What are the sign and magnitude of a point charge that produces a potential of -6.00 V at a distance of 1.00 mm? Provide the solution: _________₁0⁻¹³ C
a) Negative sign, magnitude of 6.00 10⁻¹³ C
b) Positive sign, magnitude of 6.00 10⁻¹³ C
c) Negative sign, magnitude of -6.00 10⁻¹³ C
d) Positive sign, magnitude of -6.00 10⁻¹³ C

The point charge has a negative sign and a magnitude of approximately 6.67 × 10⁻¹³ C. This is calculated using Coulomb's law, and by recognizing that a negative potential indicates a negative charge.The correct option is a.

Explanation:

The question is asking to determine the sign and magnitude of a point charge that results in an electric potential of -6.00 V at a distance of 1.00 mm. The electric potential (V) created by a point charge (q) at a distance (r) from the charge is given by the formula V = kq/r, where k is Coulomb's constant (approximately 8.99 × 109 N·m2/C2). Since the potential is negative, the point charge must be negative as well. The magnitude of the charge can be calculated by q = Vr/k. Thus, we have:

q = (-6.00 V * 1.00 × 10-3 m) / (8.99 × 109 N·m2/C2)

The magnitude of the charge is:

q ≈ 6.67 × 10-13 C

Therefore, the charge has a negative sign, and its magnitude is 6.67 × 10-13 C. Option 'a' is the correct answer because magnitude should always be reported as a positive quantity.