Three point charges each of value +q are placed on three vertices of a square of side a metre. W

Three point charges each of value +q are placed on three...

Key Concepts

Vector Addition in Electrostatics

Vector addition involves combining forces that have both magnitude and direction. When multiple charges exert forces on a point charge, each force must be decomposed into its components, and then these components are summed to determine the magnitude and direction of the resultant force. This process is fundamental in calculating net forces in multi-charge systems.

Geometric Analysis in Charge Configurations

Understanding the geometric arrangement of charges is crucial in solving problems involving multiple charges. For instance, in a square configuration, the distances between the centre and the vertices, as well as the directions of the forces, can be determined using basic geometry. This analysis is essential for applying Coulomb's Law and the superposition principle effectively.

Coulomb's Law

Coulomb's Law is the fundamental principle in electrostatics that quantifies the force between two point charges. It states that the magnitude of the electric force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law lays the groundwork for analyzing interactions in any configuration of charges.

Superposition Principle

The superposition principle is a key concept in electromagnetism which states that the net force exerted on a charge by multiple other charges is the vector sum of the individual forces exerted by each charge. This allows for the independent calculation of forces from various charges before summing them to find the total effect.

Transcript

00:01 Question here tells us that we have a square of side length a and then out of the four vertices on three vertices there are positive plus q charges placed okay one vertex is left empty okay and there is one negative minus q point charge placed at the center of the square so we need to find out what will be the force on the minus q charge due to all the three charges at the vertices okay so to solve this question we won't have to do much calculations we'll just solve it via concepts and just a little bit of calculations okay so first look at this i'll show you this okay so let's say this is there is a charge here minus q okay and then let's say there is a charge here minus q okay so when there is there are no other charges except these two then plus q and minus q will have an attractive force and let's say plus q pulls minus q with a force of f okay this distance let's say this distance is a so this will be a force acting on minus q and plus q and let's say plus q is pulling minus q with a force f now what do we do is that we place another charge over here now this is also equal to plus q okay and let's say this distance is also equal to a all right so what will happen is that now this plus q will also pull this minus q charge with force f all right and since both these distances are equal the magnitude of both these forces will also be equal thus here at this point let's say oh the net force will be equal to zero why because both the forces will cancel each other out all right so if you look at this diagram here okay you'll see that in this diagram charge at a is plus q and here at zero it's minus q so this let's say minus q is being pulled towards a okay by plus q similarly here charge at charge at position b there is plus q charge this will also pull okay and then at c it will also pull all right so what will happen is that if you look at this carefully a is pulling b is also pulling and c is also pulling and out of these three a and c are in opposite direction a and c are in opposite direction so what will happen is that force on force at okay i'll just use your act so that you know the possessions force at oh due to a will be equal to force at o due to c thus these forces will cancel each other out in opposite directions so what remains only this force remains okay since there is no opposite forces acting to cancel this force out okay so we just need to find out the force on o due to we just need to find out this force okay so how will we do that first we need to find out this distance we need this distance here okay how do we find this distance out see if this is a square so this is a so by pythagoras theorem we can find this length okay this entire length can be found out ac and since this is a square so ac will be equal to bd the diagonal length if we half this diagonal length that will be equal to exactly this distance okay this is equal to diagonal by two so how do we do that first we will use pythagoras theorem pythagoras theorem here this will be equal to let's say diagonal is equal to diagonal square plus a square so this will be implied diagonal is equal to 2a square this will be equal to root 2 and then so diagonal by 2 will be equal to root 2 by a by 2 so this will be equal to a by root 2.

04:24 This is the distance between point 0 and point b all right so now the force will be equal to k q1 q2 by r square this will be equal to 9 into 10 to the power 9 the charges are plus q and then minus q okay and since force is counted in magnitude so we will just put mod over here and then r square will be equal to a by root 2 and then here we'll have a square so this will be equal to 9 into 10 to the power 9 and then here we will have q square here we will have 2 and then here we will have a square okay so this will be equal to 18 into 10 to the power 9 into q square by a square this will be the net force acting on the center charge minus q due to the arrangement of the three charges at the vertices of a square...

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