Chapter 25: The Electric Potential

A +3.0 nC charge is at x = 0 cm and a -1.0 nC charge is at x = 4 cm. At what point or points on the x-axis is the electric potential zero?

Two protons are launched with the same speed from point 1 inside the parallel-plate capacitor of FIGURE Q25.4. Points 2 and 3 are the same distance from the negative plate.

a. Is $\Delta U_{1\to 2}$, the change in potential energy along the path $1\to 2$, larger than, smaller than, or equal to $\Delta U_{1\to 3}$?

b. Is the proton's speed $v_2$at point 2 larger than, smaller than, or equal to $v_3$? Explain.

A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of $50,000\mathrm{m}/\mathrm{s}$. The experiment is repeated with a${\mathrm{He}}^{+}$ ion (charge $\mathrm{e}$, mass$4\mathrm{u}$ ). What is the ion's speed at the negative plate?

A -3.0 nC charge is on the x-axis at x = -9 cm and a +4.0 nC

charge is on the x-axis at x = 16 cm. At what point or points on

the y-axis is the electric potential zero?

Two small metal cubes with masses 2.0 g and 4.0 g are tied together by a 5.0-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2.0 mC. a. What is the energy of this system? b. What is the tension in the string? c. The string is cut. What is the speed of each cube when they are far apart?

The four 1.0 g spheres shown in FIGURE P25.42 are released simultaneously and allowed to move away from each other. What is the speed of each sphere when they are very far apart?

A proton’s speed as it passes point A is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton’s speed at point B? A proton’s speed as it passes point A is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton’s speed at point B?

Living cells “pump” singly ionized sodium ions, Na+, from the inside of the cell to the outside to maintain a membrane potential ∆Vmembrane = Vin - Vout = - 70 mV. It is called pumping because work must be done to move a positive ion from the negative inside of the cell to the positive outside, and it must go on continuously because sodium ions “leak” back through the cell wall by diffusion. a. How much work must be done to move one sodium ion from the inside of the cell to the outside? b. At rest, the human body uses energy at the rate of approximately 100 W to maintain basic metabolic functions. It has been estimated that 20% of this energy is used to operate the sodium pumps of the body. Estimate—to one significant figure—the number of sodium ions pumped per second.

An arrangement of source charges produces the electric potential

V = 5000x2 along the x-axis, where V is in volts and x is in meters.

What is the maximum speed of a 1.0 g, 10 nC charged particle that moves in this potential with turning points at +-8.0 cm?

An arrangement of source charges produces the electric potential V = 5000x2 along the x-axis, where V is in volts and x is in meters. What is the maximum speed of a 1.0 g, 10 nC charged particle that moves in this potential with turning points at 8.0 cm?