Measuring the strength of a Magnetic Field © David Hoult 2009

When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is © David Hoult 2009

When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines © David Hoult 2009

When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines The direction of the force is at 90° to both the current and the flux lines © David Hoult 2009

When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines The direction of the force is at 90° to both the current and the flux lines Fleming’s left hand rule helps to remember the relation between the three directions… © David Hoult 2009

Thumb First finger Second finger © David Hoult 2009

Motion ThuMb First finger Second finger © David Hoult 2009

Motion ThuMb Second finger Field First finger © David Hoult 2009

Motion ThuMb Field Current First finger SeCond finger © David Hoult 2009

Factors affecting the Magnitude of the Force The force depends on © David Hoult 2009

The force depends on - the current flowing through the conductor, I © David Hoult 2009

The force depends on - the current flowing through the conductor - the length of conductor in the field © David Hoult 2009

The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that © David Hoult 2009

The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I © David Hoult 2009

The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I F  length of conductor, L © David Hoult 2009

The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I F  length of conductor, L F = I L × a constant © David Hoult 2009

The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I F  length of conductor, L F = I L × a constant magnetic field strength or © David Hoult 2009

The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I F  length of conductor, L F = I L × a constant magnetic field strength or magnetic flux density © David Hoult 2009

F = I L B © David Hoult 2009

F = I L B units of B Newtons per Amp per meter, NA -1 m -1 © David Hoult 2009

F = I L B units of B Newtons per Amp per meter, NA -1 m -1 1 NA -1 m -1 is called 1 Tesla (1 T) © David Hoult 2009

F = I L B units of B Newtons per Amp per meter NA -1 m -1 The flux density of a magnetic field is 1 NA -1 m -1 is called 1 Tesla (1 T) © David Hoult 2009

F = I L B units of B Newtons per Amp per meter NA -1 m -1 The flux density of a magnetic field is the force per unit current per unit length acting on a conductor placed at 90° to the field 1 NA -1 m -1 is called 1 Tesla (1 T) © David Hoult 2009

F = I L B units of B Newtons per Amp per meter NA -1 m -1 The flux density of a magnetic field is the force per unit current per unit length acting on a conductor placed at 90° to the field F = I L B sin  1 NA -1 m -1 is called 1 Tesla (1 T) © David Hoult 2009

Force acting on a charged particle moving through a magnetic field © David Hoult 2009

Consider a conductor of length L, having n free electrons per unit volume. A current, I, is flowing through it © David Hoult 2009

Consider a conductor of length L, having n free electrons per unit volume. A current, I, is flowing through it © David Hoult 2009

In this piece of conductor there are © David Hoult 2009

In this piece of conductor there are NAL free electrons © David Hoult 2009

If all these electrons pass through end x in time t then the current, I is given by In this piece of conductor there are NAL free electrons © David Hoult 2009

n A L en A L e t If all these electrons pass through end x in time t then the current, I is given by In this piece of conductor there are NAL free electrons © David Hoult 2009

If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude © David Hoult 2009

If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B © David Hoult 2009

If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B This is the sum of the forces on all the electrons, so the force F acting on each electron is given by © David Hoult 2009

I L BI L B If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B This is the sum of the forces on all the electrons, so the force F acting on each electron is given by n A Ln A L F == I BI B n An A © David Hoult 2009

Substituting for I gives F = © David Hoult 2009

Substituting for I gives n A L e Bn A L e B t n At n A F == © David Hoult 2009

Substituting for I gives n A L e Bn A L e B t n At n A F = L e BL e B t = © David Hoult 2009

Substituting for I gives n A L e Bn A L e B t n At n A F = L e BL e B t = © David Hoult 2009

but L/t is © David Hoult 2009

but L/t is the (drift) velocity of the electrons © David Hoult 2009

but L/t is the (drift) velocity of the electrons therefore © David Hoult 2009

but L/t is the (drift) velocity of the electrons therefore F = e v B © David Hoult 2009

F = q v B In general the magnitude of the force acting on a charged particle moving with velocity v, at 90° to a magnetic field of flux density B, is given by where q is the charge on the particle © David Hoult 2009

If the particle moves at angle  to the field © David Hoult 2009

If the particle moves at angle  to the field the magnitude of the component of its velocity at 90° to the field is © David Hoult 2009

If the particle moves at angle  to the field the magnitude of the component of its velocity at 90° to the field is v cos  © David Hoult 2009

If the particle moves at angle  to the field the magnitude of the component of its velocity at 90° to the field is v cos  = v sin  Therefore, in general F = © David Hoult 2009

Therefore, in general F = q v B sin  If the particle moves at angle  to the field the magnitude of the component of its velocity at 90° to the field is v cos  = v sin  © David Hoult 2009

The Motion of Charged Particles in Magnetic Fields © David Hoult 2009

A charged particle moving parallel to the flux lines © David Hoult 2009

A charged particle moving parallel to the flux lines experiences no force © David Hoult 2009

A charged particle moving parallel to the flux lines experiences no force There are three possible paths for a charged particle moving through a uniform magnetic field © David Hoult 2009

If the angle,  between the field and the direction of motion is zero the path is © David Hoult 2009

If the angle,  between the field and the direction of motion is zero the path is a straight line © David Hoult 2009

If the angle,  between the field and the direction of motion is 90° the path is © David Hoult 2009

field into plane of diagram If the angle,  between the field and the direction of motion is 90° the path is circular © David Hoult 2009

field into plane of diagram If the angle,  between the field and the direction of motion is 90° the path is circular © David Hoult 2009

field into plane of diagram If the angle,  between the field and the direction of motion is 90° the path is circular © David Hoult 2009

If the angle between the field and the direction of motion is 0° <  < 90° the path is © David Hoult 2009

If the angle between the field and the direction of motion is 0° <  < 90° the path is © David Hoult 2009

If the angle between the field and the direction of motion is 0° <  < 90° the path is © David Hoult 2009

If the angle between the field and the direction of motion is 0° <  < 90° the path is a helix © David Hoult 2009