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Question Number 100068 by M±th+et+s last updated on 24/Jun/20

h e l l o a l l i h a v e s o m e q u e s t i o n s ?

1) w h a t i s t h e r i e m a n n h y p o t h e s i s ?

2) h o w d i d t h e y d e t e r m i n e t h e d i s t a n c e

t o t h e s u n ?

3) h o w d i d w e m e a s u r e t h e s p e e d o f l i g h t ?

Answered by JDamian last updated on 24/Jun/20

Y o u c a n f i n d t h e a n s w e r s i n g o o g l e

Commented by M±th+et+s last updated on 24/Jun/20

t h a n k y o u f o r y o u r c o m m e n t s i r .

b u t

i n g o o g l e t h e r e i s n o m a t h m a t i c s

e x p l a n i n g j u s t a s i m p l e e x p l a n a t i o n .

Answered by smridha last updated on 25/Jun/20

M a x w e l l d i f f : {e q}^{n} s a i d u s

▽^{2} \vec{E} = μ_{0} ϵ_{0} \frac{\partial^{2} \vec{E}}{\partial t^{2}} a n d ▽^{2} \vec{B} = μ_{0} ϵ_{0} \frac{\partial^{2} \vec{B}}{\partial t^{2}}

w h e r e \vec{E} = e l e c t r i c f i e l d

\vec{B} = m a g n e t i c f i e l d

μ_{0} = m a g n e t i c p e r m i a b i l i t y i n f r e e s p a c e

ϵ_{0} = p e r m i t i v i t y o f f r e e s p a c e

[t h i s i s b e s i c a l l y 3 d w a v e {e q}^{n}

t h i s t w o {e q}^{n s} d e s c r i b e l i g h t a s

a e l e c t r o m a g n e t i c w a v e]

n o w a n a l y s i s t h e d i m e n t i o n o f

t h e p r o d u c t o f μ_{0} a n d ϵ_{0} . .

d i m [ϵ_{0} μ_{0}] = [M^{- 1} L^{- 1} T^{4}] . [{M L}^{- 1} T^{- 2}]

= [L^{- 2} T^{2}]

n o w d i m [\frac{1}{\sqrt{μ_{0} ϵ_{0}}}] = [L . T^{- 1}] = d i m (v)

w h e r e v = v e l o c i t y b u t t h i s n o t

a n y o d i n a r y v e l o c i t y t h i s i s v e r y

s p e c i a l, t h e s p e e d o f l i g h t i n

f r e e s p a c e d e n o t e d b y C . .

s o o u r {e q}^{n} l o o k s l i k e :

▽^{2} \vec{E} = \frac{1}{C^{2}} \frac{\partial^{2} \vec{E}}{\partial t^{2}} a n d ▽^{2} \vec{B} = \frac{1}{C^{2}} . \frac{\partial^{2} \vec{B}}{\partial t^{2}}

n o w s p e e d o f l i g h t :

C = \frac{1}{\sqrt{μ_{0} ϵ_{0}}} = \frac{1}{\sqrt{4 π \times 10^{- 7} \times 8.854 \times 10^{- 12}}}

= 2.99795638 \times 10^{8} \approx 3 \times 10^{8} m . s^{- 1}

h e r e I u s e d t h e e x p e r i m e n t a l v a l u e

o f μ_{0} a n d ϵ_{0} .

Commented by Rasheed.Sindhi last updated on 25/Jun/20

G \overset{⌢}{O} \overset{⌢}{O D} u s e o f m a t h e m a t i c a l n o t a t i o n

i n t h e f i e l d o f h u m a n e m o t i o n s!

Commented by M±th+et+s last updated on 24/Jun/20

v e r y n i c e e x p l a n a t i o n .

g o d b l e s s y o u

Commented by smridha last updated on 24/Jun/20

\underset{i = 1}{\sum^{\infty}} {(t h a n k)}_{i}

Commented by Rasheed.Sindhi last updated on 25/Jun/20

C a n w e c o n s i d e r

h u m a n - e m o t i o n s - f i e l d

a s a m a t h e m a t i c a l - f i e l d ?

O f c o u r s e, w h y n o t

i f w e c a n d e f i n e t h a n k s,

s o r r y & o t h e r h u m a n - e m o t i o n s!

Commented by smridha last updated on 25/Jun/20

y e a h w h y n o t!! a f t e r a l l

M a t h e m a t i c s i s n o t h i n g m o r e t h a n

a l a n g u a g e . i f t h e r e i s a w i s h

t h e r e i s a w a y . .

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