Four point charges are at the corners of a square of side a as shown in Figure P23.21. (a) Deter

Four point charges are at the corners of a square of side a...

Key Concepts

Coulomb's Law

Coulomb's Law states that the electric force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law forms the basis for calculating individual force contributions in systems with multiple charges.

Electric Field

The electric field is defined as the force per unit charge experienced by a small positive test charge placed in the field. It provides a way to quantify the influence of source charges in space and is represented as a vector field, indicating both the magnitude and direction of the force that would act on a test charge.

Superposition Principle

The superposition principle is fundamental in electromagnetism, asserting that in a system with multiple charges, the total electric field at any point is the vector sum of the electric fields produced by each individual charge. This principle is crucial for analyzing complex charge distributions by breaking them down into simpler parts.

Electric Force

Electric force refers to the interaction between charged particles and is described by the equation F = qE, where q is the charge experiencing the force and E is the electric field at the location of the charge. This concept links the phenomena of electric fields and forces on charges.

Vector Analysis

Vector analysis involves the addition of vectors, each having magnitude and direction, to determine the resultant vector. In the context of electric fields and forces, it is used to compute the net effect from multiple sources, taking into account both magnitude and directional components, and is essential when dealing with non-linear or symmetric charge arrangements.

Transcript

0:00 High.

00:01 In the given problem, there are four charged particles which are kept at the corners of a square.

00:10 Let the square be a, b, c and d.

00:17 Then the charge is kept at its corners are, here this is charge having a magnitude of 2q.

00:26 Here this is the charge having a magnitude of just q.

00:31 Then here this is the charge having a magnitude of 4q.

00:37 And finally, this is the charge at corner d having a magnitude of 3 q.

00:43 Each side of this square is given as a.

00:49 So it's diagonal will become side into root 2 means a root 2.

00:58 So in the first part of the problem, we have to find net electric field acting at this charge q, acting at the position of this charge q means at point b.

01:11 So if you look, there are four electric fields.

01:16 There are three electric fields acting at this point b.

01:21 One, because of the charge 2q kept at a.

01:25 And as we know, the direction of electric field is away from the positive charge.

01:30 So if we consider all these charges to be positive, so this is electric field due to the charge kept at a.

01:38 Then the electric field at position of q means at b, due to the charge kept at c means 4q.

01:45 This is like this away from 4q.

01:51 Then finally, electric field due to this 3q, and that is also away from 3q means this is like this.

02:01 So we can name these electric fields as this is e a electric field due to the charge kept at a this is e c electric field due to the charge kept at c and this is e d electric field due to the charge kept at d now we know expression for the electric field due to a charge q at a distance r is given as k k k by r squared where k is a constant for air whose value is 1 by 4 pi epsilon not but we have to find this answer in terms of constants so we will keep this as k only so first of all as all the distances are a except this diagonal the diagonal is having a length a root 2 so first of all electric field e a will become equal to k into 2 q the charge at a divided by a square then e c electric field at b due to c this is k into 4 q and distance again a square and finally ed is equal to k 3q divided by the square of distance which is a root 2.

03:32 So the square of this a root 2 will become 2a square...

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