Final answer:
To calculate the energy needed to position three 2.0µC charges at the corners of a 2.0 cm equilateral triangle, we use the formula for electric potential energy and consider the charges pairwise, with Coulomb's constant and conversions for units.
Step-by-step explanation:
To calculate the energy needed to place three charges, each being 2.0µC, at the corners of an equilateral triangle with sides of 2.0 cm, we can use the formula for the electric potential energy due to point charges. The electric potential energy (U) between two point charges is given by:
U = k × q1 × q2 / r
where k is Coulomb's constant (≈9.0 × 109 N·m2/C2), q1 and q2 are the magnitudes of the charges, and r is the separation between the charges.
Since we have an equilateral triangle, the distances between each pair of charges are equal. For three charges, we have three pairs. Thus, the total potential energy will be three times the potential energy between one pair of charges:
Utotal = 3 × (k × q² / r)
Plugging in the values, we have:
Utotal = 3 × (8.99 × 109 N·m2/C2 ×(2.0 × 10-6 C)² / 0.02 m)
Simplifying, we can calculate the energy required. Remember that the charges are in µC and distances in cm, so we convert units as needed.