The charges on three identical metal spheres are -12 μC +4.0 μC, and +2.0 μC . The spheres are b

The charges on three identical metal spheres are -12 μC +4.0...

The charges on three identical metal spheres are $-12 \mu \mathrm{C}$ $+4.0 \mu \mathrm{C},$ and $+2.0 \mu \mathrm{C} .$ The spheres are brought together so they simultaneously touch each other. They are then separated and placed on the $x$ and $y$ axes, as shown in the figure. Treat the spheres as if they were particles. Concepts: (i) Is the net charge on the system comprising the three spheres the same before and after touching? Why? (ii) After the spheres touch and are separated, how is the charge distributed, and what is the value of the charge on each sphere? (iii) Do $q_{2}$ and $q_{3}$ exert forces of equal magnitude on $q_{1} ?$ (iv) Is the magnitude of the net force exerted on $q_{1}$ equal to $2 F,$ where $F$ is the magnitude of the force that either $q_{2}$ or $q_{3}$ exerts on $q_{1} ?$ Calculations: What is the net force (magnitude and direction) exerted on the sphere at the origin?

The charges on three identical metal spheres are $-12 \mu \mathrm{C}$ $+4.0 \mu \mathrm{C},$ and $+2.0 \mu \mathrm{C} .$ The spheres are brought together so they simultaneously touch each other. They are then separated and placed on the $x$ and $y$ axes, as shown in the figure. Treat the spheres as if they were particles. Concepts: (i) Is the net charge on the system comprising the three spheres the same before and after touching? Why?
(ii) After the spheres touch and are separated, how is the charge distributed, and what is the value of the charge on each sphere? (iii) Do $q_{2}$ and $q_{3}$ exert forces of equal magnitude on $q_{1} ?$ (iv) Is the magnitude of the net force exerted on $q_{1}$ equal to $2 F,$ where $F$ is the magnitude of the force that either $q_{2}$ or $q_{3}$ exerts on $q_{1} ?$ Calculations: What is the net force (magnitude and direction) exerted on the sphere at the origin?

Key Concepts

Conservation of Charge

This principle states that the total electric charge in an isolated system remains constant over time. The charge cannot be created or destroyed but only redistributed, which ensures that the aggregate amount of charge before and after any process (such as the spheres touching) is the same.

Charge Redistribution Among Conductors

When identical conductive spheres come into contact, free electrons will move between them until they reach the same electric potential, leading to an equal division of the total charge among the spheres. This equilibrium is a key concept in understanding how charges distribute themselves across connected conductors.

Coulomb’s Law

Coulomb's Law quantitatively describes the force between two point charges, stating that the force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. It is fundamental for calculating the forces between charged bodies in electrostatic situations.

Vector Addition of Forces

Since the forces on a charge are vector quantities, both magnitude and direction must be taken into account when summing individual forces to determine the net force. This principle is essential for analyzing the combined effect of multiple charges exerting forces on a single charge.

Transcript

00:02 In this question, we are first going to touch three charged metal spheres together and then arrange them as shown in the diagram, and then we are going to discuss and calculate the net force on charge q1.

00:20 So let's start with, so part one asks, is the net charge of the system comprising the three spheres the same before and after touching? and let's first of all calculate the net charge.

00:34 So the net charge is going to be negative 12 microcoulombs plus 4 .0 microcoulombs plus 2 microcoulombs, which gives me negative 6 .0 microcoulombs.

01:03 And part one asks, is the net charge in the system the same before and after charging? why? so i'm going to be doing a lot of typing for this one because it's really just a lot to try.

01:27 Maybe i can type.

01:28 Okay, apparently my cursor's down there, so we're just going to write.

01:35 Yes, so the answer for part one is yes, the net charge is the same.

01:57 And we can think of negatively charged objects carry excess electrons while positively charged objects have a deficit of electrons.

02:36 So we can think of positively charged objects as having atoms that have the ability to receive electrons.

02:53 They've given up electrons at some point and so they now have the ability to receive them to come back to neutral.

03:03 And so we can think here that there are six microcoulombs worth of excess electrons whether, oh what was that, whether the spheres have touched or not.

03:36 I don't know what happened there.

03:37 Why did my writing give me an arrow? but okay.

03:58 For part two, after the spheres touch and are separated, how is the charge distributed and what's the value of the charge on each sphere? so for part two, since the spheres are identical, the excess electrons will split evenly among the three.

04:44 We'll say evenly among them.

04:48 Golly, what was that? leaving each with negative two microcoulombs.

05:09 And now looking at do forces q2 and q3 exert forces of equal magnitude on q1 since, actually i want to leave a little bit of room for sketching on that diagram, since q2 and q3 have equal charges and are equidistant from q1, they do exert equal charges, or sorry equal forces, well equal magnitude forces.

06:23 Let me, equal magnitude forces...

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