A proton is traveling horizontally to the right at $4.50\times {10}^6$ m/s. Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of $3.20$ cm.

Three point charges are arranged along the $x$-axis. Charge $q_1=+3.00$ $\mu$C is at the origin, and charge $q_2=-5.00$ $\mu$C is at $x=0.200$ m. Charge $q_2=-8.00$ $\mu$C. Where is $q_3$ located if the net force on $q_1$ is $7.00$ N in the $-x$-direction?

A proton is traveling horizontally to the right at $4.50\(\times\)10^6$ m/s. How much time does it take the proton to stop after entering the field?

A positive charge $q$ is fixed at the point $x=0$, $y=0$, and a negative charge $-2q$ is fixed at the point $x=a$, $y=0$. Show the positions of the charges in a diagram.

Three point charges are arranged on a line. Charge $q_3=+5.00$ nC and is at the origin. Charge $q_2=-3.00$ nC and is at $x=+4.00$ cm. Charge $q_1$ is at $x=+2.00$ cm. What is $q_1$ (magnitude and sign) if the net force on $q_3$ is zero?

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 proton is traveling horizontally to the right at $4.50\(\times\)10^6$ m/s. What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)? Note: Part (a) asks for how much time does it take the proton to stop after entering the field.