Three particles are placed in a line. The left particle has...

Three particles are placed in a line. The left particle has a charge of $-55 \mu \mathrm{C},$ the middle one has a charge of $+45 \mu \mathrm{C},$ and the right one has a charge of $-78 \mu \mathrm{C}$. The middle particle is $72 \mathrm{cm}$ from each of the others, as shown in Figure $20-16$ a. Find the net force on the middle particle. b. Find the net force on the right particle. (FIGURE CAN'T COPY)

Three particles are placed in a line. The left particle has a charge of $-55 \mu \mathrm{C},$ the middle one has a charge of $+45 \mu \mathrm{C},$ and the right one has a charge of $-78 \mu \mathrm{C}$. The middle particle is $72 \mathrm{cm}$ from each of the others, as shown in Figure $20-16$
a. Find the net force on the middle particle.
b. Find the net force on the right particle.
(FIGURE CAN'T COPY)

Key Concepts

Vector Addition of Forces

Since forces are vector quantities, their magnitudes and directions must both be taken into account during addition. Vector addition involves breaking each force into its components and summing these components accordingly, ensuring that the overall net force is determined accurately in both magnitude and direction.

Coulomb's Law

Coulomb's Law is fundamental in describing the electrostatic force between two point charges. It states that the magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance separating them. This principle forms the basis for calculating forces among charged particles, regardless of the specific charge values given.

Principle of Superposition

The principle of superposition asserts that when multiple forces act on a single particle, the net force is the vector sum of all individual forces. This concept is critical for analyzing systems with several charges, as it allows one to calculate the overall effect by considering each pairwise interaction independently before summing them.

Sign of Electric Charges

The sign of an electric charge determines whether the force between two charges is attractive or repulsive. Like charges repel each other, while opposite charges attract, affecting the direction of the force vectors. This concept is crucial for establishing the correct directional relationships when applying Coulomb's Law and the superposition principle in charge systems.

Transcript

00:01 So to start, i've drawn a diagram where i've labeled the particles, a, b, and c, where a is the one in the left, b is the one in the middle, and c is the one on the right.

00:11 And then i've written out our constant k, our values for the charges, and our values were given for the separation.

00:19 So the first thing i want to do for part a is to figure out the force between particles a and b.

00:27 So to find that, we're going to take k times a charge on a times a charge on b over the separation between a and b squared.

00:37 If we plug in our values for that, you find that this is equal to about 43 newton's.

00:44 And on particle b, the direction of that is going to be to the left, since it's an attractive force towards particle a.

00:52 So next, we want to find the force between particles b and c.

00:58 So for that, we use the same equation, but we use the charge of particles b and c, a separation between b and c squared.

01:09 And that's equal to about 61 newtons.

01:13 It's also an attractive force.

01:15 So the force on particle b is going to be to the right.

01:19 Then to find the net force, since these are in opposite directions, all we need to do is subtract these values.

01:26 So this is equal to force between b and c, minus the force between a and b, and that's equal to 18 newtons to the right.

01:38 The net force on b is 18 newtons to the right...

Please give Ace some feedback