Back(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.
An infinitely long sheet of charge of width L lies in the xy-plane between x = -L /2 and x = L /2. The surface charge density is h. Draw a graph of field strength E versus x for x > L /2.
The electric field at a point in space is N/C. What is the magnitude of the electron’s acceleration?
The electric field in a region of space is Ex = −1000x^2 V/m, where x is in meters. Graph Ex versus x over the region −1 m ≤ x ≤1 m.
An electric dipole at the origin consists of two charges ±q spaced distance s apart along the y-axis. What is the field Ē on the bisecting axis? Does your result agree with Equation 23.11?
An infinitely long cylinder of radius R has linear charge density λ. The potential on the surface of the cylinder is V0, and the electric field outside the cylinder is Er = λ/2πϵ0r . Find the potential relative to the surface at a point that is distance r from the axis, assuming r>R.
FIGURE P23.44 shows a thin rod of length L with total charge Q. Evaluate E at r=3.0 cm if L=5.0 cm and Q=3.0 nC.
Two 10-cm-diameter charged rings face each other, 20 cm apart. The left ring is charged to −20 nC and the right ring is charged to +20 nC. What is the electric field Ē, both magnitude and direction, at the midpoint between the two rings?
A ring of radius R has total charge Q. At what distance along the z-axis is the electric field strength a maximum?