In the diagram of two point charges \( +q \) and \( -q \), the potential at point A is given by the formula. Calculate the potential at point A if the distance between the charges is \( 2l \).
Show Hint
To calculate the potential at a point due to multiple charges, sum the individual potentials due to each charge at the point of interest.
Step 1: Understanding the potential formula.
The electric potential at a point due to a point charge is given by:
\[
V = \frac{kq}{r}
\]
where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge. The total potential at point A will be the sum of the potentials due to both charges.
Step 2: Applying the formula for multiple charges.
Using the distances from point A to each of the charges and substituting the appropriate values, the total potential at point A is calculated as:
\[
V_A = \frac{2kg}{l} \left( 1 - \frac{1}{\sqrt{5}} \right)
\]
Step 3: Conclusion.
The correct potential at point A is \( \frac{2kg}{l} \left( 1 - \frac{1}{\sqrt{5}} \right) \), so the correct answer is (A).
