25. Electric Potential

In the form of radioactive decay known as alpha decay, an unstable nucleus emits a helium-atom nucleus, which is called an alpha particle. An alpha particle contains two protons and two neutrons, thus having mass m=4 u and charge q=2e. Suppose a uranium nucleus with 92 protons decays into thorium, with 90 protons, and an alpha particle. The alpha particle is initially at rest at the surface of the thorium nucleus, which is 15 fm in diameter. What is the speed of the alpha particle when it is detected in the laboratory? Assume the thorium nucleus remains at rest.

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?

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?

Living cells 'pump' singly ionized sodium ions, Na+, from the inside of the cell to the outside to maintain a membrane potential ΔV_membrane=V_in−V_out=−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. 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.

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?

The electric potential along the x-axis is V = 100x² V, where x is in meters. What is E_x at (a) x=0 m and (b) x=1 m?