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
What is the main difference between velocity and speed?
Marina86 [1]
Speed is scalar, meaning it's only going to be like 74 mph, doesn't matter which direction. Velocity is a vector, meaning it has direction. You can go -74mph when talking about velocity, not speed.
4 0
2 years ago
Light from a single laser is directed through two slits that are separated by a small distance. On the other side of the slits i
nekit [7.7K]
The answer is destructive interference.  You have this for both C and D.  I suspect one of C or D is supposed to be constructive interference...  But destructive interference is the answer
3 0
2 years ago
When a object is at rest, what is it’s speed??
nadya68 [22]

Answer:

0   (there is no speed)

Explanation:

If an object is at rest, it is not moving, and it doesn't have a speed, so the speed is zero.

3 0
3 years ago
Read 2 more answers
Nucleus A decays into the stable nucleus B with a half-life of 22.07 s. At t=0 s there are 1,293 A nuclei and no B nuclei. At wh
Alexeev081 [22]

Answer:

29.38 seconds

Explanation:

Half life, T = 22.07 s

No = 1293

Let N be the number of atoms left after time t

N = 1293 - 779 = 514

By the use of law of radioactivity

N=N_{0}e^{-\lambda t}

Where, λ is the decay constant

λ = 0.6931 / T = 0.6931 / 22.07 = 0.0314 decay per second

so,

514=1293e^{-0.0314t}

2.5155=e^{0.0314t}

take natural log on both the sides

0.9225 = 0.0314 t

t = 29.38 seconds

5 0
2 years ago
When a wire with a current is placed in a magnetic field, electrical energy is transformed into mechanical energy
babymother [125]

Answer:

TRUE

Explanation:

When a wire with a current is placed in a magnetic field, electrical energy is transformed into mechanical energy. The transformation happens when the magnetic field produced by the current causes the wire to move.

8 0
2 years ago
Other questions:
  • The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of -5.7
    13·1 answer
  • Objects that conduct electricity poorly are called
    5·2 answers
  • PLEASE HELP ME ASAP!!!!!!! <br> giving brainliest for correct answers
    8·1 answer
  • Need a little help here :(
    15·2 answers
  • The force, F, of the wind blowing against a building is given by where V is the wind speed, rho the density of the air, A the cr
    8·1 answer
  • Physics help please..............
    11·1 answer
  • Basalt, formed from magma, contains iron-rich minerals. Why is this important?
    15·1 answer
  • In order for a color to be seen by a human, the light must be
    5·1 answer
  • What is a law in physics?​
    6·1 answer
  • What two things does gravitational force depend upon?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!