Electric Charges and Fields

1.6

In the adjoining figure ABCD is a square with sides AB = BC = CD = DA = 10 cm

Diagonals, AC = BD  = $\sqrt[]{{10}^2+{10}^2}$ = $10\sqrt[]{2}$cm

AO = OC = DO = BO = $5\sqrt[]{2}$ cm

At the centre of the square ABCD, O, a charge of 1 $\mu Cisplaced.$$\text{exception 25:}$

The force of repulsion between the charges placed at A and at O is equal in magnitude but opposite in direction between the charges placed at point C and centre O. Similarly ,the force of attraction between the charges placed at B & O and D & O will be equal in magnitude but opposite in direction. These charges will cancel each other.

Hence, the net charge at centre O will be zero.

Here is a deeper explanation. 

What you just saw is the use of the superposition principle. The total force on the 1 μC charge at the centre (O) is the vector sum of the forces from each of the four corner charges. 

Pairs can break down the analysis. 

• Forces from qA and qC: The force exerted by qA (+2 μC) on the central charge is repulsive. The force from qC (+2 μC) is also repulsive. Now, since qA and qC are equal and are at an equal distance from the centre, the forces they exert are equal in magnitude. But they point in opposite directions along the diagonal AC. So, they cancel each other out.

• Forces from qB and qD: Similarly, the force exerted by qB (–5 μC) is attractive, and the force from qD (–5 μC) is also attractive. Because these charges are equal and equidistant from the centre, the forces are equal in magnitude but opposite in direction along the diagonal BD. That causes them to cancel out as well.

As both pairs of forces nullify each other, the net electrostatic force on the central charge is zero. Read more about Coulomb's Law

A region around a charged object, where another object experiences a force is called an electric field. The formula is - E = F / q? where E is the electric field at a point, q? is the small positive test charge placed at that point, and F is the force experienced by q?
The electric field is a vector quantity that has both magnitude and direction. The electric fields are visually represented by the electric field lines. The electric field starts with positive charges and ends with negative charges. The field's strength is indicated by the density of the field lines. The electric fields can be measured in V/m (volts per meter) and N/C (newtons per coulomb).

According to Shiksha's electric charges and fields class 12 notes, Coulomb's law states that if there are two stationary point charges, the electrostatic force between them is inversely proportional to the square of the distance between them and directly proportional to the product of the charges.
Mathematically,
F = (1 / 4? ) * (q? / r²)
Here r is the distance between the charges, q? and q? are charges and? is the permittivity of free space. Coulomb's law assumes charges are at rest and it is valid for point charges in vacuum or air. When the medium is not a vacuum and the charges are moving, the limitations include inaccuracy. This law cannot be applied without modifications to the extended bodies.