A rod of length L with uniform charge density per unit length is in the XY-plane and rotating about Z-axis passing through one of its edge with an angular velocity as shown in the figure below. ( r,\, ,\, z ) refer to the unit vectors at Q, A is the vector potential at a distance d from the origin O along Z-axis for d ≪ L and J is the current density due to the motion of the rod. Which one of the following statements is correct?

A rod of length L with uniform charge density $$\lambda$$ per unit length is in the XY-plane and rotating about Z-axis passing through one of its edge with an angular velocity $$\overrightarrow{\omega }$$ as shown in the figure below. $$\left(\hat{\mathbf{r}},\hat{\varphi },\hat{\mathbf{z}}\right)$$   refer to the unit vectors at Q, $$\overrightarrow{\mathbf{A}}$$ is the vector potential at a distance d from the origin O along Z-axis for d ≪ L and $$\overrightarrow{\mathbf{J}}$$ is the current density due to the motion of the rod. Which one of the following statements is correct?

Answer: Option D