A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, $1.60$ cm distant from the first, in a time interval of $3.20\(\times\)10^{-6}$ s. Find the speed of the proton when it strikes the negatively charged plate.

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, $1.60$ cm distant from the first, in a time interval of $3.20\times {10}^{-6}$ s. Find the magnitude of the electric field.

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 would be the force of repulsion between two people each with the charge calculated in part (a) and separated by a distance of $100$ m? Is use of the earth's electric field a feasible means of flight? Why or why not? Note: Part (a) asked for 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.

Calculate the magnitude and direction (relative to the $+x$-axis) of the electric field in Example $21.6$. Example $21.6$: A point charge $q=-8.0$ nC is located at the origin. Find the electric-field vector at the field point $x=1.2$ m, $y=-1.6$ m.

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?

Two positive point charges $q$ are placed on the $x$-axis, one at $x=a$ and one at $x=-a$. Find the magnitude and direction of the electric field at $x=0$.

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$21.34$. Find the tension in the wire.