**Field at the Centre of a Regular Polygon**

To find the electric field at the center of a regular polygon, we can consider the electric field contribution from each charge at the corners of the polygon.

**Electric Field Contribution from each Charge**

The electric field contribution from each charge at the corners of the polygon can be calculated using Coulomb's Law. Coulomb's Law states that the magnitude of the electric field due to a point charge is given by:

E = k * Q / r^2

where E is the electric field, k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2), Q is the magnitude of the charge, and r is the distance between the charge and the point where the electric field is being measured.

**Electric Field from each Corner**

In a regular polygon of n sides, each corner is at a distance r from the center. Identical charges of magnitude Q are placed at (n-1) corners. Therefore, the electric field contribution from each charge at the corners can be given as:

E = k * Q / r^2

Since there are (n-1) charges at the corners, the total electric field at the center can be calculated by considering the vector sum of the electric field contributions from each charge.

**Vector Sum of Electric Fields**

Since the charges are placed at the corners of the polygon, their positions can be represented as vectors. Let's denote the position vector of each charge as r_i, where i ranges from 1 to (n-1).

To calculate the total electric field at the center, we need to calculate the vector sum of the electric field contributions from each charge. This can be done by summing up the individual electric field vectors.

E_total = E_1 + E_2 + ... + E_(n-1)

**Magnitude of Total Electric Field**

The magnitude of the total electric field at the center can be calculated by taking the magnitude of the vector sum.

|E_total| = |E_1 + E_2 + ... + E_(n-1)|

Since the charges are placed symmetrically at the corners of the regular polygon, the electric field contributions from each charge will cancel out in pairs. This is because the electric field vectors from opposite charges will have equal magnitudes but opposite directions.

Therefore, the magnitude of the total electric field at the center of the regular polygon will be zero.