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
sukhopar [10]
3 years ago
7

Two tiny particles having charges of +5.00 μC and +7.00 μC are placed along the x-axis. The +5.00-µC particle is at x = 0.00 cm,

and the other particle is at x = 100.00 cm. Where on the x-axis must a third charged particle be placed so that it does not experience any net electrostatic force due to the other two particles? Two tiny particles having charges of +5.00 μC and +7.00 μC are placed along the x-axis. The +5.00-µC particle is at x = 0.00 cm, and the other particle is at x = 100.00 cm. Where on the x-axis must a third charged particle be placed so that it does not experience any net electrostatic force due to the other two particles? 4.58 cm 50 cm 9.12 cm 91.2 cm 45.8 cm

Physics
1 answer:
Liula [17]3 years ago
8 0

Answer:

The third charged particle must be placed at x = 0.458 m = 45.8 cm

Explanation:

To solve this problem we apply Coulomb's law:  

Two point charges (q₁, q₂) separated by a distance (d) exert a mutual force (F) whose magnitude is determined by the following formula:  

F = \frac{k*q_1*q_2}{d^2} Formula (1)  

F: Electric force in Newtons (N)

K : Coulomb constant in N*m²/C²

q₁, q₂: Charges in Coulombs (C)  

d: distance between the charges in meters (m)

Equivalence  

1μC= 10⁻⁶C

1m = 100 cm

Data

K = 8.99 * 10⁹ N*m²/C²

q₁ = +5.00 μC = +5.00 * 10⁻⁶ C

q₂= +7.00 μC = +7.00 * 10⁻⁶ C

d₁ = x (m)

d₂ = 1-x (m)

Problem development

Look at the attached graphic.

We assume a positive charge q₃ so F₁₃ and F₂₃ are repulsive forces and must be equal so that the net force is zero:

We use formula (1) to calculate the forces F₁₃ and F₂₃

F_{13} = \frac{k*q_1*q_3}{d_1^2}

F_{23} = \frac{k*q_2*q_3}{d_2^2}

F₁₃ = F₂₃

\frac{k*q_1*q_3}{d_1^2} = \frac{k*q_2*q_3}{d_2^2} We eliminate k and q₃ on both sides

\frac{q_1}{d_1^2}= \frac{q_2}{d_2^2}

\frac{q_1}{x^2}=\frac{q_2}{(1-x)^2}

\frac{5*10^{-6}}{x^2}=\frac{7*10^{-6}}{(1-x)^2} We eliminate 10⁻⁶ on both sides

(1-x)^2 = \frac{7}{5} x^2

1-2x+x^2=\frac{7}{5} x^2

5-10x+5x^2=7 x^2

2x^2+10x-5=0

We solve the quadratic equation:

x_1 = \frac{-b+\sqrt{b^2-4ac} }{2a} = \frac{-10+\sqrt{10^2-4*2*(-5)} }{2*2} = 0.458m

x_2 = \frac{-b-\sqrt{b^2-4ac} }{2a} = \frac{-10-\sqrt{10^2-4*2*(-5)} }{2*2} = -5.458m

In the option x₂, F₁₃ and F₂₃ will go in the same direction and will not be canceled, therefore we take x₁ as the correct option since at that point the forces are in  opposite way .

x = 0.458m = 45.8cm

You might be interested in
Read this quotation:
Brums [2.3K]

Answer:

the Princess in "St. George and the Dragon"

4 0
2 years ago
Read 2 more answers
Earth's magnetic field is generated by
evablogger [386]
The movement of electrical charges inside the earth
6 0
3 years ago
Read 2 more answers
a car is traveling at velocity of 15m/s.it accelerates to a velocity 35m/s in 10s calculate the acceleration? ​
vlada-n [284]

Answer:

2m/s is acceleration I hope it helps you

3 0
2 years ago
Read 2 more answers
Place the items in order from MOST gravitational force (1) to LEAST gravitational force (5).
oksano4ka [1.4K]

Answer:

Explanation:

Sun - - - - - Earth----Capital building----Human----Atom

The sun would exert more gravitational force because it is the massive.

Gravitational force is directly proportional to mass.

5 0
3 years ago
Why can't passenger planes fly very high?
Archy [21]
<span>It is not that jet engines perform better at higher altitude, but rather they are more fuel efficient. Performance is far greater at lower altitudes. Just think about when you are taking off and the airplane accelerates quickly and pitches way up. There's lots of extra thrust down low to allow that. The fuel/air ratio remains somewhat constant through the climb. As altitude increases, the air thin outs and therefore, so can the fuel flow. Airlines try for the most efficient routes and altitudes as possible to save money. They do however change altitudes in flight (higher or lower) when needed for weather and turbulence avoidance. --- And a note about the jet stream, it is relatively narrow and always curving, so the time an airliner would spend there is very short. And another thing, it flows mostly west to east isn't the U.S. so a westbound flight would be at a disadvantage. Airlines still fly high whether traveling East or West.</span>
4 0
3 years ago
Other questions:
  • What is the weight (in newtons) of a bowling ball that has a mass of 3 kilograms?
    14·1 answer
  • A train locomotive is pulling two cars of the same mass behind it. Determine the ratio of the tension in the coupling (think of
    5·1 answer
  • It takes 63 W to power a ceiling fan. The energy output of the fan is 50 W. Calculate the efficiency of the fan. Round your answ
    5·1 answer
  • What is the function of the lens of an eye
    6·2 answers
  • A certain bridge is 4,224 feet long. What constant rate, in miles per hour, must be maintained in order to walk across the bridg
    14·1 answer
  • Temperature Dependence of the pH of pure Water
    6·1 answer
  • PLS HELP FOR PHYSICS PLS
    10·1 answer
  • (4.3 x 10-2 )4.950 x 105)<br> O 21.285 x 103<br> O 2.13 x 104<br> O 21 x 103<br> O 2.1 x 104
    8·1 answer
  • True or False: The basketball should be dribbled below the waist.
    14·1 answer
  • Please someone do this <br>please ​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!