(II) Two point charges, Q 1 = - 25 μ C and Q 2 = + 45 μ C are separated by a distance of

step 1 This is chapter 21, problem number 36. We're given this figure that consists of two point charge

(II) Two point charges, Q 1 = - 25 μ C and Q 2 = + 45...

Key Concepts

Electric Field of a Point Charge

This concept describes how a point charge produces an electric field in the surrounding space. The magnitude of the electric field is given by Coulomb’s law, which depends on the magnitude of the charge and decreases with the square of the distance from the charge. The field’s direction is radially outward from a positive charge and radially inward toward a negative charge.

Coulomb's Law

Coulomb's law quantitatively expresses the electrostatic force between two point charges, stating that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is fundamental in determining the strength and distribution of the electric field in problems involving point charges.

Superposition Principle

The superposition principle in electrostatics states that the net electric field created by multiple charges is the vector sum of the electric fields produced by each individual charge. This concept is essential when determining locations where the contributions from different charges cancel each other out, resulting in a zero net field.

Zero Net Electric Field Point

In problems involving multiple charges, there may exist specific points in space where the electric fields from different charges exactly cancel each other. Identifying these points involves setting up an equation where the magnitudes and directions of the individual electric fields are equal and opposite, allowing one to solve for the distance from the charges where the net electric field is zero.

Transcript

00:01 This is chapter 21, problem number 36.

00:04 We're given this figure that consists of two point charges, q1 and q2, and p, at a point p, x away from q1, the net electric field due to these two charges are given to us as zero.

00:19 And we're asked what x is.

00:24 So at point p, there are two contributions, right? due to q1, there is going to be the electric field emanating from q1 at point p, and then there's going to be the electric field generated by q2 at point p.

00:40 So let's look at the direction of these electric fields, and then we can calculate the magnitudes.

00:46 So since q1 is a negative charge, the electric field emanating from a negative charge is always a radio towards the charge itself.

00:54 So then if we want to show the direction of e1, the electric field generated due to q1, then it's going to be towards q1.

01:04 Using the same logic, if you have a positive charge, the electric field at an arbitrary point away from this charge is going to be away from this charge.

01:17 So here it goes our e2.

01:19 Then, as you can see, e1 is a long positive extraction, and e2 is a long negative x direction.

01:25 And the magnitudes, let's see, the magnitude of e1 is going to be equal to k times the magnitude of the charge divided by the distance between the charge and the point of interest.

01:38 In this case, it's going to be x squared.

01:41 And then let's write it vectorly.

01:43 Then we're going to only put i hat there because e1 is in the positive x direction.

01:49 If we write the vector form of e2, again, first let's write the magnitude k k2 the absolute value of q2 divided by the distance between the charge and the point that we're interested in so it's going to be x plus 0 .12 in i converted it to meters from centimeters squared right now since you're writing it in the vector form we're going to put negative i have there because the electric field e2 is in the negative x direction now when we add these two vectors to each other, it's given to us in the problem, then that field at point p gives us 0...

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