What do we call a 31 sided polygon ?

Magnetic field on the axis of a curent carrying ring of radius $R$ at a distance $x$ from the centre of the ring is given by

$\frac { \mu _{ 0 }I }{ 2({ x }^{ 2 }+{ R }^{ 2 })^{ 3/2 } }$ ; where $I$ is the current flowing through the ring.

The result can be derived either from

• integration approach or

• by deriving a result for $n$ sided regular polygon and then taking the limit as $n\rightarrow \infty$ .

Finally, your job is to find the magnitude of the magnetic field on the axis of a $31$ sided regular polygon of sidelength $l$ carrying current $I$ at a distance $x$ from the centre of the polygon. If the magnitude of magnetic field comes out to be $a$ ,

Give your final answer as $a\times \ {10 }^{ 7 }$

• Details and Assumptions

• $l=0.1m$ , $x=0.1m$ , $I=1ampere$ .

• ${ \mu }_{ o }\ =\ 4\pi \times \ { 10 }^{ -7 }$
• $\sin { \frac { \pi }{ 31 } } \approx \ 0.1$ and so the other Trigonometric ratios can be calculated from it.