24. Electric Force & Field; Gauss' Law

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 E_r = 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?

A rod of length L lies along the y-axis with its center at the origin. The rod has a nonuniform linear charge density $\lambda =a\mid y\mid$, where a is a constant with the units C/m². Find the electric field strength of the rod at distance x on the x-axis.

An infinite plane of charge with surface charge density 3.2 μC/m² has a 20-cm-diameter circular hole cut out of it. What is the electric field strength directly over the center of the hole at a distance of 12 cm? Hint: Can you create this charge distribution as a superposition of charge distributions for which you know the electric field?