When I'm calculating the divergence of a cylinder with uniform magnetic field ($B=K=\text{constant}$) according to the formula of divergence in cylindrical coordinates I'm getting the same constant value as the divergence.
$$\nabla\cdot B=K.$$
But from the physical explanation of divergence it should be 0 in a uniform field. What's the loophole here?
You wrote $B=K$ but this is not a correct way to describe the magnetic field, the magnetic field is a vector. In cylindrical coordinates, you could have $\vec{B}=K\hat{r}$, $\vec{B}=K\hat{\varphi}$ or $\vec{B}=K\hat{z}$. Now, the divergence operator in cylindrical coordinates would imply, for each case
$$\nabla \cdot \vec{B} = \frac{1}{r}\frac{\partial(rB_r)}{\partial r}=\frac{K}{r}, \ \nabla \cdot \vec{B}=\frac{1}{r}\frac{\partial B_{\varphi}}{\partial \varphi}=0, \ \nabla\cdot \vec{B}=\frac{\partial B_z}{\partial z}=0.$$
As you can see, for two of those magnetic fields the divergence is zero, while the first one has a non-zero divergence. This implies that the first option is not a possible magnetic field in a cylindrical configuration.
