Question

The value of the resultant magnetic field of an Amperian loop is B = μoI/2πr . Explain four major findings for this relation.

Answer 1

Answer:

Ampere’s circuital law states that line integral of magnetic field forming a closed loop around the current(i) carrying wire, in the plane normal to the current, is equal to the μo times the net current passing through the close loop.

Here μo = permeability of free space = 4π×10-15N/A2

This law is based on the assumption that the closed loop consists of small elemental parts of length dl, and the total magnetic field of the closed loop will be the integral of magnetic field and the length of these elements This closed loop is called Amperian loop

Further, this integral will be equal to the multiplication of net current passing through this closed loop and the permeability of free space(μoi)

Proof-1(Regular coil):

To prove: ∫B.dl = μoi

Starting from the left hand side, we can see in the diagram that angle between the element dl and magnetic field B is 0°

We know that magnetic field due to a long current carrying wire is:

B = μoi/(2πr)

Also, the integral of element will form the whole circle of circumference (2πr):

∫ dl = 2πr

Now putting the value of B and ∫ dl in the equation, we get:

B∫ dl = μoi/(2πr) × 2πr = μoi

∴∫B.dl = μoi

Answer 2

The output value of the Amperian loop field is B = μoI / 2πr and the four main findings of this relationship are:

• Ampere's Circuital Law refers to the relationship between a magnetic field surrounding a closed loop and the power of an electric current beyond the loop.
• Ampere Law is based on Maxwell's statistics:
• Ampere Circuital Law is another way of expressing the Biot-Savart Act.
• In comparison, Circuit law is nothing new compared to the content of Biot-Savart law.
• Both of these laws define and link magnetic fields to current ones.
• The physical significance of static power is also shown.