The electric potential (\( V_P \)) at a point \( P \) due to a point charge is calculated using the formula:
\[V_P = \frac{KQ}{r}\]
The constants and variables are defined as:
\( K = \frac{1}{4\pi \epsilon_0} = 9 \times 10^9 \, {Nm}^2{C}^{-2} \) (Coulomb's constant)
\( Q = 5 \times 10^{-9} \, {C} \) (the point charge)
\( r \) (the distance from the charge to point \( P \))
\( V_P = 50 \, {V} \) (the electric potential at point \( P \))
To find the distance \( r \), the formula is rearranged:
\[r = \frac{KQ}{V_P}\]
Substituting the given values:
\[r = \frac{(9 \times 10^9) \times (5 \times 10^{-9})}{50}\]
Performing the calculation:
\[r = \frac{45 \times 10^0}{50}\]
\[r = 0.9 \, {m}\]
Therefore, point \( P \) is located 0.9 meters (or 90 cm) from the point charge.