Answer:
To solve this problem, we need to use the formulas for electric field and electric potential due to a point charge.
The electric field E due to a point charge is given by:
E = kQ/r²
where:
E is the electric field,
k is Coulomb's constant (8.99 × 10⁹ N m²/C²),
Q is the charge, and
r is the distance from the charge.
The electric potential V due to a point charge is given by:
V = kQ/r
where:
V is the electric potential,
k is Coulomb's constant (8.99 × 10⁹ N m²/C²),
Q is the charge, and
r is the distance from the charge.
Electric Field Calculation
Let's calculate the electric field at the bottom left corner due to each charge:
Electric field due to charge 1 (E₁):
E₁ = kQ₁/r₁²
E₁ = (8.99 × 10⁹ N m²/C²) * (4.00 × 10−2 C) / (2.00 m)²
Electric field due to charge 2 (E₂):
E₂ = kQ₂/r₂²
E₂ = (8.99 × 10⁹ N m²/C²) * (-3.00 × 10−2 C) / (2.00 m)²
Electric field due to charge 3 (E₃):
E₃ = kQ₃/r₃²
E₃ = (8.99 × 10⁹ N m²/C²) * (-1.00 × 10−2 C) / (2.00 m)²
The total electric field E at the bottom left corner is the vector sum of E₁, E₂, and E₃.
Electric Potential Calculation
Let's calculate the electric potential at the bottom left corner due to each charge:
Electric potential due to charge 1 (V₁):
V₁ = kQ₁/r₁
V₁ = (8.99 × 10⁹ N m²/C²) * (4.00 × 10−2 C) / (2.00 m)
Electric potential due to charge 2 (V₂):
V₂ = kQ₂/r₂
V₂ = (8.99 × 10⁹ N m²/C²) * (-3.00 × 10−2 C) / (2.00 m)
Electric potential due to charge 3 (V₃):
V₃ = kQ₃/r₃
V₃ = (8.99 × 10⁹ N m²/C²) * (-1.00 × 10−2 C) / (2.00 m)
The total electric potential V at the bottom left corner is the sum of V₁, V₂, and V₃.
Please note that the distances r₁, r₂, and r₃ are the distances from each charge to the bottom left corner of the square. You may need to use the Pythagorean theorem to calculate these distances if they are not along the same axis.