24. Electric Force & Field; Gauss' Law

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?

A $-12\text{nC}$ charge is located at $(x,y)=(1.0\text{cm},0\text{cm})$. What are the electric fields at the positions $(x,y)=(5.0\text{cm},0\text{cm}),(-5.0\text{cm},0\text{cm)}$, and $(0\text{cm},5.0\text{cm})$? Write each electric field vector in component form.

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?

Two 10-cm-long thin glass rods uniformly charged to +10 nC are placed side by side, 4.0 cm apart. What are the electric field strengths E₁ to E₃ at distances 1.0 cm, 2.0 cm, and 3.0 cm to the right of the rod on the left along the line connecting the midpoints of the two rods?

A 10-cm-long thin glass rod uniformly charged to +10 nC and a 10-cm-long thin plastic rod uniformly charged to −10 nC are placed side by side, 4.0 cm apart. What are the electric field strengths E₁ to E₃ at distances 1.0 cm, 2.0 cm, and 3.0 cm from the glass rod along the line connecting the midpoints of the two rods?

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.37? Give your answer (a) in component form and (b) as a magnitude and angle measured cw or ccw (specify which) from the positive x-axis.

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?

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 thin, horizontal, 10-cm-diameter copper plate is charged to 3.5 nC. If the charge is uniformly distributed on the surface, what are the strength and direction of the electric field 0.1 mm above the center of the top surface of the plate?

Charge Q is uniformly distributed along a thin, flexible rod of length L. The rod is then bent into the semicircle shown in FIGURE P23.48. Find an expression for the electric field Ē at the center of the semicircle. Hint: A small piece of arc length Δs spans a small angle Δθ=Δs/R , where R is the radius.

FIGURE P23.41 is a cross section of two infinite lines of charge that extend out of the page. Both have linear charge density λ. Find an expression for the electric field strength E at height y above the midpoint between the lines.

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?

An electron moving to the right at 7.5 x 10⁵ m/s enters a uniform electric field parallel to its direction of motion. If the electron is to be brought to rest in the space of 5.0 cm,

(a) what direction is required for the electric field, and

(b) what is the strength of the field?

A proton is released in a uniform electric field, and it experiences an electric force of 1.68 x 10^-14 N toward the south. Find the magnitude and direction of the electric field.

Determine the magnitude of the acceleration experienced by an electron in an electric field of 756 N/C. How does the direction of the acceleration depend on the direction of the field at that point?