In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of 
, where value of ' 
' and ' 
' are
Text Solution
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To solve this problem, we need to find the dimensions of the electric flux and the magnetic flux, and then take their ratio.
Determine the dimension of electric flux 
:
Electric flux is defined as
The electric field 
has dimensions:
Since force has dimensions 
, and charge (in SI) has dimensions 
, we get:
.
The area element 
has dimensions 
.
Thus, the electric flux has dimensions:
Determine the dimension of magnetic flux ( 
):
Magnetic flux is defined as
The magnetic field 
has dimensions determined via the Lorentz force law (using 
), giving:
Again, the area element has dimensions 
.
So the magnetic flux has dimensions:
Find the ratio of electric flux to magnetic flux:
Taking the ratio:
Canceling like terms:
Mass ( 
) cancels.
Current ( 
) cancels.
For length, 
.
For time, 
.
Therefore, the ratio has dimensions:
This means in the expression
the exponents for length and time are 
and 
.
Looking at the options provided, this corresponds to Option D: ( 
).
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