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
Xelga [282]
3 years ago
10

2 particles having charges q1=0.500 nC and q2=8.00 nC are separated by a distance of 1.20m. at what point along the line connect

ing the two charges is the total electric field due to the two chares equal to zero?

Physics
2 answers:
laila [671]3 years ago
7 0
Refer to the figure shown below.

Charge q₁ = 0.5 nC = 0.5x10⁻⁹ C
Charge q₂ = 8 nC = 8x10⁻⁹ C
d = 1.2 m, the distance between the two charges.

x is the distance between the two charges, measured from the charge q₁.

From Coulomb's Law,
The electric field generated along x by q₁ is
E₁ = k(q₁/x²)
The electric field generated along x by q₂ is
E₂ = -k[q₂/(d-x)²]
where
k = 8.988x10⁹ (N-m²)/C² is the Coulomb constant/

When the electric field along x is zero, then
E₁ + E₂ = 0
k[q₁/x² - q₂/(d-x)²] = 0

That is,
0.5/x² = 8/(1.2 - x)²
8x² = 0.5(1.2 - x)²
16x² = 1.44 - 2.4x + x²
15x² + 2.4x - 1.44 = 0

Solve with the quadratic formula.
x = (1/30)*[-2.4 +/- √(5.76 + 86.4)]
   = 0.24 or -0.4 m

Reject the negative answer to obtain
x = 0.24 m
d-x = 0.96 m

Answer
The electric field is zero between the charges so that
(a) It is at 0.24 m from the 0.5 nC charge, and
(b) It is at 0.96 m from the 8 nC charge.

Rus_ich [418]3 years ago
4 0

The location of the point is at the distance of \boxed{0.24{\text{ m}}}from first particle and \boxed{0.96{\text{ m}}} from second particle.

Further explanation:

Here, we have to calculate the location of the point on the line which connects the both charges at which the net electric field due to these charges is zero.

Given:

Charge on the first particle \left( {{q_1}}\right) is 0.5{\text{nC}}=5\times {10^{- 10}}{\text{C}}.

Charge on the second particle \left({{q_2}}\right) is 8{\text{ nC}}=80\times{10^{-10}}{\text{C}}.

Distance between the first particle and the second particle \left(r\right) is 1.2{\text{ m}}.

Formula and concept used:

Let us assume that the point is lying in between the charges as shown in Figure 1.

For, net electric field to be zero at that point,

The electric field due to first particle’s charge will be equal to the electric field due to second particle’s charge.

The expression can be written as,

\boxed{{E_1}={E_2}}

First of all we will know about the electric field.

Electric field: The electric field at a point due to a charge is define as the amount of force experienced by a unit charge also known as test charge at that point.

E=\dfrac{1}{{4\pi{\varepsilon_0}}}\cdot \dfrac{q}{{{r^2}}}

Here, E is the electric field, q is the charge and r is the distance between charge and point at which electric field has to be measured.

Substitute the values of {\vec E_1} and {\vec E_2}

We get,

\dfrac{1}{{4\pi{\varepsilon_0}}} \cdot\dfrac{{{q_1}}}{{{x^2}}}=\dfrac{1}{{4\pi{\varepsilon_0}}} \cdot \dfrac{{{q_2}}}{{{{\left( {1.2 - x} \right)}^2}}}

Simplify the above equation,

\boxed{\dfrac{{{q_1}}}{{{{\left( x \right)}^2}}}=\dfrac{{{q_2}}}{{{{\left( {1.2 - x} \right)}^2}}}}                              …… (1)

Calculation:

Substitute 5 \times {10^{- 10}}{\text{ C}} for {q_1} and 80 \times {10^{ - 10}}{\text{ C}} for {q_2} in equation (1).

\begin{aligned}\frac{{5 \times {{10}^{- 10}}}}{{{{\left( x \right)}^2}}}&=\frac{{80\times {{10}^{- 10}}}}{{{{\left( {1.2 - x} \right)}^2}}}\\\frac{5}{{{x^2}}}&=\frac{{80}}{{{{\left( {1.2 - x} \right)}^2}}}\\5{\left( {1.2 - x}\right)^2}&=80{x^2}\\\end{aligned}

Simplify the above equation,

75{x^2} + 12x - 7.2 = 0

Solve the above equation,  

\begin{gathered}x=\frac{{-12 \pm \sqrt {{{12}^2} - 4\times75\times\left({-7.2} \right)}}}{{2 \times 75}}\\=\frac{{-12 \pm \sqrt {2304} }}{{150}}\\=\frac{{-12\pm48}}{{150}}\\\end{gathered}

Taking positive value,

\begin{aligned}x&=\frac{{ - 12 + 48}}{{150}}\\&=\frac{{36}}{{150}}\\&=0.24{\text{ m}}\\\end{aligned}

Distance of the point from the second particle will be,

\begin{aligned}\left({1.2-x}\right)&=1.2-0.24\\&=0.96{\text{ m}}\\\end{aligned}

Thus, the location of the point is at the distance of \boxed{0.24{\text{ m}}}from first particle and \boxed{0.96{\text{ m}}} from second particle.

Learn more:

1. Momentum change due to collision: brainly.com/question/9484203.  

2. Expansion of gas due to change in temperature: brainly.com/question/9979757.  

3. Conservation of momentum brainly.com/question/4033012.

Answer details:

Grade: Senior School  

Subject: Physics  

Chapter: Electric charges and fields

Keywords:

Two particles, separated by distance, point along line, zero electric field, coulomb law, charges, electric field, position vector, location of charge, 0.96m, 1m.

You might be interested in
Question is in the picture below
Sati [7]

may vary depending on the organization.

4 0
2 years ago
A sanding disk with rotational inertia 1.2 10-3 kg·m2 is attached to an electric drill whose motor delivers a torque of 10 N·m a
tensa zangetsu [6.8K]

Answer:

Angular momentum = 0.7 kg.m²/s

Angular velocity = 583.3 rad/s

Explanation:

1. The torque τ  is related to the angular momentum L by the relation

τ = ΔL/Δt

ΔL = τΔt

τ = 10 N. m

Δt = 70 ms = 70 × 10⁻³s

ΔL = (10 N. m) × (70 × 10⁻³s) = 700 × 10⁻³ kg.m²/s = 0.7 kg.m²/s

2. The rotational inertia I relates the angular momentum L to the angular velocity w

L = Iw

w = L/I

L =  0.7 kg.m²/s

I = 1.2 × 10⁻³ kg.m²

w = (0.7 kg.m²/s)/(1.2 × 10⁻³ kg.m²) = 583.3 rad/s

4 0
3 years ago
A ray diagram is shown.
Rufina [12.5K]

Answer:

X

Explanation:

8 0
3 years ago
Read 2 more answers
Write a short description of how the motion of the racers might change from the start of the race to the finish line
Ad libitum [116K]
The motion of the racers might change from the start because the pressure goes up so all the racer wants is to speed up and win, so when the racer first starts he or she is calm because he's not driving yet and when he or she is on his/hers way to he finish line he/she just wants to win and gets under pressure so he speeds up even more and drifts. Your welcome
6 0
3 years ago
What are the SI units of thermal conductivity?​
kotykmax [81]

Answer:

The SI unit of thermal conductivity is watts per meter-kelvin (W/(m⋅K)).

Explanation:

hope this will help u

7 0
2 years ago
Other questions:
  • A boat takes 4.0 h to travel 36 km down a river, then 5.0 h to return.how fast is the river flowing
    5·1 answer
  • The car salesman tells you that the car can go from a stopped position to 60 miles per hour in 6 seconds. He is giving you the c
    9·2 answers
  • What season is it when the earth axis is tilted so that it is facing toward the sun?
    6·2 answers
  • Ricardo, mass 85 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 20 kg canoe. When the canoe is at rest
    11·1 answer
  • A 25-ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.18 ft/sec, ho
    13·1 answer
  • For an object to appear blue, what must the object do to blue light waves?
    15·1 answer
  • The diagram shows the electric field lines around two charges. Based on the field lines, what is the best description of the cha
    14·2 answers
  • What must you do if you plan to exercise everyday
    7·2 answers
  • Which best describes Earth's magnetic pole?
    10·2 answers
  • As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!