Question

Show that units of 1√εo⋅μo= ms−1 ?

Answer 1

Hey mate here is ur ans

There are many methods by which we can attempt to show the units of

1

√

ε

0

⋅

μ

0

. Two are as shown below.

ε

0

is permittivity of free space and its SI units are farad per meter

F

⋅

m

−

1

.

We know that derived unit of farad in SI base units‎ are ‎

s

4

⋅

A

2

⋅

m

−

2

⋅

k

g

−

1

As such SI units of permittivity become

s

4

⋅

A

2

⋅

m

−

3

⋅

k

g

−

1

.....(1)

Now

μ

0

is permeability of free space and its SI units are henry per meter

H

⋅

m

−

1

Reduced to base SI units of henry is

k

g

⋅

m

2

⋅

s

−

2

⋅

A

−

2

.

As such SI units of permeability become

k

g

⋅

m

⋅

s

−

2

⋅

A

−

2

.....(1)

Now we that LHS of equation has units as of

1

√

(

s

4

⋅

A

2

⋅

m

−

3

⋅

k

g

−

1

)

(

k

g

⋅

m

⋅

s

−

2

⋅

A

−

2

)

⇒

1

√

s

2

⋅

m

−

2

⇒

m

s

−

1

Hence proved.

.-.-.-.-.-.-

We know that by definition

c

≡

1

√

ε

0

⋅

μ

0

where

c

is velocity of light in vacuum (free space).

Since units of velocity are

m

s

−

1

,

∴

units of RHS are also

m

s

−

1

Hence proved

I hope its helpfull for u

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