IF B is the magnetic field at the centre of a circular loop of area A and its magnetic dipole moment is found to be `n(BA^(m))/(mu_(0)sqrt(pi))`, then what is the value of `n+m`?

Answer

`3.5`

Explanation

Let r be the radius of the circular loop.
`:.A=pir^(2)`
`impliesr=sqrt(A/(pi))`
Magnetic field at the centre of the loop is
`B=(mu_(0)I)/(2r)`
`impliesB`
`=(mu_(0)I)/(2sqrt(A/(pi)))=I=(2B)/(mu_(0))sqrt(A/(pi))`
now magnetic moment of the loop is
`M=IA`
`=(2B)/(mu_(0))sqrt(A/(pi)).A`
`=(2B)/(mu_(0))(A^(3/2))/(sqrt(pi))`
`implies N=2"and" Q=1.5`
`:.N+Q=3.5`