24. Electric Force & Field; Gauss' Law

Three positive particles of equal charge, +17.0 μC, are located at the corners of an equilateral triangle of side 15.0 cm (Fig. 21–55). Calculate the magnitude and direction of the net force on each particle due to the other two.

Space explorers discover an 8.7×10¹⁷ kg asteroid that happens to have a positive charge of 4400 C. They would like to place their 3.3×10⁵ kg spaceship in orbit around the asteroid. Interestingly, the solar wind has given their spaceship a charge of −1.2C. What speed must their spaceship have to achieve a 7500-km-diameter circular orbit?

Two 1.0 g spheres are charged equally and placed 2.0 cm apart. When released, they begin to accelerate at 150 m/s². What is the magnitude of the charge on each sphere?

A positive point charge Q₁ = 2.5 x 10^-5 C is fixed at the origin of coordinates, and a negative point charge Q₂ = -5.0 x 10^-8 C is fixed to the 𝓍 axis at 𝓍 = +3.2 m. Find the location of the place(s) along the 𝓍 axis where the electric field due to these two charges is zero.

Two point charges, $q_a$ and $q_b$, are separated by a distance $r$. What is the magnitude of the electric force on charge $q_a$ due to $q_b$ according to Coulomb's Law?

What is the magnitude of the net force on charge A in FIGURE EX22.17?

A positive charge $q$ is fixed at the point $x=0$, $y=0$, and a negative charge $-2q$ is fixed at the point $x=a$, $y=0$. Show the positions of the charges in a diagram.

You have two small, 2.0 g balls that have been given equal but opposite charges, but you don't know the magnitude of the charge. To find out, you place the balls distance apart on a slippery horizontal surface, release them, and use a motion detector to measure the initial acceleration of one of the balls toward the other. After repeating this for several different separation distances, your data are shown below. Use an appropriate graph of the data to determine the magnitude of the charge.

What is the force F on the 1.0 nC charge in FIGURE EX22.20? Give your answer as a magnitude and a direction.

You have a lightweight spring whose unstretched length is 4.0 cm. First, you attach one end of the spring to the ceiling and hang a 1.0 g mass from it. This stretches the spring to a length of 5.0 cm. You then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. This stretches the spring to a length of 4.5 cm. What is the magnitude of the charge (in nC) on each bead?

Two small aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. What fraction of all the electrons in each sphere does this represent?

Three point charges are arranged on a line. Charge $q_3=+5.00$ nC and is at the origin. Charge $q_2=-3.00$ nC and is at $x=+4.00$ cm. Charge $q_1$ is at $x=+2.00$ cm. What is $q_1$ (magnitude and sign) if the net force on $q_3$ is zero?

(II) At each corner of a square of side ℓ there are point charges of magnitude Q, 2Q, 3Q, and 4Q (Fig. 21–57). Determine the magnitude and direction of the force on the charge 2Q.