What is the electric field at the center of the square in...

Key Concepts

Electric Field

This is a vector field that represents the force per unit charge at any point in space. It is a fundamental concept in electromagnetism used to determine how charges interact, whether through point charges or continuous distributions, and its direction and magnitude are crucial for solving problems related to forces and potentials.

Coulomb's Law

Coulomb's Law quantifies the electric force between two point charges. It establishes that the force (and hence the field produced by a point charge) is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating the contributions to the electric field from individual charges.

Superposition Principle

The superposition principle states that the total electric field created by multiple charges is the vector sum of the individual fields produced by each charge. This principle is vital in solving problems involving complex geometries or distributions, where the overall field can be computed by summing simpler contributions.

Symmetry Analysis

Symmetry analysis involves using the geometric symmetry of a charge configuration to simplify the calculation of electric fields. When charges are arranged in regular shapes like squares, symmetry can help determine which components of the field cancel out and which contribute to the net field, making computational or conceptual insights more accessible.

Integration Techniques

When dealing with continuous charge distributions or extended objects, integration techniques are used to sum the contributions of infinitesimal charge elements to the overall electric field. This method is crucial in applying Coulomb's Law over a region where the charge is distributed non-pointwise, leading to an accurate determination of the field at a given point.

Transcript

00:01 Have a square of side 0 .10 so this is say for example our square and it has sides of 0 .10 and let us draw first of all it's diagonal so this is one diagonal and this is another diagonal of the square okay so now the sides are 0 .10 meter as per the question all the sides are equal to this and the charges are are placed at q1 equals to minus 10 micropulum and here is charge q2 which is also minus 10 microculum and here is charge q4 which is plus 5 microculum and here is charge q3 which is plus 5 microculum okay and we have to calculate the electric field at this point 4 okay this is the center of the square so now the electric field due to this charge q4 will be in this direction away from the charge.

01:02 So e4 and elective field due to this charge q2 will be in this direction.

01:08 So let us suppose this is, sorry, this will be in the opposite direction of because this is negative charge.

01:15 So electric field e2 will also be in this direction e2 and this charge is positive.

01:21 So electric field will be away from the charge so it will be in this direction.

01:25 So let us suppose this is e3 and this charge is negative.

01:28 So, the electric field will be in towards a direction.

01:31 So this is even.

01:32 Okay.

01:33 Now, let us suppose this is point a and this is point b, this is point c and this is point d.

01:40 So we can see that from the properties of square, so oa will be equals to o b equals to oc, this will be equal to od, and this will be equals to 0 .1 .0 multiplied by root 2 divided by 2.

01:54 Okay because this will be the diameter and this is the half of the diameter so it comes out to be 0 .0707 meter now we can see that q3 and q4 charges are equivalent magnitude and the distances are same so lactically due to e3 q3 charge and q4 will be equals to k q3 divided by say this distance is x so x square okay so substituting values we get 9 into 10 to the power 9 multiplied by q3 which is 5 10 to the power minus 6 divided by 0 .07 07 meter whole square okay so after solving this we get this will be equals to this comes out to be a 3 equals to e 4 this will be equals to 0 .9 multiplied by 10 to the power 7 newton per cooler...

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