Consider a circular current-carrying loop of radius R in the x-y plane with centre at the origin. Consider the line integral\(\Im (L)=\left| \left. \int_{-L}^{L}{B.dl} \right| \right.\)a) show that\(\Im (L)\)monotonically increases with L b) use an appropriate Amperian loop to that\(\Im (\infty )={{\mu }_{0}}I\)where I is the current in the wire c) verify directly the above result d) suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about\(\Im (\infty )\text{and }\Im \text{(L)}\)
a) A circular current-carrying loop’s magnetic field is given as
\(\Im (L)=\int_{-L}^{+L}{Bdl}=2Bl\)
It is a L function that increases monotonically.
b) The Amperian loop is defined as follows:
\(\Im (\infty )=\int_{-\infty }^{+\infty }{\vec{B}dl}={{\mu }_{0}}I\)
c) The magnetic field at the circular coil’s axis is provided by 0I.
d) When a circular coil is swapped out for a square coil, the result is
\(\Im {{(\infty )}_{square}}=\Im {{(\infty )}_{\text{circular coil}}}\)
