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Let 
be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of 
, the divergence of the radial vector field 
is independent of 
?
1
2
Step 1: Compute Divergence in Spherical Coordinates
For a purely radial field 
, the divergence is:
Given 
, substitute:
Step 2: Simplify the Expression
.
Take the derivative:
Thus, the divergence becomes:
.
Step 3: Identify When Divergence is Independent of R
For the divergence to be independent of R, the exponent of R must vanish:
But wait! There's another case where the divergence is independent of R:
If the prefactor 
, the divergence becomes zero (trivially independent of R).
This occurs when:
Verification for Both Cases:
1. For 
:
2. For 
:
