Electric Potential

10-1

In a typical lightning flash, the potential difference between discharge points is about $10^{9} \rm V$ and the quantity of the charge transferred is about 30 C. (a) How much energy is released? (b) If all the energy released could be used to accelerate a 1000-kg automobile from rest, what would be its final speed? (c) If it could be used to melt ice, how much ice would it melt at 0 degrees Celsius? The heat of fusion of ice is $3.3\times 10^{5} \rm J/kg$

10-2

What potential difference is needed to stop an electron having an initial speed of $4.20\times 10^5  \rm m/s$?

10-3

Two large parallel conducting plates are 12 cm apart and carry equal but opposite charges on their facing surfaces. An electron placed midway between the two plates experiences a force of $3.9\times 10^{-15} \rm N$. (a) Find the electric field at the position of the electron. (b) What is the potential difference between the plates?

10-4

A uniform electric field of magnitude 325 V/m is directed in the $-y$ direction. The coordinates of point $A$ are $(-0.200, -0.300) \rm m$, and those of point $B$ are (0.400, 0.500) m. Calculate the potential difference $V_B - V_A$, using the path $ACB$ that connects from point $A$ to point $C$ at $(-0.200, 0.500) \rm m$ and subsequently from point $C$ to point $B$.

10-5

Given two $2.00 \rm\mu C$ charges located at $(0, \pm 0.800)  \rm m$ on a plane, and a positive test charge $q=1.28\times 10^{-18} \rm C$ at the origin, (a) what is the net force exerted on $q$, by the two $2.00 \rm\mu C$ charges? (b) What is the electric field at the origin due to the two $2.00 \rm\mu C$ charges? (c) What is the electric potential at the origin due to the two $2.00 \rm\mu C$ charges?

10-6

The Bohr model of the hydrogen atom states that the single electron can exist only in certain allowed orbits around the proton. The radius of each Bohr orbit is $r=n^2(0.0529 \rm nm)$ where $n=1, 2, 3, ...$. Calculate the electric potential energy of a hydrogen atom when the electron is in the (a) first allowed orbit, $n=1$; (b) second allowed orbit $n=2$; and (c) when the electron has escaped from the atom $(r=\infty)$. Express your answer in electron volts.

10-7

Much of the material comprising Saturn's rings is in the form of tiny dust particles having radii on the order of $10^{-6} \rm m$. These grains are in a region containing a dilute ionised gas, and they pick up excess electrons. If the electric potential at the surface of a grain is -400 V, how many excess electrons has it picked up?

10-8

Compute the escape speed for an electron from the surface of a uniformly charged sphere of radius 1.0 cm and total charge $1.6 \times 10^{-15} \rm C$. Neglect gravitational forces.

10-9

Two point charges of equal magnitude ($Q$) are located along the $y$ axis equal distances above and below the $x$ axis, i.e. at $(0,\pm a)$. (a) Plot a graph of the potential at points along the $x$ axis over the interval $-3a < x < 3a$. You should plot the potential in units of $k_e Q/a$. (b) Let the charge located at $(0,-a)$ be negative ($-Q$) and plot the potential along the $y$ axis over the interval $-4a < y < 4a$.

10-10

Two charged spherical conductors are connected by a long conducting wire, and a charge of $20.0  \rm\mu C$ is placed on the combination. (a) If one sphere has a radius of 4.00 cm and the other has a radius of 6.00 cm, what is the electric field near the surface of each sphere? (b) What is the electric potential of each sphere?