 ENROLLMENT NO  NAME. KARAN SHARMA MAGNETIC FIELD

 A magnetic field is a region in which a body with magnetic properties experiences a force. Magnetic Field

 Magnetic fields are produced by electric currents, which can be macroscopic currents in wires, or microscope currents associated with electrons in atomic orbits. Sources of Magnetic Field

 A magnetic field is visualised using magnetic lines of force which are imaginary lines such that the tangent at any point gives the direction of the magnetic field at that point. Magnetic Field Lines

Magnetic Flux Pattern

 Magnetic lines of force never intersect.  By convention, magnetic lines of force point from north to south outside a magnet (and from south to north inside a magnet).  Field lines converge where the magnetic force is strong, and spread out where it is weak. (Number of lines per unit area is proportional to the magnetic field strength.) Properties of Magnetic Field Lines

Magnetic flux pattern due to current in a straight wire at right angles to a uniform field Net flux is lesser on this side of the wire Net flux is greater on this side of the wire I

 If you point your left forefinger in the direction of the magnetic field, and your second finger in the direction of the current flow, then your thumb will point naturally in the direction of the resulting force! Fleming’s Left Hand Rule

 The direction of magnetic force always perpendicular to the direction of the magnetic field and the direction of current passing through the conductor. Force on a current-carrying conductor

 The magnetic flux density is defined as the force per unit length per unit current acting on a current-carrying conductor at right angle to the field lines. Magnetic Flux Density Unit : tesla (T) or gauss (G), 1 G = T or weber/m 2

Typical Values of the magnetic flux density SourceB-Field (Tesla) Human Brain Interstellar Space Near Household Wiring10 -4 Sunlight3x10 -5 Earth's Magnetic Field at Pole5x10 -4 Sunspots0.3 Largest man-made Magnet5.0 Surface of a Nucleus10 6

 Using a current balance (d.c.)  Using a search coil (a.c.)  Using a Hall probe (d.c.) Magnetic Field Measurements

 Experiments show that the magnetic flux density at a point near a long straight wire is Magnetic flux density due to a straight wire r P  This relationship is valid as long as r, the perpendicular distance to the wire, is much less than the distance to the ends of the wire.

Calculation of B near a wire Where  o is called the permeability of free space. Permeability is a measure of the effect of a material on the magnetic field by the material.

 The magnetic field is strongest at the centre of the solenoid and becomes weaker outside. Magnetic Field due to a Solenoid

 Experiments show that the magnetic flux density inside a solenoid is Magnetic Flux Density due to a Solenoid and So we have or where

 B is independent of the shape or area of the cross- section of the solenoid.  At a point at the end of the solenoid, Variation of magnetic flux density along the axis of a solenoid B Distance from the centre of the solenoid 0

Magnetic Flux Density due to Some Current- carrying conductors(1) Circular coil Helmholtz coils Where r is the separation of the coil Where r is the radius of the coil

Magnetic Flux density due to Some Current-carrying Conductors (2)

 The force on a moving charge is proportional to the component of the magnetic field perpendicular to the direction of the velocity of the charge and is in a direction perpendicular to both the velocity and the field. Force on a moving charge in a magnetic field

 Direction of force on a positive charge given by the right hand rule. Right Hand Rule

 If the motion is exactly at right angles to a uniform field, the path is turned into a circle. Free Charging Moving in a Uniform Magnetic Field In general, with the motion inclined to the field, the path is helix round the lines of force.

Mass Spectrometer The mass spectrometer is used to measure the masses of atoms. Ions will follow a straight line path in this region. Ions follow a circular path in this region.

 Charged ions approach the Earth from the Sun (the “solar wind” and are drawn toward the poles, sometimes causing a phenomenon called the aurora borealis. Aurora Borealis (Northern Lights)

 The charged particles from the sun approaching the Earth are captured by the magnetic field of the Earth.  Such particles follow the field lines toward the poles.  The high concentration of charged particles ionizes the air and recombining of electrons with atoms emits light. Causes of Aurora Borealis

 When a current carrying conductor is held firmly in a magnetic field, the field exerts a sideways force on the charges moving in the conductor.  A buildup of charge at the sides of the conductor produces a measurable voltage between the two sides of the conductor. Hall Effect The presence of this measurable transverse voltage is called the Hall effect.

 The transverse voltage builds up until the electric field it produces exerts an electric force on the moving charges that equal and opposite to the magnetic force.  The transverse voltage produced is called the Hall voltage. Hall Voltage

 The Hall voltage has a different polarity for positive and negative charge carriers.  That is, the Hall voltage can reveal the sign of the charge carriers. Charge Carriers in the Hall Effect

 Basically the Hall probe is a small piece of semiconductor layer. Hall Probe When control current I C is flowing through the semiconductor and magnetic field B is applied, the resultant Hall voltage V H can be measured on the sides of the layer. Four leads are connected to the midpoints of opposite sides.

1.Parallel wires with current flowing in the same direction, attract each other. 2.Parallel wires with current flowing in the opposite direction, repel each other. Force between two parallel current- carrying straight wires (1)

 Note that the force exerted on I 2 by I 1 is equal but opposite to the force exerted on I 1 by I 2. Force between two parallel current- carrying straight wires (2)

 The ampere is the constant current which, if maintained in two parallel conductors of infinite length, of negligible cross-section, and placed one metre apart in a vacuum, would produce between these conductors force of 2 x N per metre of length. Definition of the ampere

 A loop of wire carrying a current experiences a torque.  This torque can cause it to rotate up to   = NBAI Torque on Current Loop

 A galvanometer that is operated by the force exerted by an electric current flowing in a movable coil suspended in a magnetic field. Moving Coil Galvanometer

Construction of a Moving Coil Galvanometer Linear scale Soft iron cylinder Moving coil Concave pole piece pointer Hair spring

 A coil, with current I flowing through it, placed in a magnetic field, can experience a torque .  = NBAI Moving Coil (1)

 The moving coil is hung from a spring which winds up as the coil rotates; this winding up produces a restoring torque  ’ proportional to the winding up (or twisting) of the spring, i.e. to the angular deflection of the coil .  ’ = c   The coil comes to equilibrium when  =  ’ Moving Coil (2)

 In order to have a meter with a linear scale, the angle between the coil and the field must remain constant.  The angle can remain constant (90°) if we have a radial magnetic field.  The soft iron cylinder gives us this field shape. Radial Field

 The current sensitivity is defined as the deflection per unit current. Current Sensitivity (1) Unit : rad/A or mm/  A

The current sensitivity can be increased by  Increasing the number of turn of coils but the armature will be too bulky and the size of the air gap cannot be too small.  Increasing the magnetic field in the air gap stronger magnet is used and the air gap should be as narrow as possible.  Increasing the area of the coil but the coils will swing about its deflected position.  Using weaker hairspring, but if the opposition of the suspension is too weak the coil will also swing about its deflected position. (reading again take time). Current Sensitivity (2)

Voltage sensitivity  The voltage sensitivity is defined as the deflection per unit voltage. Unit : mm/  A

d.c. Motor

 The speed can be obtained from the equation  q v B = q E, or v= E / B Velocity selector for charged particles