Question

A 7.7 μC charge is at x1 = 17 cm , y1 = 8.0 cm and a -4.6 μC charge is at x2 = 4.3 cm , y2 = 12 cm .

Find the force on the negative charge.

Express your answer using two significant figures. Enter the answer in the indicated order separated with a comma.

Answer 1

A)

q = 7.7 x 10^-6 C

r = distance of the point from origin = sqrt (X₁² + Y₁²) = sqrt ((0.17)² + (0.08)²) = 0.18 m

Electric field is given as

E = k q /r² = (9 x 10⁹) (7.7 x 10^-6 )/ (0.18)² = 2.13 x 10⁶ N/C

= tan^-1(Y₁/X₁) = tan^-1(0.08/0.17) = 25.2

E_x = E Cos25.2 = 1.92 x 10⁶ N/C

E_y = E Sin25,2 = 0.906x 10⁶ N/C

B)

q = -4.6 x 10^-6 C

r = distance of the point from origin = sqrt (X₂² + Y₂²) = sqrt ((0.043)² + (0.12)²) = 0.127 m

Electric field is given as

E = k q /r² = (9 x 10⁹) (-4.6 x 10^-6 )/ (0.127)² = -2.56 x 10⁶ N/C

= tan^-1(Y₂/X₂) = tan^-1(0.12/0.043) = 70.2  

E_x = - E Cos70.2 = -0.8671x 10⁶ N/C

E_y = E Sin70.2 = -2.4 x 10⁶ N/C