24. Electric Force & Field; Gauss' Law

Consider an oil droplet of mass m and charge q. We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge is positive and that the electric field between the plates points upward. A spherical object of radius r moving slowly through the air is known to experience a retarding force F_drag = −6πηrv where η is the viscosity of the air. Use this and your answer to part b to show that a spherical droplet of density ρ falling with a terminal velocity v_term has a radius. $r=\sqrt{\frac{9\eta v_{term}}{2\rho g}}$

For a point charge located at the origin, what is the direction of the electric field at any point on the $z$ axis?

(II) A positive charge q is placed at the center of a circular ring of radius R. The ring carries a uniformly distributed negative charge of total magnitude -Q. (a) If the charge q is displaced from the center a small distance x as shown in Fig. 21–71, show that it will undergo simple harmonic motion when released. (b) If its mass is m, what is its period?

Which of the following statements about electric field lines for point charges is incorrect?

If a point charge $q$ is located at a distance $r$ from point C in vacuum, the magnitude of the electric field at point C is:

A −15 nC charge is at x=+2.0 cm on the x-axis. A second charge q is located somewhere on the x-axis to the left of the origin. The electric field at y=2.0 cm on the y-axis is $\overrightarrow{E}=3.0\times {10}^5\hat{i}$N/C . What are (a) the charge q in nC and (b) its distance from the origin?

Which of the following best describes what electric $E$ and magnetic $B$ fields contain and transport?

Consider two points, A and B, located at distances $r=1$ m and $r=2$ m from a point charge, respectively. At which point is the electric field stronger?

(II) A very long uniformly charged wire (linear charge density λ = 2.5 C/m) lies along the x-axis in Fig. 21–59. A small charged sphere (Q = -2.0 C) is at the point x = 0 cm, y = -5.0 cm. What is the electric field at the point x = 7.0 cm, y = 7.0 cm? ${\overrightarrow{E}}_{\text{wire}}$ and ${\overrightarrow{E}}_q$ represent fields due to the long wire and the charge Q, respectively.

The electric field strength 1.5 cm from an electric dipole, on the axis of the dipole, is 1.5×10⁵ N/C. What is the dipole moment in nC mm?

An infinitely long cylinder of radius R has linear charge density λ. The potential on the surface of the cylinder is V₀, and the electric field outside the cylinder is E_r = λ/2πϵ₀r . Find the potential relative to the surface at a point that is distance r from the axis, assuming r>R.

All electric currents generate __________ fields.

In the figure, the electric field lines on the left are shown to be closer together than those on the right. What does this indicate about the strength of the electric field on the left compared to the right?

New units of the electric field were introduced in this chapter. Which of the following are the correct new units for electric field?

Which of the following best illustrates the electromagnetic force in action?