Physics with Calculus
Which statement correctly distinguishes RR, R→\(\overrightarrow{R}\), and R^\(\hat{R}\) in Coulomb's law?
Which expression is the correct vector form of Coulomb's law after substituting R^=R→R\(\hat{R}\)=\(\frac{\overrightarrow{R}\)}{R} into F→=kq1q2R2⋅R^\(\overrightarrow{F}\)=\(\frac{kq1q2}{R^2}\[\cdot\]\hat{R}\)?
A displacement vector between two charges is R→=3i^−4j^\(\overrightarrow{R}\)=3\(\hat{i}\)-4\(\hat{j}\) meters. What is the value of R3R^3 used in the vector Coulomb formula?
Two point charges are q1=2.0q1 = 2.0 microcoulombs and q2=3.0q2 = 3.0 microcoulombs. For the force on q2q2, the displacement vector is R→=0.30i^+0.40j^\(\overrightarrow{R}\)=0.30\(\hat{i}\)+0.40\(\hat{j}\) meters. Using k=8.99×109k=8.99\(\times\)10^9 Nm2/C2\(\text{Nm}\)^2\(\text{/C}\)^2, what is the force vector?
A uniformly charged disk of radius aa lies in the xyxy-plane with surface charge density σ\(\sigma\). A test charge qq is on the zz-axis at height zz. Which setup is the most appropriate first step for an integral solution using concentric rings?