# 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 :**

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

**Observation :**

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

**Conclusion :**

**The magnetic filed due to a current in a circular loop is similar to the magnetic field of a short magnet .****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 **

**Number of turns of the circular loop ( N ) is directly proportional .****Electric current intensity ( I ) is directly proportional .****The permeability of the medium ( μ ) is directly proportional .****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 N _{1} to N_{2} and connecting it with the same source .**

**B _{1} / B_{2} = N_{1} r_{2 }/ N_{2} r_{1
}**

**∴ N _{1} / N_{2 } = r_{2} / r_{1}**

**B _{1} / B_{2} = N_{1}² / N_{2}² = r_{2}² / r_{1}²**

**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 :**

** B _{t} = B_{coil} − B_{wire} **

**I****f the field of each of the wire and the coil** **in the opposite directions , Therefore :**

**B _{t} = B_{coil} − B_{wire} , ( B_{coil} > B_{wire} ) , B_{t} = B_{wire }− B_{coil} , ( B_{wire} > B_{coil} ) . **

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

**B _{coil} = B_{wire , }**

**μ I**

_{1}N / 2r = μ I_{2}/ 2πd**N I**_{1} = I_{2} / π

_{1}= I

_{2}/ 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 .
**

**B _{t} = B_{1} + B_{2} **

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

**B _{t} = B_{1} − B_{2} , ( B_{1} > B_{2} ) .**

**In case of two circular loops having the same center and perpendicular to each other : ****B _{t}² = B_{1}² + B_{2}²**

**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**

**The number of turns of the coil ( N ) is directly proportional .****Electric current intensity ( I ) is directly proportional .****The permeability of the different media is directly proportional .****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 B _{t} = B_{1} + B_{2} .**

**In two opposite directions , so , the resultant of the magnetic flux density at the axis center is B _{t} = B_{1} − B_{2} , ( B_{1} > B_{2} ) .**

**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 .**

**B _{circular} − B_{solenoid} = L_{solenoid} / 2 r_{circular} **

**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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