the
magnetic susceptibility? Consider an H-atom. Guess an expression for 
upto a constant by constructing
a quantity of dimensions of out of
parameters of the atom : 
Here, 
is the electronic mass, 
is electronic velocity, 
is Bohr radius. Estimate the
number so obtained and compare with the value of
for
many solid materials.
Answer:
Magnetic susceptibility
As 
and 
have same units and dimensions,
hence 
has no dimensions.
In this
question, is to be related with 
We know that dimensions of 
[From
Biot Savart's law, 
or
Dimensions
of
Where
is for charge]
As is dimensionless, it should have
no involvement of charge in its
dimensional formula. It will be so if 
and
together should have the value 
, as e has the dimensions of
charge.
Let
......
where
a, b, c are the powers of 
, 
and 
such
that relation is satisfied.
Dimensional
equation ofis 
Equating
the powers of 
and 
, we get
0 =
1 + 
or =
-1 ; 0 = 1 + b + c ??
0 =
-b or b = 0 ; From, 0 = 1 + 0 + c or c =
-1
Putting
values in, we get
Here,
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