Two point charges q1 and q2 are held in place 4.50 cm apart....

Two point charges $q_1$ and $q_2$ are held in place $4.50 cm$ apart. Another point charge $Q = -1.75 \space \mu C$, of mass 5.00 g, is initially located $3.00 cm$ from both of these charges ($\textbf{Fig. P21.72}$) and released from rest. You observe that the initial acceleration of $Q$ is 324 m$/$s$^2$ upward, parallel to the line connecting the two point charges. Find $q_1$ and $q_2$.

Key Concepts

Newton's Second Law in Force Analysis

Newton's Second Law relates the net force acting on an object to its acceleration by the equation F = ma. In the context of charged particles, this law allows one to connect the computed electric forces from Coulomb's Law to the resulting acceleration, thereby providing a means to determine unknown quantities such as charge magnitudes when the observed acceleration is known.

Electric Field Concept

The electric field is a vector field that represents the force per unit charge experienced by a small positive test charge at any point in space. It provides an alternative way of describing the influence of charges and can be used to determine the force acting on any charge placed within the field. Calculations involving electric fields are often parallel to those using direct force analysis via Coulomb's Law.

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 charge magnitudes and inversely proportional to the square of the distance between them. This fundamental law of electrostatics is essential for analyzing how charges interact when separated by a distance.

Superposition Principle in Electrostatics

The superposition principle holds that when multiple charges exert forces on a test charge, the net force is the vector sum of the individual forces produced by each charge. This principle allows for the calculation of the overall force acting on a charge by considering contributions from each source charge separately, which is crucial when dealing with systems of multiple charges.

Transcript

00:03 Alright, so in this problem we have set up capital q over here and we have two other cues here and there.

00:16 And we know the distance between the capital q and the q1, so this is 3 centimeters.

00:24 This is 3 centimeters as well.

00:27 And the distance between q1 and q2 is 4 .5 centimeters.

00:31 And we know the capital q is negative 1 .75 microchorms.

00:40 So the mass of capital q is 5 grams.

00:49 And initially we know that the acceleration of the capital q is 324 meters per second square.

01:00 So we want to find out the charge of q1, q2.

01:03 And yeah, another condition is this acceleration is pointing up.

01:09 Okay? so by using these conditions, we can see that the q1, q2, they have to, i mean, their charge have the same magnitude.

01:19 The reason is if q1 and q2 have different charges like a different magnitude, then the force will be something like this.

01:29 They do not have the same magnitude, right? in this case, there will be a net residue on the x direction.

01:39 So the acceleration will not be pointing to the y direction.

01:43 So based on this reason, we can just say that the q1 equal to q2, sorry, equal to, yeah, and another condition is since q1 and since the force is pointing up, so by using the force division, it has to be like this, right? so because q is a q is negative, q is negative charge, so q1 has to be positive and q2 has to be negative.

02:09 So we just say that this is equal to q.

02:13 Okay.

02:15 So the net force on the capital q, we can have the expression f equal 1 .4 pi epsilon not times q times q times capital q, which is n...

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