25. Electric Potential

A student wants to make a very small particle accelerator using a 9.0 V battery. What speed will an electron have after being accelerated from rest through the 9.0 V potential difference?

A 250 pg dust particle has charge −250e. Its speed is 2.0 m/s at point 1, where the electric potential is V₁=2000 V. What speed will it have at point 2, where the potential is V₂=−5000 V? Ignore air resistance and gravity.

An electron with an initial speed of 500,000 m/s is brought to rest by an electric field. Did the electron move into a region of higher potential or lower potential?

In proton-beam therapy, a high-energy beam of protons is fired at a tumor. As the protons stop in the tumor, their kinetic energy breaks apart the tumor's DNA, thus killing the tumor cells. For one patient, it is desired to deposit 0.10 J of proton energy in the tumor. To create the proton beam, protons are accelerated from rest through a 10,000 kV potential difference. What is the total charge of the protons that must be fired at the tumor?

A 3.0-cm-diameter parallel-plate capacitor has a 2.0 mm spacing. The electric field strength inside the capacitor is 1.0×10⁵ V/m. What is the potential difference across the capacitor?

A 3.0-cm-diameter parallel-plate capacitor has a 2.0 mm spacing. The electric field strength inside the capacitor is 1.0×10⁵ V/m. How much charge is on each plate?

Two 2.00 cm×2.00 cm plates that form a parallel-plate capacitor are charged to ±0.708 nC. What are the electric field strength inside and the potential difference across the capacitor if the spacing between the plates is 1.00 mm?

Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is 5.0×10⁵ V/m. An electron is launched from the negative plate. It strikes the positive plate at a speed of 2.0×10⁷ m/s. What was the electron's speed as it left the negative plate?

A room with 3.0-m-high ceilings has a metal plate on the floor with V=0 V and a separate metal plate on the ceiling. A 1.0 g glass ball charged to +4.9 nC is shot straight up at 5.0 m/s. How high does the ball go if the ceiling voltage is +3.0×10⁶ V?

A 0.25 pg dust particle with 50 excess electrons is sitting at rest on top of a 5.0-cm-diameter metal sphere. Closing a switch charges the sphere almost instantaneously. To what potential must the sphere be charged to launch the dust particle to a height of 5.0 m? Ignore air resistance.

What is the escape speed of an electron launched from the surface of a 1.0-cm-diameter glass sphere that has been charged to 10 nC?

A 2.0-cm-diameter copper ring has 5.0×10⁹ excess electrons. A proton is released from rest on the axis of the ring, 5.0 cm from its center. What is the proton's speed as it passes through the center of the ring?

Two 10-cm-diameter electrodes 0.50 cm apart form a parallel-plate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. After a long time, the capacitor is disconnected from the battery but is not discharged. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes after the original electrodes (not the modified electrodes of part b) are expanded until they are 20 cm in diameter?

A proton is fired from far away toward the nucleus of an iron atom. Iron is element number 26, and the diameter of the nucleus is 9.0 fm. What initial speed does the proton need to just reach the surface of the nucleus? Assume the nucleus remains at rest.

An electric dipole consists of 1.0 g spheres charged to ±2.0 nC at the ends of a 10-cm-long massless rod. The dipole rotates on a frictionless pivot at its center. The dipole is held perpendicular to a uniform electric field with field strength 1000 V/m, then released. What is the dipole's angular velocity at the instant it is aligned with the electric field?