To practice Problem-Solving Strategy 21.2 Electric-Field Calculations. Three pos

Question

To practice Problem-Solving Strategy 21.2 Electric-Field Calculations. Three positive point charges (Figure 1) are spaced equally along the y axis (x = 0), q_1 = 3.50 nC at y = +8.00 cm, q_2 = 3.50 nC at y = 0, and q_3 = 3.50 nC at y = -8.00 cm. Find the x and y components of the total electric field E_x and E_y at point P, which is located on the x axis at x = 6.00 cm. Find the x and y components of the total electric field at point P, which is located on the x axis at x = 6.00 cm. Enter the values for E_x and E_y in newtons per coulomb separated by commas. E_x, E_y = (1.52, 0) N/C

Explanation / Answer

Given, q1 = 3.5 nC = 3.5*10^-9 C at y = 0.08 m
q2 = 3.5 nC at y = 0
q3 = 3.5 nC at y = -0.08 m
Coordinates of P = (0.06,0) m

now from summetry, the y component of electric field has top be 0 as the top and bottom chasrgesd apply same field in opposite directions at point P in y diurection and they both cancel each other out, the x components adds up

so Ey = 0
Ex = 2*kq1*0.06/(0.08^2 + 0.06^2)^3/2 + kq2/0.06^2 = 8.98[2*3.5*0.06/(0.08^2 + 0.06^2)^3/2 + 3.5/0.06^2] = 12502.155 V/m

so (Ex,Ey) = (12502.155 , 0) V/m

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