What is the force F⃗ on the 1.0 nC charge in the middle of...

Key Concepts

Superposition Principle

The Superposition Principle states that when multiple charges exert forces in a region, the total force on any given charge is the vector sum of the forces exerted by each of the other charges individually. This principle allows one to calculate the net force by computing and then adding together all individual forces.

Vector Decomposition and Addition

Since forces are vector quantities having both magnitude and direction, it is often necessary to break them into components, typically along the x and y axes, to properly account for their directional nature. Once forces are decomposed into their components, vector addition is used to sum these components to obtain the net force on a charge.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges. The force is directly proportional to the product of the charge magnitudes and inversely proportional to the square of the distance between them. This law provides the fundamental equation used to calculate the forces between individual pairs of charges.

Transcript

00:01 Hi, here in this given problem first of all this is the square structure, each side of this is square that is 1 .0 centimeter and there are 4 charges kept at its 4 vertices.

00:24 Suppose this is vertex a, a charge of minus 2 .0 nano coulomb kept over it.

00:30 This is vertex b, having a charge of plus 2 .0 nano coulomb kept over it.

00:38 Vertex c, this is also having a positive charge 2 .0 nano coulomb and finally vertex d, negative charge minus 2 .0 nano coulomb.

00:55 Then a charge, another charge, fifth charge is kept at its center and that is 1 .0 nano coulomb.

01:05 We have to find the magnitude and direction of the net force acting over this 1 .0 nano coulomb charge.

01:13 This is the center o.

01:15 So it will be having 4 forces acting on it due to the 4 charges.

01:21 So starting from this minus 2 .0 nano coulomb kept at a as this, the charge that is positive.

01:30 So it will be attracted by a force f oa due to a and then due to c it will be repelled in the same direction like this.

01:41 So this is f at o due to c.

01:45 Now due to minus 2 also it will be attracted towards d, f at o due to d and due to b positive it will be repelled f at o due to b.

02:00 Now r means distance of all the vertices from the center.

02:07 This distance will be given by the half of length of diagonal.

02:15 Diagonal that is given as side multiplied by root 2 divided by 2.

02:21 So the side that is 1 .0 cm into root 2 divided by 2 calculated to be equal to 0 .707 cm...

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