Question

An infinitely long line, with uniform positive charge density, lies along the z-axis. In cylindrical coordinates \( (r, \phi, z) \), at any point \( \mathbf{P} \) not on the z-axis, the direction of the electric field is

• A. \( \hat{r} \)
• B. \( \hat{\phi} \)
• C. \( \hat{z} \)
• D. \( \frac{(\hat{r} + \hat{z})}{\sqrt{2}} \)

Hint:

For a uniformly charged infinite line, the electric field is always radial, pointing outward from the line if the charge is positive.

Answer 1

The Correct Option is A

The electric field due to a uniformly charged infinite line is radial and points directly away from the line (if the charge is positive). In cylindrical coordinates, the radial direction is denoted by \( \hat{r} \), and the electric field at a point \( \mathbf{P} \) not on the z-axis will always point in the \( \hat{r} \) direction, perpendicular to the z-axis. Thus, the direction of the electric field is along \( \hat{r} \), which is option (A). Final Answer: \( \hat{r} \)