24. Electric Force & Field; Gauss' Law

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?

What is the electric field strength at a point in space where a proton experiences an acceleration of 2.4 million “g’s”?

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 $E=(400\hat{i}+100\hat{j})$ N/C. What is the electric force on a proton at this point? Give your answer in component form.

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.

The identical small spheres shown in FIGURE P22.64 are charged to +100 nC and −100 nC. They hang as shown in a 100,000 N/C electric field. What is the mass of each sphere?

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?

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 $-4.00$-nC point charge is at the origin, and a second $-5.00$-nC point charge is on the $x$-axis at $x=0.800$ m. Find the electric field (magnitude and direction) at each of the following points on the $x$-axis: (i) $x=0.200$ m; (ii) $x=1.20$ m; (iii) $x=-0.200$ m.

The earth has a net electric charge that causes a field at points near its surface equal to $150$ $N/C$ and directed in toward the center of the earth. What magnitude and sign of charge would a $60$-kg human have to acquire to overcome his or her weight by the force exerted by the earth's electric field?

A $+8.75$-mC point charge is glued down on a horizontal frictionless table. It is tied to a $-6.50$-mC point charge by a light, nonconducting $2.50$-cm wire. A uniform electric field of magnitude $1.85\(\times\)10^8$ $N/C$ is directed parallel to the wire, as shown in Fig. E$21.34$. What would the tension be if both charges were negative?

(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.

A very long, straight wire has charge per unit length $3.20\times {10}^{-10}$ C/m. At what distance from the wire is the electric field magnitude equal to $2.50$ N/C?