# 7.2 Electric potential and potential difference  (Page 8/12)

 Page 8 / 12

## Conceptual questions

Discuss how potential difference and electric field strength are related. Give an example.

What is the strength of the electric field in a region where the electric potential is constant?

The electric field strength is zero because electric potential differences are directly related to the field strength. If the potential difference is zero, then the field strength must also be zero.

If a proton is released from rest in an electric field, will it move in the direction of increasing or decreasing potential? Also answer this question for an electron and a neutron. Explain why.

Voltage is the common word for potential difference. Which term is more descriptive, voltage or potential difference?

Potential difference is more descriptive because it indicates that it is the difference between the electric potential of two points.

If the voltage between two points is zero, can a test charge be moved between them with zero net work being done? Can this necessarily be done without exerting a force? Explain.

What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential energy?

They are very similar, but potential difference is a feature of the system; when a charge is introduced to the system, it will have a potential energy which may be calculated by multiplying the magnitude of the charge by the potential difference.

Voltages are always measured between two points. Why?

How are units of volts and electron-volts related? How do they differ?

An electron-volt is a volt multiplied by the charge of an electron. Volts measure potential difference, electron-volts are a unit of energy.

Can a particle move in a direction of increasing electric potential, yet have its electric potential energy decrease? Explain

## Problems

Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be $1.67\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-27}\phantom{\rule{0.2em}{0ex}}\text{kg}\text{.}$

$\begin{array}{ccc}\frac{1}{2}{m}_{e}{v}_{e}^{2}\hfill & =\hfill & qV,\phantom{\rule{0.2em}{0ex}}\frac{1}{2}{m}_{\text{H}}{v}_{\text{H}}^{2}=qV,\phantom{\rule{0.2em}{0ex}}\text{so that}\hfill \\ \frac{{m}_{e}{v}_{e}^{2}}{{m}_{\text{H}}{v}_{\text{H}}^{2}}\hfill & =\hfill & 1\phantom{\rule{0.2em}{0ex}}\text{or}\phantom{\rule{0.2em}{0ex}}\frac{{v}_{e}}{{v}_{\text{H}}}=42.8\hfill \end{array}$

An evacuated tube uses an accelerating voltage of 40 kV to accelerate electrons to hit a copper plate and produce X-rays. Non-relativistically, what would be the maximum speed of these electrons?

Show that units of V/m and N/C for electric field strength are indeed equivalent.

$1\phantom{\rule{0.2em}{0ex}}\text{V}=1\phantom{\rule{0.2em}{0ex}}\text{J/C;}\phantom{\rule{0.2em}{0ex}}1\phantom{\rule{0.2em}{0ex}}\text{J}=1\phantom{\rule{0.2em}{0ex}}\text{N}·\text{m}\to 1\phantom{\rule{0.2em}{0ex}}\text{V/m}\phantom{\rule{0.2em}{0ex}}=1\phantom{\rule{0.2em}{0ex}}\text{N/C}$

What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of $1.50\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{V}$ ?

The electric field strength between two parallel conducting plates separated by 4.00 cm is $7.50\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{V}$ . (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be zero volts. What is the potential 1.00 cm from that plate and 3.00 cm from the other?

a. ${V}_{AB}=3.00\phantom{\rule{0.2em}{0ex}}\text{kV}$ ; b. ${V}_{AB}=7.50\phantom{\rule{0.2em}{0ex}}\text{kV}$

The voltage across a membrane forming a cell wall is 80.0 mV and the membrane is 9.00 nm thick. What is the electric field strength? (The value is surprisingly large, but correct.) You may assume a uniform electric field.

Two parallel conducting plates are separated by 10.0 cm, and one of them is taken to be at zero volts. (a) What is the electric field strength between them, if the potential 8.00 cm from the zero volt plate (and 2.00 cm from the other) is 450 V? (b) What is the voltage between the plates?

a. ${V}_{AB}=Ed\to E=5.63\phantom{\rule{0.2em}{0ex}}\text{kV/m}$ ;
b. ${V}_{AB}=563\phantom{\rule{0.2em}{0ex}}\text{V}$

Find the maximum potential difference between two parallel conducting plates separated by 0.500 cm of air, given the maximum sustainable electric field strength in air to be $3.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}\text{V/m}$ .

An electron is to be accelerated in a uniform electric field having a strength of $2.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}\text{V/m}\text{.}$ (a) What energy in keV is given to the electron if it is accelerated through 0.400 m? (b) Over what distance would it have to be accelerated to increase its energy by 50.0 GeV?

a. $\begin{array}{ccc}\text{Δ}K\hfill & =\hfill & q\text{Δ}V\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{V}_{AB}=Ed,\phantom{\rule{0.2em}{0ex}}\text{so that}\hfill \\ \text{Δ}K\hfill & =\hfill & 800\phantom{\rule{0.2em}{0ex}}\text{keV;}\hfill \end{array}$
b. $d=25.0\phantom{\rule{0.2em}{0ex}}\text{km}$

Use the definition of potential difference in terms of electric field to deduce the formula for potential difference between $r={r}_{a}$ and $r={r}_{b}$ for a point charge located at the origin. Here r is the spherical radial coordinate.

The electric field in a region is pointed away from the z-axis and the magnitude depends upon the distance s from the axis. The magnitude of the electric field is given as $E=\frac{\alpha }{s}$ where $\alpha$ is a constant. Find the potential difference between points ${P}_{1}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{P}_{2}$ , explicitly stating the path over which you conduct the integration for the line integral.

One possibility is to stay at constant radius and go along the arc from ${P}_{1}$ to ${P}_{2}$ , which will have zero potential due to the path being perpendicular to the electric field. Then integrate from a to b : ${V}_{ab}=\alpha \phantom{\rule{0.2em}{0ex}}\text{ln}\left(\frac{b}{a}\right)$

Singly charged gas ions are accelerated from rest through a voltage of 13.0 V. At what temperature will the average kinetic energy of gas molecules be the same as that given these ions?

Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
how was the check your understand 12.7 solved?
Who is ISSAAC NEWTON
he's the father of 3 newton law
Hawi
he is Chris Issaac's father :)
Ethem
how to name covalent bond
Who is ALEXANDER BELL
LOAK
what do you understand by the drift voltage
what do you understand by drift velocity
Brunelle
nothing
Gamal
well when you apply a small electric field to a conductor that causes to add a little velocity to charged particle than usual, which become their average speed, that is what we call a drift.
graviton
drift velocity
graviton
what is an electromotive force?
It is the amount of other forms of energy converted into electrical energy per unit charge that flow through it.
Brunelle
How electromotive force is differentiated from the terminal voltage?
Danilo
in the emf power is generated while in the terminal pd power is lost.
Brunelle
what is then chemical name of NaCl
sodium chloride
Azam
sodium chloride
Brunelle
How can we differentiate between static point and test charge?
Wat is coplanar in physics
two point charges +30c and +10c are separated by a distance of 80cm,compute the electric intensity and force on a +5×10^-6c charge place midway between the charges
0.0844kg
Humble
what is the difference between temperature and heat
Heat is the condition or quality of being hot While Temperature is ameasure of cold or heat, often measurable with a thermometer
Abdul
Temperature is the one of heat indicators of materials that can be measured with thermometers, and Heat is the quantity of calor content in material that can be measured with calorimetry.
Gamma
the average kinetic energy of molecules is called temperature. heat is the method or mode to transfer energy to molecules of an object but randomly, while work is the method to transfer energy to molecules in such manner that every molecules get moved in one direction.
2. A brass rod of length 50cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°c( degree Celsius) if the original length are 40°c(degree Celsius) is there at thermal stress developed at the junction? The end of the rod are free to expand (coefficient of linear expansion of brass = 2.0×10^-5, steel=1.2×10^-5k^1)
A charge insulator can be discharged by passing it just above a flame. Explain.
of the three vectors in the equation F=qv×b which pairs are always at right angles?
what is an ideal gas?
What is meant by zero Kelvin ?
Justine
Why does water cool when put in the pot ?
Justine
when we pour the water in a vessel(pot) the hot body(water) loses its heat to the surrounding in order to maintain thermal equilibrium.Thus,water cools.
rupendra
when we drop water in the pot, the pot body loses heat to surrounded in order to maintain thermal equilibrium thus,water cool.
Srabon
my personal opinion ideal gas means doesn't exist any gas that obey all rules that is made for gases, like when get the temp of a gas lower, it's volume decreases.since the gas will convert to liquid when the temp get lowest.. so you can imagine it, but you can't get a gas at the lowest T
Edit An ideal gas is a theoretically gascomposed of many randomly moving point particles whose only interactions are perfectly elastic collisions.
Gamma
ideal gases are real gases at low temperature
Brunelle