Four charges `+Q, -Q, +Q, -Q` are placed at the corners of a square taken in order. At the centre of the square

Options

A. `E = 0, V = 0`
B. `E = 0, V != 0`
C. `E != 0, V = 0`
D. `E = 0, V != 0`

Explanation

To solve the problem of finding the electric field and electric potential at the center of a square with charges +Q, -Q, +Q, and -Q placed at its corners, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Configuration**:
- We have a square with charges placed at its corners in the following order: +Q (top left), -Q (top right), +Q (bottom right), -Q (bottom left).

2. **Determine the Position of the Center**:
- The center of the square is equidistant from all four charges. Let the distance from the center to any corner of the square be denoted as \( r \).

3. **Calculate the Electric Field Due to Each Charge**:
- The electric field \( E \) due to a point charge \( Q \) at a distance \( r \) is given by the formula:
\[ E = \frac{k |Q|}{r^2} \]
- Here, \( k \) is Coulomb's constant.

4. **Direction of Electric Fields**:
- The electric field due to the positive charges (+Q) will point away from the charge, while the electric field due to the negative charges (-Q) will point towards the charge.

5. **Calculate the Electric Field at the Center**:
- For the two positive charges (+Q), the electric fields at the center will be directed towards the center from the respective corners, and they will cancel each other out due to symmetry.
- Similarly, for the two negative charges (-Q), their electric fields will also cancel each other out due to symmetry.

6. **Net Electric Field**:
- Since the electric fields from the positive charges cancel the electric fields from the negative charges, the net electric field at the center of the square is:
\[ E_{\text{net}} = 0 \]

7. **Calculate the Electric Potential at the Center**:
- The electric potential \( V \) at a point due to a charge \( Q \) is given by:
\[ V = \frac{kQ}{r} \]
- The total potential at the center due to all four charges is:
\[ V_{\text{total}} = V_{+Q1} + V_{-Q2} + V_{+Q3} + V_{-Q4} \]
- Substituting the values:
\[ V_{\text{total}} = \frac{kQ}{r} + \frac{-kQ}{r} + \frac{kQ}{r} + \frac{-kQ}{r} \]
- This simplifies to:
\[ V_{\text{total}} = 0 \]

8. **Conclusion**:
- The electric field at the center of the square is zero, and the electric potential at the center is also zero.

### Final Answer:
- The electric field at the center is \( 0 \) and the electric potential at the center is \( 0 \).