conductor.

The magnitude of the magnetic field within this current carrying conductor is 0.30 T. 

Calculate the magnitude of the force on the electrons in the conductor.