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
Gnesinka [82]
3 years ago
13

Three charges lie along the x axis. The positive charge q1 = 15 μC is at x= 2.0 m and the positive charge q2 = 6.0μC is at the o

rigin. Where must the negative charge q3 be placed on the x axis so that the resultant electric force on it is zero?

Physics
2 answers:
Delicious77 [7]3 years ago
6 0

Answer:

x = 0.775m

Explanation:

Conceptual analysis

In the attached figure we see the locations of the charges. We place the charge q₃ at a distance x from the origin. The forces F₂₃ and F₁₃ are attractive forces because the charges have an opposite sign, and these forces must be equal so that the net force on the charge q₃ is zero.

We apply Coulomb's law to calculate the electrical forces on q₃:

F_{23} = \frac{k*q_{2}*q_{3}}{x^2} (Electric force of q₂ over q₃)

F_{13} = \frac{k*q_{1}*q_{3}}{(2-x)^2} (Electric force of q₁ over q₃)

Known data

q₁ = 15 μC = 15*10⁻⁶ C

q₂ = 6 μC = 6*10⁻⁶ C

Problem development

F₂₃ = F₁₃

\frac{k*q_{2}*q_{3}}{x^2} = \frac{k*q_{1}*q_{3}}{(2-x)^2} (We cancel k and q₃)

\frac{q_2}{x^2}=\frac{q_1}{(2-x)^2}

q₂(2-x)² = q₁x²

6×10⁻⁶(2-x)² = 15×10⁻⁶(x)² (We cancel 10⁻⁶)

6(2-x)² = 15(x)²

6(4-4x+x²) = 15x²

24 - 24x + 6x² = 15x²

9x² + 24x - 24 = 0

The solution of the quadratic equation is:

x₁ = 0.775m

x₂ = -3.44m

x₁ meets the conditions for the forces to cancel in q₃

x₂ does not meet the conditions because the forces would remain in the same direction and would not cancel

The negative charge q₃ must be placed on x = 0.775 so that the net force is equal to zero.

Allushta [10]3 years ago
6 0

Answer:

The charge q3 must lie in x=0.775(m).

Explanation:

For the net force to be zero in q3, the positive charges must be pulling with the same force but in opposite directions. So

F_{13}=F_{23},

where F_{13} is the force exerted by q1 on q3 and  F_{23} is the force exerted by q2 on q3.

Recalling the Coulomb's law, we know that the magnitud of the electric force between two charges q_{a} and q_{b} is:

F=k_{e}\frac{q_{a}q_{b}}{r^{2}},

where k_{e} is Coulomb's constant and r is the distance between the charges.

In addition to this, it is also important to remember that like charges repel each other and unlike charges attract.

So, we have:

F_{13}=F_{23},

k_{e}\frac{q_{1}q_{3}}{(x_{1}-x_{3})^{2}}=k_{e}\frac{q_{2}q_{3}}{(x_{2}-x_{3})^{2}},

\frac{q_{1}}{(x_{1}-x_{3})^{2}}=\frac{q_{2}}{(x_{2}-x_{3})^{2}},

and remembering that x_{2}=0

\frac{q_{1}}{(x_{1}-x_{3})^{2}}=\frac{q_{2}}{x_{3})^{2}},

\frac{q_{1}}{q_{2}}(x_{3})^{2}=(x_{1})^{2} -2x_{1}x_{3}+(x_{3})^{2},

wich leads us to

(\frac{q_{1}}{q_{2}}-1)(x_{3})^{2}-(x_{1})^{2} +2x_{1}x_{3}=0,

(1.5)(x_{3})^{2}-(4)^{2} +4x_{3}=0

and this is a quadratic equation.

The solutions to this equation are:

  • x_{1}=0.775m
  • x_{2}=-3.44m

This two are solutions of the equation, even so, only one is a correct solution to the problem. The correct answer is

x_{1}=0.775m.

This is because q3 must lie between q1 and q2 so the attractive forces cancel each other.

You might be interested in
PLEWSE SOMEONE HELP ILL MARK BRAINLIST
Margaret [11]

Answer:

D)

Explanation:

ffhjjxghjjcdddhhgfd

Brainliest pls ❤️

3 0
3 years ago
Read 2 more answers
A block with mass m =6.4 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.28 m.
Zanzabum

Answer

given,

mass of block (m)= 6.4 Kg

spring is stretched to distance, x = 0.28 m

initial velocity = 5.1 m/s

a) computing weight of spring

    k x = m g

k = \dfrac{mg}{x}

k = \dfrac{6.4 \times 9.8}{0.28}

      k = 224 N/m

b) f = \dfrac{\omega}{2\pi}

    \omega = \sqrt{\dfrac{k}{m}}= \sqrt{\dfrac{224}{6.4}} = 5.92 \ rad/s

   f = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}

   f = \dfrac{1}{2\pi}\sqrt{\dfrac{224}{6.4}}

  f =0.94\ Hz

c)  v_b = -v cos \omega t

    v_b = -5.1 \times cos (5.92 \times 0.42)

    v_b = 4.04\ m/s

d)  a_{max} = v \omega

    a_{max} = 4.04 \times 5.92

    a_{max} =23.94\ m/s^2

e)  Y =- A sin (\omega t)

    A = \dfrac{v}{\omega}

    A = \dfrac{4.04}{5.92}

        A = 0.682 m

    Y =- 0.682 \times sin (5.92 \times 0.42)

    Y =- 0.42

Force =m \omega^2 |Y|

          =6.4 \times 5.92^2\times 0.42

F = 94.20 N

4 0
3 years ago
What is it called when a reading is converted into computer language? computerizing surveying digitizing converting
disa [49]
Digitizing is the correct answer
3 0
3 years ago
What is the power of a circuit with voltage 12 V and current 8.0<br> A?
SVEN [57.7K]

Answer:96 W

Explanation:

3 0
3 years ago
A _______ satellite records reflected wavelengths from Earth's surface.
Oksana_A [137]
<span>It is LandSat, a NASA based satelite that records, on a daily basis, multiple reflected wavelengths from the Earth's surface. The satelite measures reflection from both land and ocean upon the Earth. The system is utilised by scientists an policy makers around the world. </span>
3 0
3 years ago
Read 2 more answers
Other questions:
  • A fugitive tries to hop on a freight train traveling at a constant speed of 5.0 m/s. Just as an empty box car passes him, the fu
    11·2 answers
  • SECTION B<br>THEORY QUESTIONS<br>(1a) Define the following<br>(a) Work:​
    6·1 answer
  • A spherical balloon has a radius of 7.40 m and is filled with helium. Part A How large a cargo can it lift, assuming that the sk
    11·1 answer
  • PLS HELP ASAP!!! <br> I don’t understand this at all
    5·1 answer
  • Most of the resistance of the human body comes from the skin, as the interior of the body contains aqueous solutions that are go
    7·1 answer
  • 2. A block of mass 1.2 kg lies on a frictionless surface. A man slides the block
    14·1 answer
  • Ruby was training for a race at the high school track. She took her dog walked 2250 meters in 15 minutes. Calculate the average
    12·1 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
  • Which equation contains only scalar quantities
    12·1 answer
  • As the people sing in church, the sound level everywhere inside is 101 dB . No sound is transmitted through the massive walls, b
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!