A -2C charge lies at rest. (a) What is the potential difference between point A, which is 1.5m from the charge, and point B, which is 4m from the charge? (b) What would the work on a 4C charge be to move it from A to B?

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?

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?

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?