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The relation between the electric current passing from the loop and the integrated magnetic field of a closed loop is defined by the Ampere Circuital Law. The Law defines the proportionality between the magnetic field developed in space around an electric current and the electric current at the point of source. The law states that the product of the total current threading the closed path 0 is equal to the line integral of the magnetic field induction B around any closed path in a vacuum. Therefore, it can be written as,
Bdl=0I,
Where the value of I can be written as I= I1+I2+I3+…+In
Application of the Ampere’s Law
There is an enormous application of the Ampere’s Law, but a few of the important applications are:
To calculate the Magnetic field at the inner side of a long solenoid.
To calculate the magnetic field inside of a conductor.
To calculate the Magnetic field inside of a toroidal coil.
To calculate the forces between two currents.
To calculate the magnetic field of a long straight wire around it.
Ampere’s Law for an Infinitely long straight wire
The magnetic field generated by an infinitely long straight wire with radius R using the Ampere’s law can be written as,
LBdl=0jIj
Case I: When the radius R<r, then
LBdl=B(r)2r=0IB(r)=0I2r
Case II: When the radius R>r
B=0Ir2R2
As in both the cases radius and current are the two factors on which magnetic field produced is dependent, therefore, the magnetic field produced by an Infinitely long straight wire is inversely proportional to the radius of the wire and directly proportional to the current.
Solenoid
A solenoid is a helical coil whose diameter is less than its length, and it is a type of electromagnet. When the current is allowed to flow through a solenoid, it produces a constant magnetic field near it in a volume of space, even though the solenoid can produce a uniform magnetic field. Yet, an iron core is generally added to increase the magnet’s strength.
In a normal solenoid, the core or the centre inside the solenoid has the magnetic field in consolidated form, while the field outside of the solenoid is weaker. The calculation of a magnetic field for a solenoid, such that the current that the solenoid is carrying is ‘I’, is done using the formula:
B=nl
In the expression above, n represents the number of turns per unit length of the solenoid.
Few Applications of Solenoids
A few of the uses of a solenoid in real life are:
It is used as an electromagnet in the inductor, solenoid valves, antennas, etc.
It is used in the manufacturing of locking systems, such as doorbells and a few medical types of equipment.
It is also used in computer component manufacturing, such as computer printers, etc.
Toroid
A toroid can be defined as a coil of insulated wire (Often copper) wrapped around a powered iron in the form of a doughnut. A toroid is used as an inductor in an electronics circuit at low frequencies where large inductance is significant.
Inside the toroid, every loop of wire on the toroid produces a magnetic field; the field’s direction points to the inner space of the toroid. Therefore, this place has the most concentrated magnetic field. Ampere’s Law plays a significant part in determining the magnetic field inside of the toroid. Since the current at the mean radius of the toroid is the product of the current each loop is carrying and the number of loops. The ampere’s Law for a toroid can be written as
B2(rmean)=NI
B=NI2(rmean)
The mean radius is half the sum of the inner and outer radius of the toroid.
Few applications of toroid
The use of a toroid in real life is used in Medical devices, musical instruments, electronic brakes, industrial equipment, ballasts, refrigeration equipment, electromagnetic clutches, Telecommunication devices, etc.
Difference between straight and circular solenoid.
Similarities between Toroid and Solenoid
A few of the similarities between toroid and solenoid are:
Both toroid and solenoid work on the same principle of electromagnetism.
Both toroid and solenoid work as an electromagnet when the current is passed.
Conclusion
The Ampere Circuital Law defines the relationship between the electric current travelling through the loop and the integrated magnetic field around a closed loop. The magnetic field produced by an Infinitely long straight wire is inversely proportional to the radius of the wire and directly proportional to the current. A solenoid is an electromagnet with a helical coil whose diameter is smaller than its length, while the toroid is a doughnut-shaped powered iron with a coil of insulated (often copper) wire wrapped around it.
