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
What happens to gas in a ball that's been placed in a hot climate
ladessa [460]
What happens is that if u put gas in a ball and placed in a hot climate it will start burning Bc u have gas inside the ball
4 0
3 years ago
Water flows from the bottom of a storage tank at a rate of r(t) = 300 − 6t liters per minute, where 0 ≤ t ≤ 50. Find the amount
SSSSS [86.1K]

r(t) models the water flow rate, so the total amount of water that has flowed out of the tank can be calculated by integrating r(t) with respect to time t on the interval t = [0, 35]min

∫r(t)dt, t = [0, 35]

= ∫(300-6t)dt, t = [0, 35]

= 300t-3t², t = [0, 35]

= 300(35) - 3(35)² - 300(0) + 3(0)²

= 6825 liters

7 0
3 years ago
if you run off the pavement, you should: turn the steering wheel quickly toward the road steer straight and slow down before att
omeli [17]

pavement is defined as the surface of Road or sidewalk.

for example, the surface of Expressway.

There are two types of pavement.

rigid pavement which consists of one layer.

flexible pavement which consist of multiple layers.

While driving on roads of rural areas, if our right wheel moves off the pavement, we should always hold the steering wheel firmly and then take our foot off the pedal, then apply brake lightly until we are moving at a low speed.

if you run off the pavement, you should: turn the steering wheel quickly toward the road steer straight and slow down before attempting to return to the pavement steer straight ahead and speed up apply the brakes hard

To know more about pavement:

brainly.com/question/28456065

#SPJ4

5 0
1 year ago
A 5.0-μC charge is placed at the 0 cm mark of a meter stick and a -4.0 μC charge is placed at the 50 cm mark. At what point on a
Maksim231197 [3]

Answer:

The distance from charge 5 μ C = 26.45 cm and the distance from - 4 μ C is 23.55 cm.

Explanation:

Given that

q₁ = 5 μ C

q₂ = - 4 μ C

The distance between charges = 50 cm

d= 50 cm

Lets take at distance x from the charge μ C ,the electrical field is zero.

That is why the distance from the charge - 4 μ C =  50 - x cm

We know that ,electric field is given as

E=K\dfrac{q}{r^2}

K\dfrac{5\ \mu}{x^2}=K\dfrac{4\mu }{(50-x)^2}\\\\\dfrac{5}{x^2}=\dfrac{4 }{(50-x)^2}\\\\\\5(50-x)^2=4x^2\\(50-x)^2=0.8x^2\\\\50-x =0.89x\\\ x=\dfrac{50}{1.89}\ cm\\\\\\x=26.45\ cm\\

Therefore the distance from charge 5 μ C = 26.45 cm and the distance from - 4 μ C is 23.55 cm.

3 0
3 years ago
Maple syrup, which comes from the sap of maple trees, contains water and natural sugars. It's a clear, brown liquid and the suga
Amanda [17]
The answer would be colloid

7 0
3 years ago
Other questions:
  • Periodic motion can BEST be defined as motion
    15·1 answer
  • Please verify these are correct. No work needs to be shown unless I've made a mistake. Thank you.
    8·2 answers
  • What will happen to the density of an object when it's mass increases?
    6·2 answers
  • 50 points!
    14·1 answer
  • HELP ASAP PLEASE!!!
    8·1 answer
  • When using the lens equation, a negative value as the solution for di indicates that the image is
    13·1 answer
  • The ____ is a particle with one unit of positive change
    7·2 answers
  • How do you find the speed of a hraph
    9·1 answer
  • Hat is the processes called when matter, that is a liquid, transforms into a gas?
    5·1 answer
  • What is the kinetie energy of a 3-kilogram ball that is rolling at 2 meters per second?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!