A+8.75-μC point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-μ

A+8.75-μC point charge is glued down on a horizontal...

Key Concepts

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 charges and inversely proportional to the square of the distance between them. This principle is essential in determining the interaction between charged objects in electrostatics.

Electric Field

An electric field represents the force per unit charge exerted on any charges placed in the field. A uniform electric field has the same magnitude and direction at every point in space, making it useful for analyzing how charged particles experience consistent forces.

Equilibrium of Forces

The principle of equilibrium of forces involves the condition where the net force acting on an object is zero, leading to no acceleration. In problems involving multiple forces—such as those due to electric fields and inter-charge interactions—this concept allows one to set up equations balancing these forces to solve for unknowns like tension.

Vector Addition of Forces

When forces act in different directions, they must be combined using vector addition. This process involves breaking each force into components and summing the components along each axis. It is pivotal in determining the net force acting on an object when the forces do not align along a single direction.

Tension Force

Tension is the force transmitted through a string, rope, or wire when it is pulled tight by forces acting from opposite ends. In the context of electrostatic problems, tension acts as a reactive force that balances the net force on a charged particle tied to a wire, ensuring that the system remains in equilibrium.

Transcript

00:01 In this exercise, we have two point charges a and b, where a is free to move on the x direction, and b is fixed to this place.

00:11 Besides, a and b are connected to each other by a massless and non -conducting wire here.

00:19 And also, they are subjected to an external magnetic field here in green.

00:26 I also wrote on the right -hand side some important quantities we must.

00:31 Keep in mind to solve the exercise.

00:34 So first i wrote the charge of particle a, which is negative.

00:39 I wrote the charge of particle b, which is positive, and i wrote the the external electric field e.

00:51 And here in parentheses, i'm emphasizing that it's pointing to the positive x direction.

00:56 And finally, i wrote the quillum constant, which will need to calculate the electric field generated by this point charges.

01:09 Okay, so question a asks us to calculate the tension on the wire.

01:17 So notice that since particle b is fixed, the tension on the wire should be equal to the force on particle a.

01:28 But the force on particle a is the force that the external field exerts.

01:37 On particle a plus the force that the particle b exerts on particle a.

01:53 So in starting with the force generated by the external magnetic field, we have that, sorry, the electric force is particle a's charge, which i'll write as just a times the external magnetic field.

02:22 But since particle a is negative, has negative charge, we have that the force of the external field is pointing to the negative x direction here.

02:44 And it is, and it is, the value of charge a, which minus 6 .5 times 10 to the minus 6 quorum times the value of the electric field, 1 .8 5 times 10 to the 8 new term per quillum on the x direction.

03:16 If we substitute all these values, we find that the force that the external electric field exerts on the the on particle a is just 1 .20 times 10 to the third newton.

03:42 So highlight this value here because we'll need it later on.

03:50 Great, now we only have to know what is the force that particle b exerts on a.

04:00 Well, just like the other case, the value is the charge, of the particle, which is a, times the electric field that the particle b generates.

04:17 But to calculate what is the electric field that particle b generates, we must recall culum's law.

04:28 And from coulomb's law, we have that the electric field generated by charge b is k, which is the culum constant, times the charge of the particle.

04:40 Particle b, which i've read it just as b, over the distance between those two particles squared.

04:53 I forgot to mention that a distance between those two particles is equal to 2 .5 times 10 to the minus 2 meters, which is this distance here, the length of the wire.

05:15 Okay, now if we just substitute all these values inside this little equation here, we have that the force that the particle b exerts on particle a is equal to 8 .18 times 10 to the 2 newton...

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