Answer:
To calculate the magnitude of the electric field at the location of q, we need to know the charge density of the square. If we assume that the square is uniformly charged, then the charge density can be calculated as follows:
ρ = Q / A
where ρ is the charge density, Q is the total charge on the square, and A is the area of the square. Since we know that the square is 5.00 cm on a side, its area can be calculated as:
A = (5.00 cm)^2 = 25.00 cm^2
Converting this to meters, we get:
A = (0.0500 m)^2 = 0.00250 m^2
Now, let’s assume that the total charge on the square is Q = 1.00 nC. Then, we can calculate the charge density as:
ρ = (1.00 nC) / (0.00250 m^2) = 4.00 x 10^-7 C/m^2
Using Coulomb’s law and assuming that q is located at the center of the square, we can calculate the magnitude of the electric field at q as follows:
E = k * Q / r^2
where E is the magnitude of the electric field, k is Coulomb’s constant (8.99 x 10^9 N m^2 C^-2), Q is the total charge on the square (1.00 nC), and r is the distance from q to any corner of the square (2.50 cm or 0.0250 m). Substituting these values into the formula, we get:
E = (8.99 x 10^9 N m^2 C^-2) * (1.00 x 10^-9 C) / (0.0250 m)^2 E ≈ 1.44 x 10^6 N/C
Therefore, the magnitude of the electric field at q is approximately 1.44 x 10^6 N/C.