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
iragen [17]
3 years ago
13

A point charge is at the origin. With this point charge as the source point, what is the unit vector r^ in the direction of (a)

the field point at x = 0 , y = -1.35m; (b) the field point at x = 12.0cm, y = 12.0cm; (c) the field point at x = - 1.10m, y = 2.60m? Express your results in terms of the unit vectors i^ and j^. You may want to review (Pages 695 - 699) . For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Electric-field vector for a point charge.
Physics
1 answer:
KiRa [710]3 years ago
3 0

Answer:

  • a. \hat{r} =- \hat{j}
  • b. \hat{r} = \ \frac{1}{\sqrt{2}} \ \hat{i} + \ \frac{1}{\sqrt{2}} \ \hat{j}
  • c. \hat{r} = \ -0.3871 \ \hat{i} + \ 0.91501\ \hat{j}

Explanation:

Using Coulomb's Law we know that the electric field E at point \vec{r} is:

\vec{E(\vec{r})} = k_e \frac{q}{d^2} \frac{\vec{r}-\vec{r'}}{d}

where  k_e is the Coulomb's Constant, q is the source charge, d is the distance between point and position of the source point charge, and \vec{r}' is the position of the source point charge.

Taking all this in consideration, the unit vector clearly is:

\hat{r} =\frac{\vec{r}-\vec{r'}}{d}

For our problem, \vec{r'} = (0,0), as the charge is located at the origin.

So

\hat{r} =\frac{\vec{r}}{d}

and d will be the magnitude of \vec{r}

Now, we can take the values for each point.

<h3>a.</h3>

\vec{r}= (0,-1.35 \ m)

and, the magnitude of the vector is

|\vec{r}| = \sqrt{r_x^2 + r_y^2}

|\vec{r}| = \sqrt{(0 \ m)^2 + (-1.35 \ m )^2}

|\vec{r}| =1.35 \ m

So, the unit vector is:

\hat{r} =\frac{(0,-1.35 \ m)}{1.35 \ m}

\hat{r} =(0,-1,0)

\hat{r} =- \hat{j}

<h3>b.</h3>

\vec{r}= (12 \ cm,12 \ cm)

and, the magnitude of the vector is

|\vec{r}| = \sqrt{r_x^2 + r_y^2}

|\vec{r}| = \sqrt{(12 \ cm)^2 + (12 \ cm )^2}

|\vec{r}| = \sqrt{2} \ 12 \ cm

So, the unit vector is:

\hat{r} =\frac{(12 \ cm,12 \ cm)}{\sqrt{2} \ 12 \ cm}

\hat{r} =(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},0)

\hat{r} = \ \frac{1}{\sqrt{2}} \ \hat{i} + \ \frac{1}{\sqrt{2}} \ \hat{j}

<h3>c.</h3>

\vec{r}= (-1.10 \ m, 2.60 \ m)

and, the magnitude of the vector is

|\vec{r}| = \sqrt{r_x^2 + r_y^2}

|\vec{r}| = \sqrt{(-1.10 \ m)^2 + (2.60 \ m)^2}

|\vec{r}| = 2.8415 \ m

So, the unit vector is:

\hat{r} =\frac{ (-1.10 \ m, 2.60 \ m)}{2.8415 \ m}

\hat{r} =(-0.3871 ,0.91501)

\hat{r} = \ -0.3871 \ \hat{i} + \ 0.91501\ \hat{j}

You might be interested in
Plz help me with this!
vagabundo [1.1K]
A conductor is something which allows electricity to pass through it
an example is a coin
An insulator is something which cannot allow electricity to pass through it
an example is plastic (or plastic cotton reel, plastic container ect.)
Static electricity is when you rub two things together to create static

I'm not sure if i helped on the last question but i am definitely sure of the first ones
7 0
3 years ago
N capacitors are connected in parallel to form a "capacitor circuit". The capacitance of first capacitor is C, second one is C/2
liberstina [14]

Answer:

2C

Explanation:

The equivalent capacitance of a parallel combination of capacitors is the sum of their capacitance.

So, if the capacitance of each capacitor is half the previous one, we have a geometric series with first term = C and rate = 0.5.

Using the formula for the sum of the infinite terms of a geometric series, we have:

Sum = First term / (1 - rate)

Sum = C / (1 - 0.5)

Sum = C / 0.5 = 2C

So the equivalent capacitance of this parallel connection is 2C.

5 0
3 years ago
How can we avoid water pollution​
Alexandra [31]

Explanation:

1.Pick up litter and throw it away in a garbage can.

2.Blow or sweep fertilizer back onto the grass if it gets onto paved areas. ...

3.Mulch or compost grass or yard waste. ...

4.Wash your car or outdoor equipment where it can flow to a gravel or grassed area instead of a street.

5.Don't pour your motor oil down the storm drain.

8 0
3 years ago
Read 2 more answers
Two objects are electrically charged. The net charge on one object is doubled. Therefore, the electric force _____.
creativ13 [48]
If net charge on one object is doubled, then electric force will also get double. It is because they are directly proportional to each other.

Hope this helps!
7 0
3 years ago
Read 2 more answers
To demonstrate the tremendous acceleration of a top fuel drag racer, you attempt to run your car into the back of a dragster tha
Daniel [21]

Answer:

Explanation:

If the dragster  attains the speed equal to that of the car which is moving with constant velocity of v₀ , before the two close in contact with each othe , there will not be collision .

So the dragster starting from rest , must attain the velocity v₀ in the maximum time given that is tmax .

v = u + a t

v₀ = 0 + a tmax

tmax = v₀ / a

The value of tmax is v₀ / a .

5 0
3 years ago
Other questions:
  • How do you find the volume of an irregular shaped object
    6·1 answer
  • What is this process called when a liquid turns into gas
    13·1 answer
  • Find the length l of one "arch" of this cycloid, that is, find the distance traveled by a small stone stuck in the tread of a ti
    5·2 answers
  • Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is 28.0
    14·1 answer
  • Objects falling through the air experience a type of friction called air resistance. true or false
    8·2 answers
  • Technician A says that the tinnerman nuts are used to hold the brake drum on and should be reinstalled when the drum is replaced
    7·1 answer
  • Newton discovered that gravity affects the orbits of planets <br><br> True <br> Or<br> False
    10·2 answers
  • In Speed Study Number 1, we looked at two cars traveling the same distance at different speeds on city streets. Car "A" traveled
    10·1 answer
  • if a copper coin with a volume of exactly 50 cubic cm is dropped into the volume of water 4cubic cm,how much water will be overf
    15·1 answer
  • State and explain poiseuilles formula<br><br>​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!