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
The distance around the block is equal to 3000 feet, how many blocks would you have to run to run a total of a mile?
lesya692 [45]
You would have to run a little less than 2 blocks
7 0
3 years ago
What is the average velocity of a car if it travels from position 25m to a position of -7m in 34 seconds?
zubka84 [21]

Answer:

vp = 0.94 m/s

Explanation

Formula

Vp = position/ time

position: Initial position - Final position

Position = 25 m - (-7 m) = 25 m + 7 m = 32 m

Then

Vp = 32 m / 34 seconds

Vp = 0.94 m/s

6 0
3 years ago
Read 2 more answers
What is kirchoff s law???
kolbaska11 [484]
There are two laws named for Kirchhoff.  The both concern electrical circuits.
Here they are in my own words:

1).  The sum of the voltage drops around any closed loop in a circuit is zero.

2).  The sum of the currents at any single point in a circuit is zero.
8 0
3 years ago
Read 2 more answers
What is biasing and doping
Flura [38]

Answer:

Biasing - Biasing means being unfair to someone or something, and liking the other one or helping them.

Doping - Doping is where a person use drug to get better at sporting and get stronger muscles, such as getting stronger, getting faster and so on. It is mostly used by athletics.

5 0
3 years ago
Read 2 more answers
Which of the following statements is TRUE? The side of the Moon facing away from the Earth is in perpetual darkness. The Moon is
Ivanshal [37]

Answer:

The Moon's distance from the Earth varies during its orbit

Explanation:

The correct statement is ,The Moon's distance from the Earth varies during its orbit.

Important point regarding moon:

1 .Moon is a natural satellite of the earth.

2. Moon is the fifth largest satellite in solar system.

3.Second densest  satellite in solar system.

4.Moon rotates about earth.

5.Moon is an astronomical body .

5 0
3 years ago
Other questions:
  • A person walks one mile home and 1/2 mile back towards school. What is the distance traveled? What is the displacement?
    10·1 answer
  • The image shows streetlights powered by solar panels. Which sequence shows the energy transformation is taking place in these li
    14·2 answers
  • Assuming a vertical trajectory with no drag, derive the applicable form of the rocket equation for this application
    11·1 answer
  • Which of the following best describes why we say that light is an electromagnetic wave?
    12·1 answer
  • Tourists covered 255 km for a 4-hour ride by car and a 7-hour ride by train. what is the speed of the train, if it is 5 km/h gre
    14·1 answer
  • Which of the following prefixes represents the biggest number?
    14·1 answer
  • A ball tied on a string rotates in a circular path as shown above. The only forces acting on the ball at any point are the weigh
    8·1 answer
  • A TMS (transcranial magnetic stimulation) device creates very rapidly changing magnetic fields. The field near a typical pulsed-
    10·1 answer
  • A 72.0-kg skydiver is falling at a terminal velocity of 79.0 m/s. Which equation should be used to calculate the diver’s kinetic
    15·1 answer
  • Sam was investigating a container of water. Water can be a solid, liquid, or gas. At first, Sam said the water molecules were mo
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!