24. Electric Force & Field; Gauss' Law

A point charge of magnitude $q$ is placed at the center of a cube with sides of length $l$. What is the total electric flux through the entire surface of the cube?

Can an object with $no net charge$ produce an $electric field$?

A point charge of $5.0\times {10}^{-6}C$ is located at the origin. Calculate the magnitude of the electric field at point A, located at coordinates $(0,12.0)$ meters. (Assume vacuum, $k=8.99\times {10}^{9}N\cdot m^2/C^2$.)

A thin spherical shell of radius $r_1$ carries a total charge $Q$. Another concentric thin spherical shell of radius $r_2$ ($r_2>r_1$) carries no charge. What is the magnitude of the radial electric field at the point $r=0.5(r_1+r_2)$? Give your answer in units of $kN/C$.

What is the magnitude of the electric field at a distance $r$ from a thorium nucleus (atomic number $90$)? Assume the nucleus is a point charge and use $k$ for Coulomb's constant and $e$ for the elementary charge.

Which of the following electric field line diagrams is incorrect for isolated point charges?

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.3? Specify the direction as an angle cw from horizontal.

A point charge $q_1=-4.00$ nC is at the point $x=0.600$ m, $y=0.800$ m, and a second point charge $q_2=+6.00$ nC is at the point $x=0.600$ m, $y=0$. Calculate the magnitude and direction of the net electric field at the origin due to these two point charges.

A 1.5μC charge, with a mass of 50g, is in the presence of an electric field that perfectly balances its gravity. What magnitude does the electric field need to be, and in what direction does it need to point?

At point $p$, which is located near a positive point charge, what is the direction of the electric field at this point?

Suppose two points, point 1 and point 2, are located at different distances from a single positive point charge. What can you say about the magnitude of the electric field at point 1 compared with the field at point 2?$E$ at point 1 compared with $E$ at point 2?

A 0.10 g honeybee acquires a charge of +23 pC while flying. What electric field (strength and direction) would allow the bee to hang suspended in the air?

Two 10-cm-diameter charged disks face each other, 20 cm apart. The left disk is charged to −50 nC and the right disk is charged to +50 nC. a. What is the electric field Ē, both magnitude and direction, at the midpoint between the two disks?

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. An electric field is established by applying a potential difference to the plates. It is found that a field of strength E₀ will cause the droplet to be suspended motionless. Write an expression for the droplet's charge in terms of the suspending field E₀ and the droplet's weight mg.