Final answer:
The charge required to create a potential of 95 V at a certain distance can be found using the formula V = k(Q/d), where V is the potential, k is Coulomb's constant, Q is the charge, and d is the distance. Plugging in the given values, we can calculate the required charge.
Step-by-step explanation:
The potential due to a point charge decreases with distance, and the potential at infinity is chosen to be zero. In this case, the potential due to a point charge is 5.00 × 10² V at a distance of 15.0 m. To find the distance at which the potential is 95 V, we can use the formula:
V = k(Q/d)
Where:
- V is the potential (in volts)
- k is the Coulomb's constant (9 × 10^9 Nm²/C²)
- Q is the charge (in coulombs)
- d is the distance (in meters)
Plugging in the given values, we have:
95 = (9 × 10^9)Q/15.0
Simplifying the equation, we find:
Q = (95 × 15.0)/(9 × 10^9) ≈ 1.58333 × 10^-5 C
So, the charge that would result in the potential of 95 V at a distance is approximately 1.58333 × 10^-5 C.