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 electrodes c. 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?

The two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot?

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 μC. b. What is the tension in the string?

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 1 is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton's speed at point 2?

Living cells 'pump' singly ionized sodium ions, Na+, from the inside of the cell to the outside to maintain a membrane potential ΔVₘₑₘbᵣₐₙₑ=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. 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=5000x^2 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?

Two 2.0-mm-diameter beads, C and D, are 10 mm apart, measured between their centers. Bead C has mass 1.0 g and charge 2.0 nC. Bead D has mass 2.0 g and charge −1.0 nC . If the beads are released from rest, what are the speeds vc and vD at the instant the beads collide?

The electric potential in a region of space is given by V=V₀[(x²+2y²)/(0.10 m)²], where V₀ is a constant. A proton released from rest at (x, y)=(20 cm, 0 cm) reaches the origin with a speed of 7.5×10^5 m/s . b. At what value of y on the y-axis should a He+ ion (charge +e, mass 4 u) be released from rest to reach the origin with the same speed?

INT CALC Two positive point charges q are located on the y-axis at y = ±a. e. Your answer to part d shows that an electron experiences a linear restoring force, so it will undergo simple harmonic motion. What is the oscillation frequency in GHz for an electron moving between two 1.0 nC charges separated by 2.0 mm?

CALC The electric potential along the x-axis is V = 100x^2 V, where x is in meters. What is Ex at (a) x=0 m and (b) x=1 m?