Four charges 2C, – 3C, –4C and 5C respectively are placed at all the corners of a square. Which of the following statements is true for the point of intersection of the diagonals?

Options

A. Electric field is zero but electric potential is non-zero
B. Electric field is non-zero but electric potential is zero
C. Both electric field and electric potential are zero
D. Neither electric field nor electric potential is zero

Answer

To solve the problem step by step, we will analyze the electric field and electric potential at the point of intersection of the diagonals of the square formed by the charges.

### Step 1: Understand the Configuration of Charges
We have four charges placed at the corners of a square:
- Charge at corner A: \( +2C \)
- Charge at corner B: \( -3C \)
- Charge at corner C: \( -4C \)
- Charge at corner D: \( +5C \)

### Step 2: Determine the Position of the Point of Interest
The point of intersection of the diagonals of the square is the center of the square, which we will denote as point O.

### Step 3: Calculate Electric Potential at Point O
The electric potential \( V \) at a point due to a point charge is given by the formula:
\[ V = k \cdot \frac{q}{r} \]
where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge to the point.

Since point O is equidistant from all four charges, we can denote the distance from each charge to point O as \( L \).

The total electric potential at point O is the algebraic sum of the potentials due to each charge:
\[ V_O = k \left( \frac{2}{L} + \frac{-3}{L} + \frac{-4}{L} + \frac{5}{L} \right) \]
\[ V_O = k \left( \frac{2 - 3 - 4 + 5}{L} \right) \]
\[ V_O = k \left( \frac{0}{L} \right) = 0 \]

### Step 4: Calculate Electric Field at Point O
The electric field \( E \) due to a point charge is a vector quantity given by:
\[ E = k \cdot \frac{q}{r^2} \]
The direction of the electric field is away from positive charges and towards negative charges.

To find the resultant electric field at point O, we need to consider the contributions from each charge:
- The electric field due to \( +2C \) is directed away from it.
- The electric field due to \( -3C \) is directed towards it.
- The electric field due to \( -4C \) is directed towards it.
- The electric field due to \( +5C \) is directed away from it.

Since the charges have different magnitudes, the resultant electric field will not be zero. The contributions from the charges will not cancel out completely due to their different magnitudes and directions.

### Conclusion
- The electric potential at point O is \( 0 \).
- The electric field at point O is not \( 0 \).

Thus, the correct statement is that the electric field is non-zero while the electric potential is zero.

### Final Answer
The correct option is: **Electric field is non-zero but electric potential is zero.**