MAGNETISM

MAGNETISM

A Magnetic Field (B) exists in an otherwise empty region of space if a charge moving through that region can experience a force due to its motion.

Figure 1: Magnet bar with iron sprinkled 

around it forming line up with magnetic field

 Figure 2: A magnetic field lines

representing this magnetic field

In Figure 2, the magnetic field lines represent both the magnitude and direction of the magnetic field vector. The magnetic field vector at any point is tangent to the field line and the magnitude of the field is proportional to the number of lines per unit area perpendicular to the lines.

The bar magnet is one instant of a magnetic dipole. Magnetic dipole consists of two opposite magnetic poles:

• The end of the bar magnet where the field line emerge is called the north pole
• The lines goes back in called south pole

Magnetic field lines are all closed loops. If there are no magnetic monopole, there is no place for the field lines to begin or end.

MAGNETIC FORCE ON A POINT CHARGE

Electric field is defined as the electric force per unit charge.

q = a point charge

The electric force is either in the same direction as E or in the opposite direction depends on the sign of the point charge

The magnetic force depends on the point charge’s velocity as well as on the magnetic field. If the charge is at rest, there is no magnetic force. The magnitude and the direction of the magnetic force depend on the direction and speed of the charge’s motion. The magnetic force increases in magnitude with increasing velocity. The direction of the magnetic force on a charged particle is perpendicular to the velocity of the particle.

Factors a charge moving in a magnetic field:

• The magnitude of the charge, q
• The strength of the magnetic, H
•  The magnitude of the velocity of the charge, v or the component of the velocity                perpendicular to the field
• Sin ,  is the angle between the field lines and the velocity, v

Magnitude of the magnetic force on a moving point charge:

The SI unit of magnetic field is N/A m or tesla, T.

The direction and the magnitude of the magnetic field force depend on the vector v and B. The magnetic force can be written in term of the cross product (vector product). 

Let  and 

The vector products have perpendicular directions to the vectors. It can be determined using the right-hand-rule.

Video 1: Magnetic Force and The Right-Hand-Rule

MAGNETIC FORCE ON A CURRENT CONDUCTOR

A conductor carrying electric current has many moving charges in it. For a current carrying conductor in magnetic field, the magnetic forces  on moving charges add up to produce a net magnetic force on the wire.

A straight wire segment of length, L in a uniform magnetic field B carries a current I

The mobile carriers have charge, q

The magnetic force on any one charge is

 v is the instantaneous velocity of the charge

Multiply the average magnetic force on each charge by the number of charges 

 If N is the total number of carriers in the wire, the total magnetic force on the wire is

Magnetic force in terms of current, 

            n is the number of carriers per unit volume
            If the length, L and the cross-sectional area is A, then

Number per unit volume x volume =  nLA

             In substitution, the magnetic force on the wire is

       The magnetic force on a straight segment current carrying conductor 

        The current I times the cross product L x B gives the magnitude and direction of the               force

Figure 3: A current-carrying conductor in a magnetic field experiences a magnetic force

       (a)    A wire suspended vertically between the poles

       (b)   The blue x represents the magnetic field. When there is no current, the wire remain                 vertical

       (c)    If the current going upwards, the wire deflects to the left

       (d)   If the current going downwards, the wire deflects to the right 

       MAGNETIC FIELD DUE TO AN ELECTRIC CURRENT

       Magnetic field due to a Long Straight Wire

      Using the right-hand-rule to find the direction of the magnetic field due to a long straight wire:

•       Point the thumb of the right hand in the direction of the current in the wire
•       Curl the fingers inward toward the palm
•          The direction that the fingers curl is the direction of the magnetic field lines around the wire 

Figure 4: Right-hand-grip-rule

      The magnitude of the magnetic field at a distance r from the wire can be found using        Ampere’s Law:

       

              I   = current in the wire

           =  universal constant known as the permeability of free space, 

Video 2: Magnetic Field Pattern due to Electric Current in a Straight Wire

      Magnetic field due to a circular current loop

      Using right-hand-rule to find the direction of the magnetic field due to a circular loop of current:

• ·         Curl the fingers of right hand inward toward the palm, following the current around      the loop
• ·         The thumb points in the direction of the magnetic field in the interior of the loop

Figure 5: Magnetic fields due to a circular current loop

       The magnitude of the magnetic field at the center of circular loop is

      N = the number of turns

       I = the current

       r = radius

                     

      Torque on a coil in a uniform field,  on a coil of N loops, each carrying a current I in a               external magnetic field, B is

      A = area of the coil

   = the angle between the field lines and a perpendicular to the plane of the coil

Video 3: Magnetic Field 

      Magnetic field due to a solenoid

Figure6: Magnetic field lines due to a solenoid. The blue lines represent the wire crossing the coil with current 

       The magnetic field strength inside a solenoid is given by

       n = N/L, the number of turns per unit length

Video 4: Magnetic Field in Solenoid