24. Electric Force & Field; Gauss' Law

You are given two unknown point charges, Q₁ and Q₂. At a point on the line joining them, one-third of the way from Q₁ to Q₂, the electric field is zero (Fig. 21–64). What is the ratio Q₁/Q₂?

A point charge is placed at each corner of a square with side length $a$. All charges have magnitude $q$. Two of the charges are positive and two are negative (Fig. E$21.42$). What is the direction of the net electric field at the center of the square due to the four charges, and what is its magnitude in terms of $q$ and $a$?

What is the strength of the electric field at the position $(x,y,z)$ due to a point charge $q$ located at the origin?

Suppose a point charge of $q$ is located at a distance $r$ from the dot shown in the figure. What is the strength of the electric field at the position of the dot?

A small 1.0 g block charged to 75 nC is placed on a 30° inclined plane. The coefficients of static and kinetic friction are 0.20 and 0.10, respectively. What minimum strength horizontal electric field is needed to keep the block from sliding down the plane?

What magnitude of point charge produces an electric field of $1.0N/C$ at a distance of $1.0m$ from the charge?

What is the magnitude and direction of the electric field at a distance of $4.20\mathrm{cm}$ from a point charge of $-1.501.0\times 10{\mathrm{-6}}^{}C$ (microcoulombs)?

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 point charge $q$ is located at position $(a,0)$ on the x-axis. What is the x-component of the electric field at the origin, point O?

A point charge of mass 0.145 kg, and net charge +3.40 μC, hangs at rest at the end of an insulating cord above a large sheet of charge. The horizontal sheet of fixed uniform charge creates a uniform vertical electric field in the vicinity of the point charge. The tension in the cord is measured to be 5.18 N. (a) Calculate the magnitude and direction of the electric field due to the sheet of charge (Fig. 21–80). (b) What is the surface charge density σ(C/m²) on the sheet?

As an electron moves in the direction of the electric field lines, which of the following statements is true?

How is the direction of an $\mathrm{electric field}$ defined?