# Electromagnetism

## A Current Carrying Wire

### As was seen in Higher Physics, a wire with a Current flowing through it generates a Magnetic field around itself, as shown in the diagram below :- ### The Magnetic field lines form concentric circles around the wire, perpendicular to the direction of the Current flow. As there is no north or south pole to give direction to the field lines, the following left hand grip rule (for Electron flow) is used :- ## Force on a Current Carrying Wire

### The diagram below shows wire within a Magnetic field :- ## Example 1 - ## Fleming's Hand Rules

### The direction of the force can be determined if you know the sign on the charge and the direction of the magnetic field. Magnetic field by definition runs from north to south. ## Magnetic Induction at a distance from a Wire

### As such, the following relationship can be derived :- ## Force per unit length between two parallel Wires

### The Magnetic field generated by Wire 1 is given by :- ### By substitution of the Force calculation above, the Force applied to wire two can be derived :- ### As these fields are not based upon a point source, an extended description as a base unit is required - the Force per unit length :- ### 2. Wires carrying Current in opposite direction - Force is repulsive ## Example 2 - 2012 Past Paper Q8 ### The Magnetic Induction at a point P, 6·0 mm directly below conductor AB. ______________________________________________________________ ### Show that the force per unit length acting on each conductor can be written as:- ### Force per unit length :- ### Current :- ## The Ampere

### As seen previously with Voltage, the definition of values within Electricity require quite a high level of Physics knowledge to understand, and none are as high level at this stage as the definition of a Current of 1 Ampere. The definition of 1 Ampere is based upon above Force between two wires calculation. ## Motion in a Magnetic Field

### The diagram below shows a charged particle with a charge q moving with a constant speed of v perpendicularly to a Magnetic field of Magnetic Induction B :- ## Motion Parallel or Anti-Parallel to the Field ## Motion Perpendicularly to the Field ### By using the Centripetal Force calculations from unit 1, the radius of curvature of the charge can be found :- ### Also, by applying calculations for angular Velocity from the Circular Motion section of unit 1, the Period and Frequency of the rotation can be derived :- ## Motion at an angle to the Field

### The Motion of the charge is a combination of a circular motion within the Magnetic field and an unaltered path, giving helical motion. ## Helical Motion and Pitch

### The Pitch is therefore found using the following equation :- ## Example 3 - 2014 Past Paper Q8 ### A deuterium ion within an experimental fusion reactor is moving with a velocity of 2·4 × 107 ms–1 perpendicular to a Magnetic field. The maximum diameter of the circular motion, permitted by the design, is 0·50 m. Properties of ions present in the plasma are given in the table below:- ### Magnetic Induction (B) :- ### Period of Rotation (T) :- ____________________________________________________________________

### Another deuterium ion is travelling at 2·4 × 107 ms–1 at an angle of 40º to the direction of magnetic induction. This results in the ion undergoing helical motion as shown below :- ### The Pitch of the helical motion. ## Applications of Magnetic Fields

### The first particle accelerators were linear accelerators. The original LINAC designed by Cavendish Lab in 1930 used a potential of up to 800kV to accelerate protons down an eight foot long vacuum tube. This gave the protons an energy of 800keV (800,000 electron-Volts). The beam of particles can then be directed at a target. Modern linear accelerators are much more powerful, for example the Stanford Linear Collider give Protons an energy of 80 GeV. ### Linear Accelerators are useful but can be cumbersome due to the large length required to accelerate particles to high energies. In order to reach high energies with limited space, the Cyclotron was developed. ### The final stage in the evolution of particle accelerators is the Synchrotron. ## Mass Spectrometer

### A Mass Spectrometer is a device which uses a Magnetic field to measure the mass of charged particles. The diagram below shows the path of two charged particles through a Mass Spectrometer :- ### The following formula applies for their path :- ## Cloud Chambers

### A Cloud Chamber is a device used to detect subatomic particles by using ionisation paths. The image below shows the setup of a simple Cloud Chamber :- ### The diagram below shows a simple vapour trail within a cloud chamber that has a Magnetic field placed across it (in this case into the page) :- 