All questions
AP Physics C: E&M
8.4 Electric Fields of Charge Distributions
AdvancedMCQMathematical22.7k
A vertical schematic showing a single sphere falling downward. A dashed vertical arrow labeled E points upward. From the center of the sphere, three distinct force vectors are drawn: a straight arrow pointing vertically downward labeled F_g, a straight arrow pointing vertically upward labeled F_E, and a second straight arrow pointing vertically upward labeled F_d. No other labels, lines, text, or axes appear.
Free-body force diagram for a charged sphere falling in an upward electric field.
Three solid insulating spheres, each of radius \(R\) and uniform mass density \(\rho_m\), fall vertically through a viscous fluid in a region containing a uniform upward electric field of magnitude \(E\). The fluid exerts a resistive drag force \(F_d = b v\) on each sphere, where \(b\) is a constant. The volume charge densities \(\rho(r)\) of the spheres as a function of radial distance \(r\) from their centers (\(0 \le r \le R\)) are given in the table below.

SphereVolume Charge Density \(\rho(r)\)
I\(\rho_0 \left(\dfrac{r}{R}\right)\)
II\(\rho_0 \left(\dfrac{r}{R}\right)^2\)
III\(\dfrac{3}{5}\rho_0\)

Assuming that the gravitational force on each sphere is greater than the electric force acting on it, which of the following correctly ranks the magnitudes of the downward terminal velocities \(v_I\), \(v_{II}\), and \(v_{III}\) of the three spheres?

Log In to Continue

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

Tools for a 5