Three negative point charges lie along a line as shown in the figure. Find the magnitude of the electric field this combination of charges produces at point P, which lies 6.00 cm from the -2.00 μC charge measured perpendicular to the line connecting the three charges. (E = N/C)

   

The problem:

 Three negative point charges lie along a line as shown in Fig. E21.41.Find the magnitude and direction of the electric field this combination of charges produces at point 

P$P$, which lies 6.00 cm from the −$-$2.00-μ$\mu$C charge measured perpendicular to the line connecting the three charges.

The Illustration:

Given:

q1 = q2 = -5.00μC

q3 = -2μC

r1 = 10.00 cm  = 0.1m            r = distance

r3 = 6.00 cm = 0.06m

Couloumb Constant (k) = 9×10⁹ kg⋅m³⋅s⁻²⋅C⁻²

The equation to use: 

Solution

The electric field at P due to q1 and q2 is 

E1 = E2 = k(q1/r12) = 9x109 x (5x10-6 / (0.1)2 = 4.5x106  N/C

The electric field at P due to q3 is

E3 = k(q3/r32) = 9x109 x (2x10-6 / (0.06)2 = 5x106 N/C

cos Θ = 6/10 = 3/5

NET ELECTRIC FIELD

Enet =  2E1(cosΘ) + E3 

      = 2(4.5x106)⅗ + (5x106)

      = 1.04x107 N/C 

To the -2μC charge so to the left