Two point charges are separated by 25.0 cm (Fig. E21.39). Find the net electric field these char

Two point charges are separated by 25.0 cm (Fig. E21.39)....

Key Concepts

Vector Addition

Vector Addition is a mathematical process used to combine multiple vector quantities, such as electric fields or forces, by taking into account both their magnitudes and directions. In electrostatics, this is essential for accurately determining the net field or force when multiple charges are involved.

Electric Force

Electric force is the force experienced by a charged particle in an electric field, given by F = qE, where q is the charge of the particle and E is the electric field. It links the concepts of electric fields and the resultant mechanical effect on charged objects, dictating how they accelerate or remain in equilibrium.

Electric Field

The electric field is a vector field that represents the force per unit positive charge at any point in space due to other charges. It provides a way to visualize and calculate the influence of charges without placing a test charge in the field and is defined by the relationship E = F/q.

Coulomb's Law

Coulomb's Law describes the 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 understanding how charged particles interact and is expressed mathematically as F = k|q?q?|/r², where k is Coulomb's constant.

Superposition Principle

The Superposition Principle states that when more than one charge contributes to the electric field at a given point, the net electric field is the vector sum of the fields due to each individual charge. This principle allows for the independent calculation of each charge's effect, which can then be combined to determine the overall field.

Transcript

00:02 So here i have a diagram where i've labeled the two charges so that we can refer to them easier.

00:08 And so to start, we want to look at a and we want to find the net electric field.

00:14 And so to do that, we'll find the electric field from charge 1 and then the electric field from charge 2 and then combine them.

00:22 So to find the electric field from charge 1, we'll do the equation, electric field equal to k times q1 over the separation, which here is 0 .15 meters squared.

00:39 And that's going to be equal to 2 ,500 newtons over coulomes and the direction is going to be to the left since the electric fields go into negative charges.

00:53 And then we're going to do the same thing but find the electric field from charge two.

00:58 So that electric field is going to be k times q2 over the separation, which is now 0 .1 meter squared.

01:08 And that's going to be equal to 11 ,250 newtons over coulums, and that direction is going to be to the right, or going towards the negative charge.

01:21 And now, since we have the two components, we can subtract them from each other since they're going in opposite directions to find the net electric field.

01:31 So the net electric field is going to be 11 ,250 newtons over coulums minus 2 ,500 newtons over coulums and that's going to equal 8 ,750 newtons over coulums and it's going to be to the right so that's going to be your answer for part a now for part b we're going to do basically the same thing except instead of point a we're looking at point b now, and so the separations are going to be different and the directions.

02:15 So to find the electric field from charge 1, we'll take k times the charge of 1, divided by the separation, which is 0 .1 meter squared.

02:30 And that's going to be equal to 5 ,625 newtons over coulumes, and the direction is going to be to the right, since it's going to be going towards the negative charge.

02:43 Then we'll do the same thing with q2...

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