Hi, i'm having a lot of trouble with this one. the answer i got to was 407.91 but i'm not confident in it.

6.20×10⁴ V/m

Explanation:

The magnitude of electric field is:

E = √(Eₓ² + Eᵧ²)

where Eₓ = ∂φ/∂x and Eᵧ = ∂φ/∂y.

φ = 1.11 (x² + y²)^-½ − 429x

Eₓ = -0.555 (x² + y²)^-(³/₂) (2x) − 429

Eᵧ = -0.555 (x² + y²)^-(³/₂) (2y)

Evaluating at (0.003, 0.003):

Eₓ = -44034 V/m

Eᵧ = -43605 V/m

The magnitude is:

E = 61971 V/m

Rounded to three significant figures, the strength of the electric field is 6.20×10⁴ V/m.

magnityde and direction