Three 1.0-C charged objects are equally spaced on a straight...

Three $1.0-\mathrm{C}$ charged objects are equally spaced on a straight line. The separation of each object from its neighbor is 100 $\mathrm{m} .$ Find the force exerted on the center object if (a) all charges are positive, (b) all charges are negative, and (c) the rightmost charge is negative and the other two are positive.

Key Concepts

Effect of Charge Sign on Force Direction

The sign of a charge determines whether the resulting electric force is attractive or repulsive. Like charges repel each other, while opposite charges attract. Understanding this concept is key when analyzing the direction of forces in systems with multiple charges, as it guides the vector addition of individual forces to compute the net force on a charge.

Superposition Principle

The Superposition Principle is essential in electrostatics, stating that the net force on any charge is the vector sum of the forces exerted on it by each of the other charges individually. This principle allows for the calculation of complex scenarios by breaking them down into simpler pairwise interactions and summing their contributions to determine the overall effect.

Coulomb's Law

Coulomb's Law is a fundamental principle in electrostatics that quantifies the electric 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 between them. This law is crucial for calculating the forces exerted by one charged object on another in problems involving electric interactions.

Transcript

00:01 Okay, so the question a was asking us, find the force exerted on the center object, if all charges are positive.

00:08 Well, if all charges are positive, that means, oh, sorry, it should be positive.

00:20 So this is positive.

00:22 Well, the net force on the center object, which is q2 here, should be equal to the force from q1 to q2, plus the force from q3 to q2.

00:33 And you see here, the force from q3 to q2.

00:33 And you see here, the force from the force from q1 to q2 is to the right, and the force from q3 to q2 is to the left.

00:41 So it's opposite direction.

00:42 And also they have equal magnitude as well.

00:46 Why is that? because f1, 2 is k times q2 over r squared, plus the upper direction which is negative k times q2, q3 over r squared.

00:56 And if we derive it, we'll have k times positive 1 .0 columns times, times another positive 1 .0 columns over r square minus k times q2 and q3 has positive one cool on.

01:27 Okay? so it's negative k times positive 1 .0 cool arms times positive 1 .0 columns over r square and this will give us zero.

01:50 Okay so net force on the center object should be zero.

01:55 Okay.

01:55 And for the second one it was asking us if all the charges are negative, what's the force exerted on the center object? well, oh, sorry about that.

02:09 So this is all negative and all charges is equal to negative 1 koules.

02:25 And their distance between each other is the same.

02:29 And this will give us the net force on center object versus the q2 is equal to f1 on 2.

02:44 Plus f3 on 2 which is also equal to k times q1 q2 over r square plus negative k on k on q2 q2 2 over r square okay because the force from charge 1 to charge 2 is to the right and the force from charge 3 to charge 2 is to the left because they have the same sign of charge all of them negative so next and negative will repel each other...

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