Two unlike charges of magnitude `q` are separated by a distance `2d`. The potential at a point midway between them is

Options

A. zero
B. `(1)/(4 pi epsilon_(0))`
C. `(1)/(4 pi epsilon_(0)).(q)/(d)`
D. `(1)/(4 pi epsilon_(0)).(2q)/(d)`

Answer

To find the electric potential at the midpoint between two unlike charges of equal magnitude \( q \) separated by a distance \( 2d \), we can follow these steps:

### Step 1: Identify the Charges and Their Positions
Let’s denote the two charges:
- Charge \( +q \) is located at point A (let's say at position \( -d \)).
- Charge \( -q \) is located at point B (let's say at position \( +d \)).
The distance between the two charges is \( 2d \).

### Step 2: Determine the Midpoint
The midpoint \( O \) between the two charges is at the origin (0,0).

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

#### Contribution from Charge \( +q \):
- The distance from charge \( +q \) to point \( O \) is \( d \).
- The potential at point \( O \) due to charge \( +q \) is:
\[ V_1 = \frac{kq}{d} \]

#### Contribution from Charge \( -q \):
- The distance from charge \( -q \) to point \( O \) is also \( d \).
- The potential at point \( O \) due to charge \( -q \) is:
\[ V_2 = \frac{-kq}{d} \]

### Step 4: Combine the Potentials
Now, we can find the total potential \( V \) at point \( O \) by adding the contributions from both charges:
\[ V = V_1 + V_2 = \frac{kq}{d} + \left(-\frac{kq}{d}\right) = \frac{kq}{d} - \frac{kq}{d} = 0 \]

### Conclusion
The total electric potential at the midpoint \( O \) between the two unlike charges is:
\[ \boxed{0} \]