All questions
AP Physics C: E&M
9.2 Electric Potential
AdvancedMCQMathematicalConceptual25.1k
A uniformly charged disk of radius R with an observation point on the central z-axis.
A uniformly charged disk of radius R with an observation point on the central z-axis.
A thin insulating disk of radius \(R\) lying in the \(xy\)-plane is centered at the origin and carries a uniform positive charge \(Q\). The electric potential on the central axis at a distance \(z > 0\) from the center of the disk is given by the expression \[ V(z) = \dfrac{Q}{2\pi \varepsilon_0 R^2} \left(\sqrt{z^2 + R^2} - z\right) \] A point charge with the same total charge \(Q\) is fixed at the origin, producing an electric potential \(V_{\text{point}}(z) = \dfrac{Q}{4\pi\varepsilon_0 z}\) along the positive \(z\)-axis. Which of the following correctly compares \(V(z)\) to \(V_{\text{point}}(z)\) for all finite \(z > 0\), and gives the leading dependence of the difference \(\Delta V(z) = V_{\text{point}}(z) - V(z)\) on \(z\) in the limit \(z \gg R\)?

Log In to Continue

Accounts are free! Log in to try this question, see explanations, save progress, and more!

Tools for a 5