題組內容

6. A uniformly charged disk has radius \( R \) and surface charge density \( \sigma \) (shown in Fig. 1). Find (a) the electric potential at a point \( P \) along the perpendicular central axis of the disk (5 points), and (b) prove that the \( x \) component of the electric field at a point \( P \) along the perpendicular central axis of the disk is \[ 2\pi k_e \sigma [1 - \frac{x}{(R^2 + x^2)^{1/2}}]. (5 \text{ points}) \]Note that (b) must be solved by differentiating the result in (a) and we set the potential at infinity to be zeros.