Eight Charges In Fig. 23-36, eight charged particles form a square array; charge q=e and distanc

step 1 Hi, there is a square in the given problem. Here it is like this. And eight different charges ar

Eight Charges In Fig. 23-36, eight charged particles form a...

Key Concepts

Coulomb's Law

Coulomb's Law is used to calculate the electric field due to a point charge, stating that the magnitude of the field is proportional to the charge and inversely proportional to the square of the distance from the charge. This law is essential when determining the effect each charge has at a specific point.

Principle of Superposition

The principle of superposition asserts that the total electric field generated by multiple charges is the vector sum of the electric fields produced by each individual charge. This method is crucial for solving problems involving several charges as it allows the field contributions to be added together.

Vector Addition

Since the electric field is a vector quantity, its calculation involves both magnitude and direction. Therefore, adding the fields from various charges requires careful vector addition, taking into account both their magnitudes and directions to determine the net field.

Symmetry

Symmetry in the configuration of charges can simplify the analysis of the electric field. When charges are symmetrically arranged, certain components of the electric field may cancel out, reducing the complexity of the calculation and helping to identify the net direction of the field.

Transcript

00:02 Hi, there is a square in the given problem.

00:07 Here it is like this.

00:10 And eight different charges are arranged over it.

00:16 First of all, suppose it is named as a, b, c and d, and the midpoints of its sides are named as e, f, and and g and h.

00:42 Now the charges put over there are, first of all, this is plus 3 q at a, then here this is plus q.

00:55 At f, at b, this is minus 5q.

01:01 At g this is minus 2 q at c this is plus 3 q at h this is plus q at d this is minus 5 q and at e this is just plus q now we have to find net electric field at the center of this square and we know the center means the point of intersection of its diagonals here.

01:41 So if we find net electric field here at this point, so there are various electric fields due to all these various charges.

01:52 So using the rule that electric field always goes away from the positive charge and approaches the negative charge.

01:59 First of all, electric field at this center due to the charge put at a, that will be going away like this and due to that put at c and that is the same charge so it will also be going away.

02:15 So these two electric fields which are named as ea and e c as the distance of this center from all the vertices is the same.

02:26 So we can say e a is equal to ec and directed opposite to each other so they cancel out now we look for the electric fields at the same center due to the charge put at b and that is towards the negative charge here and similarly due to that put at d that will also be directed towards the negative charge and these these two electric fields are e b and e d.

03:13 Here again as the charges are same and the distance is also same.

03:17 So e b is equal to e d and directed opposite.

03:31 So they also cancel out.

03:40 And this we are using, we are doing using the expression for electric field.

03:45 We should also mention it here...

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