Questions 1, 2, and 3 are short free-response questions that...

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?

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?

Key Concepts

Test Charge Concept

The test charge concept involves introducing a small, hypothetical positive charge into an electric field to measure the force per unit charge without disturbing the existing charge distribution. It provides a means of probing the electric field's properties and understanding how forces, as dictated by Coulomb's law, would act on a charged particle in different regions of space.

Superposition Principle

The superposition principle in electrostatics states that the total electric field or force experienced at a point due to multiple charges is the vector sum of the fields or forces generated by each individual charge. This principle allows for the analysis of complex charge configurations, such as determining the point along a line where the electric field becomes zero by balancing the contributions from each charge.

Electric Field

The electric field represents the force per unit charge exerted on a positive test charge placed in the vicinity of other charges. It is a vector field that shows how a charged object creates an influence in the space around it, guiding how other charges would move. Understanding the concept of the electric field is essential for solving problems that involve finding points where the net field is zero or calculating the force experienced by a test charge.

Coulomb's Law

Coulomb's Law quantifies the electric force between two point charges. It states that the magnitude of the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, with the constant of proportionality being Coulomb's constant. This law also indicates that like charges repel and unlike charges attract, which is crucial for understanding the direction of forces in electrostatic interactions.

Transcript

00:01 As an example of working with coolum's law, electric force and electric field, we'll take a look at two charges that are sitting in space next to each other.

00:12 One is positive and the other is negative.

00:16 And let's just give those some values, a minus 12 nanoculums on the right and a positive three anaculums on the left, separated by 36.

00:30 Centimeters.

00:39 So kulam's 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.

00:55 Why? because this equation gives you the magnitude of the interaction.

01:03 The direction comes from basically, knowing what signs of charges there are and whether situated in space.

01:13 So the force always acts on a line joining the bear, and it will act one way if they are attracting each other.

01:24 It will act opposite that on both charges if they repel.

01:29 And the electric field has a similar type of relationship.

01:34 Again, there's a k and the absolute magnitude of a over by, divided by the distance squared.

01:44 But notice that the electric field assumes just one charge sitting there in space, creating a field, whereas the force measures in interaction.

01:55 So let's take a look at this example.

01:58 The two charges will obviously feel an attraction, and that will be a newton's third law pair.

02:07 So those are equal and opposite each other.

02:10 And hence, you don't want to be putting signs on your kulom's law calculation.

02:18 But anyway, we can calculate the magnitude of that interactive force.

02:23 The electrical constant is 9 times 10 to the 9th in si units.

02:30 And remember, we want the absolute magnitudes of those charges.

02:36 So we're going to put them in both with positive signs.

02:43 And really, it makes no sense to have a negative magnitude.

02:51 Only astronomers make that happen.

02:58 But a vector magnitude is not a negative number.

03:05 So let's see what we get in terms of newton's.

03:08 We've used everything in si units.

03:10 So this is 3 .6 times 10 to the minus 6 newtons.

03:22 The next situation we're going to think about is the electric field at a point right in between those two charges.

03:31 So we have our negative and positive charges.

03:36 And we are going to look at a point, we'll call that point p, 15 centimeters from both.

03:48 Centimeters and 15 centimeters...

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