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
Deffense [45]
3 years ago
13

At each corner of a square of side there are point charges of magnitude Q, 2Q, 3Q, and 4Q

Physics
1 answer:
Bad White [126]3 years ago
6 0

Answer:

\displaystyle |F_t|=10.9\ \frac{KQ^2}{l^2}

\displaystyle \theta =68^o

Explanation:

Electrostatic Force

It's the force that appears between two electrical charges q1 q2 when they are placed at a certain distance d. The force can be computed by using the Coulomb's law:

\displaystyle F=\frac{KQ_1Q_2}{d^2}

We have an arrangement of 4 charges as shown in the image below. We need to calculate the total force exerted on the charge 2Q by the other 3 charges. The free body diagram is also shown in the second image provided. The total force on 2Q is the vectorial sum of F1, F2, and F3. All the forces are repulsive, since all the charges have the same sign. Let's compute each force as follows:

\displaystyle |F_1|=\frac{KQ(2Q)}{l^2}=\frac{2KQ^2}{l^2}

\displaystyle |F_2|=\frac{K(2Q)(4Q)}{l^2}=\frac{8KQ^2}{l^2}

The distance between 3Q and 2Q is the diagonal of the rectagle of length l:

\displaystyle |d_3|=\sqrt{l^2+l^2}=\sqrt{2}\ l

The force F3 is

\displaystyle |F_3|=\frac{K(3Q)(2Q)}{(\sqrt{2l)}^2}=\frac{3KQ^2}{l^2}

Each force must be expressed as vectors. F1 is pointed to the right direction, thus its vertical components is zero

\displaystyle \vec{F_1}=\left \langle |F_1|,0 \right \rangle=\left \langle \frac{2KQ^2}{l^2},0 \right \rangle

F2 is pointed upwards and its horizontal component is zero

\displaystyle \vec{F_2}=\left \langle 0,\frac{8KQ^2}{l^2} \right \rangle

F3 has two components because it forms an angle of 45° respect to the horizontal, thus

\displaystyle \vec{F_3}=\left \langle \frac{3KQ^2}{l^2}\ cos45^o,\frac{3KQ2}{l^2} sin45^o\right \rangle

\displaystyle \vec{F_3}=\left \langle \frac{3\sqrt{2}KQ^2}{2l^2},\frac{3\sqrt{2}KQ^2}{2l^2}\right \rangle

Now we compute the total force

\displaystyle \vec{F_t}=\vec{F_1}+\vec{F_2}+\vec{F_3}

\displaystyle \vec{F_t}=\left \langle \frac{2KQ^2}{l^2},0 \right \rangle +\left \langle 0,\frac{8KQ^2}{l^2} \right \rangle + \left \langle \frac{3\sqrt{2}KQ^2}{2l^2},\frac{3\sqrt{2}KQ^2}{2l^2}\right \rangle

\displaystyle \vec{F_t}=\left \langle \left(2+\frac{3\sqrt{2}}{2}\right)\frac{KQ^2}{l^2},\left(8+\frac{3\sqrt{2}}{2}\right) \frac{KQ^2}{l^2}\right \rangle

\displaystyle F_t=\left \langle 4.121,10.121 \right \rangle \frac{KQ^2}{l^2}

Now we compute the magnitude

\boxed{\displaystyle |F_t|=10.9\ \frac{KQ^2}{l^2}}

The direction of the total force is given by

\displaystyle tan\theta =\frac{10.121}{4.121}=2.4558

\boxed{\displaystyle \theta =68^o}

You might be interested in
How much can having a lighted candle increase the temperature inside the shelter?
oksian1 [2.3K]
A lighted candle produces heat however not as much heat as a heater or the sun would.
8 0
3 years ago
A busy chipmunk runs back and forth along a straight line of acorns that has been set out between his burrow and a nearby tree.
saveliy_v [14]

Answer: a = 1.32m/s2

Therefore, the average acceleration is 1.32m/s2

Explanation:

Acceleration is the rate of change in the velocity per time

a = change in velocity/time

a = ∆v/t

average acceleration a = (v2 -v1)/t. ....1

Given;

Final velocity v2 = 1.63m/s

Initial velocity v1 = -1.15ms

time taken t = 2.11s

Substituting into eqn 1

a = [1.63 - (-1.15)]/2.11

a = (1.63+1.15)/2.11

a = 2.78/2.11

a = 1.32m/s2

Therefore, the average acceleration is 1.32m/s2

6 0
3 years ago
A 100 N force is applied to move an object a horizontal distance of 5 meters at constant speed in 10 seconds. How much power is
Tpy6a [65]

Answer:

50 W

Explanation:

<h3><u>Given :</u></h3>

  • Force applied = 100 N
  • Distance covered = 5 metres
  • Time = 10 seconds

<h3><u>To find :</u></h3>

Power

<h3><u>Solution :</u></h3>

For calculating power, we first need to know about the work done.

\bf \boxed{Work = Force \times displacement}

Now, substituting values in the above formula;

Work = 100 × 5

= 500 Nm or 500 J

We know that,

\bf \boxed{Power=\dfrac{Work\:done}{Time\: taken}}

Substituting values in above formula;

Power = 500/ 10

= 50 Nm/s or 50 W

Hence, power = 50 W .

5 0
3 years ago
Protons<br> Neutrons<br> Electrons<br> Location<br> Charge<br> Size
igor_vitrenko [27]
Protons are positive, and neutrons are negative, electrons are neutral. I’m not sure about the rest but I hope that helps for now
6 0
2 years ago
A net force, the magnitude of which is 3800 N, accelerates a 1260-kg vehicle for 10.0 s. The vehicle travels 50.0 m during this
Novay_Z [31]

Answer:

SEE EXPLANATION

Explanation:

p =  \frac{fd}{t}  \\ where \: \\p  = power \\  f = force \\ d = distance \\ and \: t = time \\  \\ p =  \frac{3800 \times 50}{10}  \\ p =  \frac{190000}{10}  \\ p = 19000w

7 0
3 years ago
Other questions:
  • On a hot day, you sit on the edge of a pool and dip your feet into the water, causing changes to occur that are related to the p
    11·1 answer
  • The molecules of a gas are in constant random motion. This means that they have energy in what type of energy store?
    11·1 answer
  • Using what you know about the periodic table, choose all of the correct answers,
    5·1 answer
  • I really need help asap.
    10·2 answers
  • • Be able to identify the forms of kinetic vs. potential energy, and to list some forms of each. • Be able to state the Law of C
    15·1 answer
  • Bank A has a leverage ratio of 10, while Bank B has a leverage ratio of 20. Similar losses on bank loans at the two banks cause
    8·1 answer
  • Two copper wires have the same length, but one has twice the diameter of the other. Compared to the one that has the smaller dia
    14·1 answer
  • What's being transferred between a cell phone and a cell phone tower through radio waves?
    12·1 answer
  • A 100-watt lightbulb radiates energy at a rate of 100 J/s. (The watt, a unit of power, or energy over time, is defined as 1 J/s.
    15·1 answer
  • How much work does it take to lift 345 boxes to a height of 6.00 m of each box has a mass of 7.89 kg
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!