Discussion
A field is given as \( \mathbf{A} = k\mathbf{a}_\rho/\rho \) in cylindrical coordinates. Its divergence away from the axis is
Answer: C
The cylindrical divergence is \( (1/\rho)\partial(\rho A_\rho)/\partial\rho \), and the bracket here is the constant k, so the derivative is zero. This is the field of an infinite line charge, whose divergence vanishes everywhere except on the line itself.
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