Final answer:
The magnitude and sign of a point charge are determined from the electric potential using the formula V = k*q/r. Given the potential of 5.00 x 10² V at a distance of 15.0 m, and knowing the potential is positive, the charge is positive and its magnitude can be calculated by rearranging the formula.
Step-by-step explanation:
To find the magnitude and sign of a point charge from its electric potential, one can use the formula for electric potential due to a point charge, which is V = k*q/r, where V is the electric potential, k is Coulomb's constant (8.99 x 109 Nm2/C2), q is the charge, and r is the distance from the charge. Inserting the given values, V = 5.00 x 102 V and r = 15.0 m, we can rearrange the equation to solve for q: q = V*r/k.
Therefore, the magnitude of the charge (q) is calculated as:
q = (5.00 x 102 V * 15.0 m) / (8.99 x 109 Nm2/C2)
Once the magnitude is calculated, the sign of the charge depends on whether the potential is positive (indicating a positive charge) or negative (indicating a negative charge). In this case, as the potential is positive, the charge would also be positive.