1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pshichka [43]
3 years ago
13

A uniformly charged, one-dimensional rod of length L has total positive charge Q. Itsleft end is located at x = ????L and its ri

ght end is located at x = 0. A separate positivepoint charge q is located at positive position x = x0.Find the magnitude of the force on the point charge by the rod. Evaluate the integral interms of the given variables. (This is basically the problem from the textbook, volume 2,page 584, Chapter 25, Exercise #16., but I've changed the description and variables.)
Physics
1 answer:
GREYUIT [131]3 years ago
4 0

Answer:

|\vec{F}| = \frac{1}{4\pi\epsilon_0}\frac{qQ}{L}(\ln(L+x_0)-\ln(x_0))

Explanation:

The force on the point charge q exerted by the rod can be found by Coulomb's Law.

\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}\^r

Unfortunately, Coulomb's Law is valid for points charges only, and the rod is not a point charge.

In this case, we have to choose an infinitesimal portion on the rod, which is basically a point, and calculate the force exerted by this point, then integrate this small force (dF) over the entire rod.

We will choose an infinitesimal portion from a distance 'x' from the origin, and the length of this portion will be denoted as 'dx'. The charge of this small portion will be 'dq'.

Applying Coulomb's Law:

d\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{qdq}{x + x_0}(\^x)

The direction of the force on 'q' is to the right, since both charges are positive, and they repel each other.

Now, we have to write 'dq' in term of the known quantities.

\frac{Q}{L} = \frac{dq}{dx}\\dq = \frac{Qdx}{L}

Now, substitute this into 'dF':

d\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{qQdx}{L(x+x_0)}(\^x)

Now we can integrate dF over the rod.

\vec{F} = \int{d\vec{F}} = \frac{1}{4\pi\epsilon_0}\frac{qQ}{L}\int\limits^{L}_0 {\frac{1}{x+x_0}} \, dx = \frac{1}{4\pi\epsilon_0}\frac{qQ}{L}(\ln(L+x_0)-\ln(x_0))(\^x)

You might be interested in
How much energy will a stock tank heater rated at 1790 Watts use in a 24 hour period? 1. 1790 × 24 × 3600 Joules 2. 1790 × 24 ×
Rashid [163]
<h2>Option 1 is the correct answer.</h2>

Explanation:

Power of heater, P = 1790 W

Time used, t = 24 hours = 24 x 60 x 60 = 24 x 3600 s

We have the equation

               \texttt{Power}=\frac{\texttt{Energy}}{\texttt{Time}}

We need to find energy,

Substituting

                 \texttt{Power}=\frac{\texttt{Energy}}{\texttt{Time}}\\\\1790=\frac{\texttt{Energy}}{24\times 3600}

                  Energy = 1790 x 24 x 3600 J

Option 1 is the correct answer.

3 0
3 years ago
Which planet has completed less than one orbit of the sun in the last 100 years?
OlgaM077 [116]
Since Pluto is no longer considered a planet, the correct answer would be Neptune. It is eight and farthest known planet of the Solar system. Orbital period of planet Neptune is 168 years. So planet Neptune has completed less than one orbit around the Sun in the last 100 years. 
6 0
3 years ago
Read 2 more answers
For the following statements, choose the word or words inside the parentheses that serve to make a correct statement. Each state
AnnyKZ [126]

Answer:

a) Temperatura, b) Temperature, c)    Constant , d)  None of these , e) Gibbs enthalpy and free energy (G)

Explanation:

a) the expression for ideal gases is PV = nRT

     Temperature

b) The internal energy is E = K T

      Temperature

c)  S = ΔQ/T

In an isolated system ΔQ is zero, entropy  is constant

       Constant

d) all parameters change when changing status

        None of these

e) Gibbs enthalpy and free energy

7 0
3 years ago
A crane raises a crate with a mass of 75 kg to a height of 10 m. Given that the
Crazy boy [7]

Answer: C. 7,350 J

Explanation:

Just did it in Apex

7 0
3 years ago
Rosa uses the formula (vi¡cosθ)tΔ to do a calculation. Which value is Rosa most likely trying to find?
andriy [413]
To break this problem down, let's start with what we know. The equation given finds one component of the velocity and multiplies it by the change in time. This will not find the acceleration that the first two answers say it will, meaning that the answer isn't A or B.

That leaves us with the final two answers, C and D. If the projectile was launched horizontally and we were trying to find the horizontal displacement, we wouldn't need to use cosθ to find the horizontal velocity, meaning that our answer is most likely C) <span>the horizontal displacement of a projectile launched at an angle!</span><span />
4 0
3 years ago
Other questions:
  • What Is the volume of the rectangular prism of 6cm 9cm and 5cm
    7·1 answer
  • Determine if the data are qualitative, quantitative, or neither. Zinc is a silver-gray metal. Chlorine has a density of 3.2 g/L.
    13·2 answers
  • In which situation is the maximum possible work done?
    6·1 answer
  • Which is not standing in the way of astronomers getting a good view of distant stars? A. some stars are too far away for our tel
    13·1 answer
  • An astronaut weighs 8.00 × 102 newtons on the sur- face of Earth. What is the weight of the astronaut 6.37 × 106 meters above th
    6·1 answer
  • Find avrage speed for a horse that traveled east 25 km in 4 hours
    8·1 answer
  • What is the acceleration of a 349 kg object that moved with a force of 750 N?
    5·1 answer
  • Why is deforestation a serious global environment problem
    5·1 answer
  • WHAT IS THE NET FORCE (CENTRIPETAL FORCE) FOR A 1500 KG
    14·1 answer
  • Which one of the following does not accurately describe the universal gravitational law? Question 10 options: A) Gravitational f
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!