25. Electric Potential

The x component of a uniform electric field is ${\mathrm{E}}_{\mathrm{x}}=12\mathrm{V}/\mathrm{m}$. What is the potential difference between ${\mathrm{x}}_{\mathrm{i}}=45\mathrm{m}$ and ${\mathrm{x}}_{\mathrm{f}}=12\mathrm{m}$?

The electric potential in a region of uniform electric field is $1200\mathrm{V}$ at $\mathrm{x}=-4.3\mathrm{m}$ and $2800\mathrm{V}$ at $\mathrm{x}=2.1\mathrm{m}$. What is ${\mathrm{E}}_{\mathrm{x}}$?

What is the speed of a proton that has been accelerated through $2300\mathrm{V}$?

Point A is at $-25\mathrm{V}$ and point B is at $400\mathrm{V}$. A proton moves past point A at $3.5\times {10}^5\mathrm{m}/\mathrm{s}$, what is its speed when it reaches point B?

The water molecule is a permanent electric dipole with a dipole moment of $6.2\times {10}^{-30}\mathrm{C}\mathrm{m}$. A water molecule is aligned with an electric field of magnitude $7600\mathrm{V}/\mathrm{m}$. How much energy is required to rotate the molecule 180°?

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

A 3.0-cm-diameter parallel-plate capacitor has a 2.0 mm spacing. The electric field strength inside the capacitor is 1.0×10^5 V/m.a. 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 1.0×10^5 V/m.b. 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 (a) 1.00 mm and

Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is 5.0×10^5 V/m.b. An electron is launched from the negative plate. It strikes the positive plate at a speed of 2.0×10^7 m/s. What was the electron's speed as it left the negative plate?

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?

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 electrodesc. After the original electrodes (not the modified electrodes of part b) are expanded until they are 20 cm in diameter?

Two small charged spheres are 5.0 cm apart. One is charged to +25 nC, the other to −15 nC. A proton is released from rest halfway between the spheres. What is the proton's speed after it has moved 1.0 cm?

Four small spheres, each charged to +15 nC, form a square 2.0 cm on each side. From far away, a proton is shot toward the square along a line perpendicular to the square and passing through its center. What minimum initial speed does the proton need to pass through the square of charges?