# What do we call a 31 sided polygon ?

Electricity and Magnetism Level 5

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.
×