Answer:
F = 93.49 × 10^(-9) N
Explanation:
We are given;
Length of rectangle; a = 1.1 m
Width of rectangle; b = 0.9 m
Charge on rectangle; q = 2.3 × 10^(-9) C
Formula for force is;
F = kq²/r²
Where;
k is a constant = 8.99 x 10^(9) N.m²/C²
a) on the width side, we have;
F = [8.99 x 10^(9) × (2.3 × 10^(-9))²]/0.9²
F = 58.79 × 10^(-9) N
This is on the y-axis
b) on the length side, we have;
F = [8.99 x 10^(9) × (2.3 × 10^(-9))²]/1.1²
F = 39.3 × 10^(-9) N
This is on the x-axis
C) using pythagoras theorem, for the diagonal side, we have c² = a² + b².
Thus;
F = [8.99 x 10^(9) × (2.3 × 10^(-9))²]/(1.1² + 0.9²)
F = 23.54 × 10^(-9) N
Using trigonometric ratios, we can find the angle θ.
tan θ = b/a
tan θ = 0.9/1.1
tan θ = 0.8182
θ = tan^(-1) 0.8182
θ = 39.29°
Resolving along x and y axis, we have;
F_x = 23.54 × 10^(-9) × cos 39.29°
F_x = 18.22 × 10^(-9) N
F_y = 23.54 × 10^(-9) × sin 39.29°
F_y = 14.91 × 10^(-9) N
Resultant force will be;
F = √((Σf_x)² + (ΣF_y)²)
F = √[(18.22 × 10^(-9)) + (39.3 × 10^(-9))]² + [(14.91 × 10^(-9)) + (58.79 × 10^(-9))²]
F = √[(33.0855 × 10^(-16)) + (54.317 × 10^(-16))]
F = 93.49 × 10^(-9) N
