The magnetic field due to current in a circular loop and a solenoid

The magnetic flux lines emerges from the North pole to the South pole outside the coil , A circular loop carrying an electric current is like a magnet in the form of a disk has 2 circular poles such that no individual poles exist in nature but always pole pairs , North and South poles .

Magnetic field due to current in a circular loop

The shape of the magnetic flux lines : To identify the shape of the magnetic lines , carry out the following steps :

  1. Spread iron filings on a board surrounding a circular loop carrying electric current .
  2. Tapping it gently , the iron filings arrange themselves .

Observation :

  1. The flux lines near the center of the loop are no longer circular
  2. The magnetic flux density changes from point to point .
  3. The magnetic flux lines at the center of the loop are straight parallel lines perpendicular to the plane of the coil .

Conclusion :

  1. The magnetic filed due to a current in a circular loop is similar to the magnetic field of a short magnet .
  2. The magnetic field at the center of the coil is uniform so , the magnetic filed lines are parallel and perpendicular to the plane of the coil .

Right hand screw rule

Uses : It is used to determine the direction of the magnetic flux at the center of the circular loop carrying an electric current .

Method : Imagine a right hand screw ( being ) screwed to tie along the wire in the direction of the current , the direction of fastening of the screw gives the direction of the magnetic flux at the center of the loop .

The clockwise direction rule

Uses : It is used to determine the type of the pole for each face of a circular loop carrying an electric current .

Method : The side which carries an electric current in the clockwise direction is called the South pole , The side which carries an electric current in the counter clockwise direction is called North pole .

Deduction of the magnetic flux density

The magnetic flux density at the center of a circular loop of radius ( r ) , number of turns ( N ) and carrying electric current ( I ) can be deduced as follows : 

B ∝ N   , B ∝ I  , B ∝ ( I / r )

B ∝ N I / r    ,   B = Constant × N I / r  

B = μ N I / 2 r  
The factors that affect the magnetic flux density at the center of a circular loop
  1. Number of turns of the circular loop ( N ) is directly proportional .
  2. Electric current intensity ( I ) is directly proportional .
  3. The permeability of the medium ( μ ) is directly proportional .
  4. The radius of the circular loop ( r ) is inversely proportional .

Determination of the number of turns of a circular loop : 

  • If a wire of a length ( L ) is coiled in the shape of a circular loop of radius ( r ) : Therefore , N = L / 2 π r , Where : N is either integer or not integer number .
  • If the coil is an incompleted part of a circle , then : N = θ / 360

In case of changing the number of turns of the circular loop from N1 to N2 and connecting it with the same source .

B1 / B2 = N1 r2 / N2 r1

∴  N1 / N = r2 / r1

B1 / B2 = N1² / N2² = r2² / r1²

To determine the magnetic flux density at the center of a circular loop at a certain distance from a straight wire in the same plane while an electric current is passing through each of them .

If the field of each of the wire & the coil in the same direction , Therefore :

Bt = Bcoil − Bwire

If the field of each of the wire and the coil in the opposite directions , Therefore :

Bt = Bcoil − Bwire , ( Bcoil > Bwire  ) , Bt = Bwire − Bcoil , ( Bwire > Bcoil  ) .

In case of a circular loop tangent to a straight wire causing the magnetic flux density to vanish at the center .

Bcoil = Bwire        ,      μ I1 N / 2r = μ I2 / 2πd

N I1 = I2 / π

In case of two circular loops having the same center and carrying two currents :

In the same direction then the resultant of the flux density at the center .

Bt = B1 + B2  

In the opposite direction then the resultant of the flux density at the center .

Bt = B1 − B2   , ( B1 > B2 ) .

In case of two circular loops having the same center and perpendicular to each other : Bt² = B1² + B2²

Magnetic field due to current in a solenoid

Magnetic field due to current in a solenoid

Magnetic field due to current in a solenoid

The shape of the magnetic flux lines

When the electric current passes through the solenoid ( along spiral or cylindrical coil ) , the resultant magnetic flux is very similar to that of the bar magnet , The magnetic flux lines make a complete circuit inside and outside the coil , each line is a closed path .

Right hand screw rule

Uses : It is used to determine the direction of the magnetic flux at the axis of a solenoid passing though it an electric current .

The method : As mentioned previously in the circular loop considering that the solenoid consists of a group of a circular loops having the same center .

The clockwise direction rule 

Uses : It is used to determine the type of the pole for each side of a solenoid carrying an electric current .

Method : As in the circular loop .

Amper’s right hand rule

Uses : It is used to determine the polarity of the field .

Method : When you grasp the coil with your right hand such that the fingers point to the direction of the current , the thumb points to the direction of the magnetic field due to the current .

Deduction of the magnetic flux density

Deduction of the magnetic flux density at any point of a solenoid of length ( l ) and its number of turns ( N ) carrying an electric current ( I ) is as follows :

B ∝ N   ,   B ∝ I  ,   B ∝ I / L

B = Constant × N I / L

B = μ N I / L = μ n I

n = N / L

Where : ( n ) is the number of turns for unit length of the solenoid , When the number of turns are touching each other along the length of the solenoid , then the length of the coil : L = N × 2 r¯ , Where : ( r¯ ) is the radius of the wire of the coil .

The factors that affect the magnetic flux density due to current in a solenoid
  1. The number of turns of the coil ( N ) is directly proportional .
  2. Electric current intensity ( I ) is directly proportional .
  3. The permeability of the different media is directly proportional .
  4. The length of the coil is inversely proportional .

The magnetic field may not be generated when the electric current passes in a circular loop or a solenoid , because the circular loop or the solenoid is double coiled , so the direction of the produced magnetic flux due to the flow of the current in a certain direction becomes opposite to that produced due to the flow of the same current in the opposite direction and thus they cancel each other .

If a part of a coil connected to electric source is cut , then the remaining part of the coil when connected to the same source :

  • Its current increases .
  • The number of turns decreases .
  • The length of the coil decreases .
  • Number of turns / unit length remains constants .

When the turns of the coil are touching each other , then the length of the coil : L = N × 2 r¯ , Where : ( r¯ ) is the radius of the wire in the coil .

In case of two solenoids , having the same axis and carry two currents :

In the same direction , so , the resultant of the magnetic flux density at the axis center is Bt = B1 + B2 .

In two opposite directions , so , the resultant of the magnetic flux density at the axis center is Bt = B1 − B2  , ( B1 > B2 ) .

When turns of the circular loop are moved away from each other , the loop becomes a solenoid and can be compared based on the relation .

Bcircular − Bsolenoid = Lsolenoid / 2 rcircular 

Magnetic effect of the electric current & Magnetic flux density due to current in two parallel wires

Magnetic force & Torque , Factors that affect the torque & magnetic dipole moment

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