Question

A circular coil of diameter 7 cm has 24 turns of wire carrying current of 0.75 A. The magnetic moment of the coil is
A. $6.9\times {{10}^{-2}}A{{m}^{2}}$
B. $2.3\times {{10}^{-2}}A{{m}^{2}}$
C. ${{10}^{-2}}A{{m}^{2}}$
D. ${{10}^{-3}}A{{m}^{2}}$

Answer 1

Hint:We have a direct equation for finding the magnetic moment of the coil. We have to just substitute the values and solve them. All values are given in the question itself. We have a number of turns of wire and current carried by the wire. From the diameter given we can find the radius of the coil and then we will be able to find the area.



Formula Used:
Magnetic moment is given by,
$M=NiA$
Where N is the number of turns
              i=current carried by coil.
              A=area of the coil.



Complete answer:
Magnetic moment actually indicates magnetic strength. Magnetic moment is also called a magnetic dipole moment. It measures an object’s tendency to align in a magnetic field. Magnetic moment is usually produced by either the motion of electric charge or due to spin angular momentum of electrons. It is a vector quantity. It is the torque exerted on a magnetic system when placed in a magnetic field.
We have direct equation as:
Magnetic moment, $M=NiA$
From the equation we have
Number of turns of wire, \[N=24\]
Current carried by the coil, \[i=0.75A\]
And
Area of the coil, $A=\pi {{r}^{2}}$
Where radius, \[r=0.35cm\]
Therefore, area of the coil, $A=\pi {{(0.35\times {{10}^{-2}})}^{2}}=3.85\times {{10}^{-5}}{{m}^{2}}$
Substituting these values in the main equation, we get:
Magnetic moment, $M=24\times 0.75\times 3.85\times {{10}^{-5}}=6.92\times {{10}^{-4}}A{{m}^{2}}$



Thus, the correct option is A.



Note:Remember that here N is just the number of turns, it is not the number of turns per unit volume and diameter is given in the question, not the radius. So, you should find the radius and make sure that you have converted the unit of radius to its SI unit.