The radius of a circular loop is r and a current i is flowing in it. The equivalent magnetic moment will be
a) $ir$
b) $2\pi ir$
c) $\pi i{r^2}$
d) $\dfrac{1}{{{r^2}}}$

Hint: In order to solve this question, firstly we should know that magnetic monet of an object is the ability to align itself in the presence of externa magnetic field and here we wil derive magnetic moment due to current carrying circular loop.

Formula used:
The magnetic moment due to current carrying loop of area A and number of turns N and having current i is calculated using formula:
$M = NiA$

Complete answer:
The magnetic moment of a current carrying loop can be represented by the equation $m = nIA$, where n is the number of turns, I is the current, and A is the area of the loop.

As the loop is circular, the area can be represented by $\pi r^2$, where r is the radius of the circular loop.
As there is only one turn in the loop, the equation becomes $m = I\pi r^2$

The correct answer is option c) $\pi i{r^2}$, as it matches with the equation of magnetic moment of current carrying loop.

Additional Information:
In physics, the magnetic moment of a circular coil is a measure of the strength of the magnetic field it produces. It is a vector quantity, equal to the product of the current flowing through the coil and the area of the coil. The magnetic moment is also directly proportional to the number of turns in the coil. It is also proportional to the current and area of the coil.

The direction of the magnetic moment is perpendicular to the plane of the coil, and points outwards from the centre of the coil. The magnitude of the magnetic moment is measured in units of ampere-metre square.

A circular coil with a larger area will produce a greater magnetic moment than a coil with a smaller area. likewise, a coil with more turns will have a greater magnetic moment than a coil with fewer turns.
The magnetic moment of a circular coil can be used to calculate the strength of the magnetic field it produces. The magnetic field is also directly proportional to the magnetic moment.

Note: Always remember the basic formula of magnetic moment and you can drive for any kind of lop and also don’t forget to mention number of turns it’s not always that there will be only one turn and in some problems it may given fe number of turns so don’t forget to keep N in the magnetic moment formula.