Question

Four charges +q, +2q, +q and -2q are placed at the corner of square ABCD respectively. The force on unit positive charge kept at the centre 'O' is

• A. along the diagonal AC
• B. Zero
• C. perpendicular to AD
• D. along the diagonal BD

Answer 1

Answer: (D)

along the diagonal BD

Answer 2

Let's denote the charges as follows:
+q is at corner A,
+2q is at corner B,
+q is at corner C,
-2q is at corner D.
The force between two charges is given by Coulomb's law:
F = (k * |q1 * q2|) / r2
Now, let's analyze the forces exerted by each charge individually on the unit positive charge at O.
Force exerted by +q at A:
The force will be attractive and directed along the line AO, from A to O.
Force exerted by +2q at B:
The force will be attractive and directed along the line BO, from B to O.
Force exerted by +q at C: The force will be attractive and directed along the line CO, from C to O.
Force exerted by -2q at D:
The force will be repulsive and directed along the line DO, from D to O.
Since the charges at A, B, and C are positive, they attract the unit positive charge at O. On the other hand, the charge at D is negative and repels the unit positive charge.
Considering the geometry of the square, we can see that the forces along the lines AO, BO, and CO have equal magnitudes. The force along the line DO has a different magnitude but opposite direction.
The forces along the lines AO, BO, and CO are mutually perpendicular because they are directed towards the center of a square.
When we add these forces vectorially, the forces along AO, BO, and CO will cancel out each other due to their equal magnitudes and perpendicular directions. The force along the line DO will not cancel out completely but will have a net component along the diagonal BD.
Therefore, the net force on the unit positive charge at the center 'O' is along the diagonal BD (option D).