two charge `+q` and `-q` are situated at a certain distance. At the point exactly midway between them

Options

A. Electric filed potential both are zero
B. Electric filed is zero but potential is not zero
C. Electric field is not zero but potential is zero
D. Neither electric filed nor potential is zero

Explanation

To solve the problem of finding the electric field and electric potential at the point exactly midway between two charges \( +q \) and \( -q \), we can follow these steps:

### Step 1: Define the Setup
Assume the two charges \( +q \) and \( -q \) are placed at a distance \( 2a \) apart. Therefore, the distance from each charge to the midpoint \( P \) is \( a \).

### Step 2: Calculate the Electric Field at Point P
The electric field \( E \) due to a point charge is given by the formula:
\[ E = \frac{k |q|}{r^2} \]
where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge to the point of interest.

- **Electric Field due to Charge \( +q \)**:
The electric field at point \( P \) due to charge \( +q \) will be directed away from the charge:
\[ E_{+q} = \frac{kq}{a^2} \quad \text{(to the right, let's assume positive direction)} \]

- **Electric Field due to Charge \( -q \)**:
The electric field at point \( P \) due to charge \( -q \) will be directed towards the charge:
\[ E_{-q} = \frac{kq}{a^2} \quad \text{(to the left, which is negative direction)} \]

### Step 3: Combine the Electric Fields
Since the electric field due to \( +q \) is in the positive direction and the electric field due to \( -q \) is in the negative direction, we can sum them up:
\[ E_{total} = E_{+q} + E_{-q} = \frac{kq}{a^2} - \frac{kq}{a^2} = \frac{kq}{a^2} + \left(-\frac{kq}{a^2}\right) = \frac{2kq}{a^2} \hat{i} \]
Thus, the total electric field at point \( P \) is:
\[ E_{total} = \frac{2kq}{a^2} \hat{i} \]

### Step 4: Calculate the Electric Potential at Point P
The electric potential \( V \) due to a point charge is given by:
\[ V = \frac{kq}{r} \]

- **Potential due to Charge \( +q \)**:
\[ V_{+q} = \frac{kq}{a} \]

- **Potential due to Charge \( -q \)**:
\[ V_{-q} = \frac{-kq}{a} \]

### Step 5: Combine the Potentials
Since electric potential is a scalar quantity, we can simply add the potentials:
\[ V_{total} = V_{+q} + V_{-q} = \frac{kq}{a} + \left(-\frac{kq}{a}\right) = 0 \]

### Conclusion
- The electric field at point \( P \) is \( \frac{2kq}{a^2} \hat{i} \) (non-zero).
- The electric potential at point \( P \) is \( 0 \) (zero).

### Final Answer
- Electric Field: \( \frac{2kq}{a^2} \hat{i} \)
- Electric Potential: \( 0 \)