BackThe nuclei of large atoms, such as uranium, with protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately m. What magnitude of electric field does it produce at the distance of the electrons, which is about m?
A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm. What is the electric field strength just outside the surface of the sphere when it is charged to 500,000 V?
What are the strength and direction of the electric field 1.0 mm from a proton?
A hollow copper sphere has inner radius 1.0 cm and outer radius 2.5 cm. A 5.0 A current flows radially outward from the inner surface to the outer surface. What is the electric field strength at r=2.0 cm?
Two point charges, Q1 = - 32 μC and Q2 = +45μC, are separated by a distance of 12 cm. The electric field at the point P (see Fig. 21–61) is zero. How far from Q1 is P?
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?
(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?
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?
Three very large square charged planes are arranged as shown (on edge) in Fig. 21–78. From left to right, the planes have charge densities per unit area of -0.50μC/m², +0.25 μC/m² and -0.35 μC/m². Find the total electric field (direction and magnitude) at the points A, B, C, and D. Assume the plates are much larger than the distance AD.
(II) Determine the direction and magnitude of the electric field at the point P shown in Fig. 21–66. The two point charges are separated by a distance of 2a. Point P is on the perpendicular bisector of the line joining the charges, a distance x from the midpoint between them. Express your answers in terms of Q, x, a, and k.
(III) A thin rod of length ℓ carries a total charge Q distributed uniformly along its length. See Fig. 21–69. Determine the electric field along the axis of the rod starting at one end—that is, find E(𝓍) for 𝓍 ≥ 0 in Fig. 21–69.
(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? and represent fields due to the long wire and the charge Q, respectively.
A thin glass rod is a semicircle of radius R, Fig. 21–81. A charge is nonuniformly distributed along the semicircle with a linear charge density given by λ = λ0 sin θ, where λ0 is a positive constant. Point P is at the center of the semicircle. (a) Find the electric field (magnitude and direction) at point P. [Hint: Remember sin ( -θ) = - sin θ, so the two halves of the rod are oppositely charged.] (b) Determine the acceleration (magnitude and direction) of an electron placed at point P, assuming R = 1.0 cm and λ0 = 1.0 μC/m.