Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Questions 1, 2, and 3 are short free-response questions that require about 13 minutes to answer and are worth 8 points. Questions 4 and 5 are long free-response questions that require about 25 minutes each to answer and are worth 13 points each. Show your work for each part in the space provided after that part.(DIAGRAM IS NOT AVAILABLE TO COPY)Two charges, $q_{1}=+3 \mathrm{n} \mathrm{C}$ and $q_{2}=-12 \mathrm{nC}$ , are fixed in place and separated by a distance of 3 $\mathrm{cm} .$(a) What is the magnitude of the electric force between the two charges? Is the force attractive or repulsive?(b) At what point between the two charges is the electric field equal to 0?(c) What is the electric field at the midpoint between the two charges?(d) What is the magnitude of the electric force on a charge $q_{3}=+2 \mathrm{nC}$ placed in the middle of the two charges?

No Related Courses

Chapter 14

Practice Test 4

Section 2

No Related Subtopics

03:57

Two charges, $q_{1}=+3 \ma…

07:33

Point charges $q_1 = +$2.0…

19:54

Two charges are placed as …

05:04

Two charges, +Q and +2Q, a…

05:30

08:34

Three point charges lie al…

07:00

CE Three charges, $q_{1}=+…

04:19

Two point charges $\left(q…

03:54

Point charges $q_{1}=50 \m…

03:27

Point charge $q_1 = -$5.00…

as an example of working with columns law, electric force, an electric field, we'll take a look at two charges that are sitting in space next to each other. one is positive and the other is negative. And let's just give those some values uh minus 12 anna columns on the right And a positive three and columns on the left separated by 30 centimeters. Okay, So columns law gives us two formulas for both the force of attraction between two charges, and that should be written with an absolute value around those two charges. Why? Because this equation gives you the magnitude of the interaction. The direction comes from basically knowing what signs of charges there are and whether situated in space. So the force always acts on a line joining the bear and it will Act one way if they are attracting each other, it will act opposite that on both charges if they repel. Um in the electric field has a similar type of relationship. Again, there's A. K. And the absolute magnitude of a. Q. Over by divided by the distance squared. Um but notice that the electric field assumes just one charge sitting there in space creating a field, whereas the force measures in interaction. So let's take a look at this example. Um the two charges will obviously feel an attraction and that will be a Newton's third law pair. So those are equal and opposite each other. Um And hence you don't want to be putting signs on your columns law calculation. But anyway, uh we can calculate the magnitude of that interactive force. The electrical constant is nine times 10 to the 9th in S. I. Units. And remember we want the absolute magnitudes of those charges. So we're going to put them in both with positive signs. And really it makes no sense to have a negative magnitude. Only astronomers make that happen. Um Yeah, but a vector magnitude is not a negative number. So let's see what we get in terms of Newton's, we've used everything in S. I. units. So this is 3.6 Times 10 to the -6. Um Newton's okay. The next situation we're going to think about is the electric field to add a point right in between those two charges. So we have our negative and positive charges and we are going to look at a point, we'll call that point P. So one 15 cm from both 15 centimeters and 15 centimeters. Now, the electric field is calculated at all points in space by taking however many point charges you have here there too, and adding up their individual electric fields. Um So electric field is a vector and it usually tells you um the force a positive charge would experience if it were placed at a point here we're talking. Look looking at point P. And in order to get the vector right, what you really want to do is imagine the vectors at that point that are created by your two charges. So in our situation, electric field always emanates outwards from a positive charge. And we could draw a bunch of lines coming out of that charge. But what we're interested in is that vector that's on the side with P similarly, electric field is going into um a negative charge. Sorry, that should be minus. And again, we could draw all sorts of factors going into that charge, but what we see is is at point P. Both fields point to the right. So our electric field is going to be the sum of their magnitudes will give us the magnitude of that electric field and the direction will be pointing to the right And again, to find those magnitudes, Remember, we do not want to put in a sign of a charge, we put in a magnitude of charge because if you don't do that, you will wind up subtracting something when you meant to add it and that would be bad. Yeah, and r E minus. We do the same thing. Of course. This is even more critical that we put in a absolute value of the charge. And if all come out, if all quantities are put in S. I. Units, the unit should be newtons per Coolum. Okay, and that works out to be 60 newtons per column. He plus plus c minus turns out to be 60 Newtons per Coolum. And the direction is to the right. And I'll tell you if you put in the wrong sign of charge in this this relationship, you'll think that the positive charge cannot create a electric field to the left and vice versa. The negative charge can't create an electric field to the right. And we see that that's definitely not true that the electric field points of different directions in space around each charge. Um So you have to be careful with that, and finally, if we put another charge into the situation, um So let's put a charge of 2-plus 2. Yeah, the columns there, right smack dab in the middle. We could work out the force on it based on the forest from the two charges nearby, but it is much easier to say F equals Q three times the electric field. Um Where e is the total electric field experienced by that charge at that point, which is 60 Newton columns practical. Um To the right standard minus nine. And that will be to the right as well. So, a thing to remember is that the electric field gives the sense of the force that would be directed on a positive charge. So this would be 1.2 Types 10 of -7 Newtons, and to the right.

View More Answers From This Book

Find Another Textbook

Two charges, $q_{1}=+3 \mathrm{nC}$ and $q_{2}=-12 \mathrm{nC},$ are fixed i…

Point charges $q_1 = +$2.00 $\mu$C and $q_2 = -$2.00 $\mu$C are placed at ad…

Two charges are placed as shown in Fig. P21. 106. The magnitude of $q_{1}$ i…

Two charges, +Q and +2Q, are fixed in place along the y-axis of an x-yco…

Two charges are placed as shown in $\textbf{Fig. P21.96}$. The magnitude of …

Three point charges lie along a straight line as shown in Figure $\mathrm{P}…

CE Three charges, $q_{1}=+q, q_{2}=-q,$ and $q_{3}=+q,$ are at the vertices …

Two point charges $\left(q_{1}=+4 \mu \mathrm{C} \text { and } q_{2}=+3 \mu …

Point charges $q_{1}=50 \mu \mathrm{C}$ and $q_{2}=-25 \mu \mathrm{C}$ are p…

Point charge $q_1 = -$5.00 nC is at the origin and point charge $q_2 = +$3.0…

02:06

An object of charge $+q$ feels an electric force $\mathbf{F}_{\mathrm{E}}$ w…

02:43

Questions 39-41 refer to the following figure:FIGURE CANNOT COPYDete…

02:14

A sound wave travels through a metal rod with wavelength ? and frequency f. …

06:16

Consider two small spheres, one carries a charge of $q_{1}=+4 q$ and the oth…

01:22

A soccer ball, at rest on the ground, is kicked with an initial velocity of …

01:58

Directions: For each of the questions 46-50, two of the suggested answers wi…

01:14

If the voltage drop across a 3$\Omega$ resistor is $2 \mathrm{V},$ how long …

01:53

Two objects, one of mass 3 kg moving with a speed of 2 $\mathrm{m} / \mathrm…

02:37

A flute supports standing waves with pressure nodes at each end. The lowest …

01:13

A string, fixed at both ends, supports a standing wave with a total of 4 nod…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.