In the figure the particles have charges q1 q2 590 nC and

In the figure, the particles have charges q₁ = -q₂ = 590 nC and q₃ = -q₄ = 98 nC, and distance a = 7.2 cm. What are the (a) x and (b) y components of the net electrostatic force on particle 3?

Solution

force between two charge points = kq1q2 / d^2

force due to 1 on 3 = kq1q3 / a^2 ( -j )

force due to 4 on 3 = kq3q4 / a^2 (i)

force due to 2 on 3 = kq3q2 / (a^2 + a^2) ( i/sqrt(2) + j/sqrt(2)

= kq2q3/2sqrt(2)a^2 (i) + kq2q3/2sqrt(2)a^2 (j)

a) x components = summation of i terms

= kq3q4 / a^2 + kq2q3/2sqrt(2)a^2

=[ ( 9 x 10^9 x 98 x10^-9 x 98 x10^-9) / 0.072^2 ] + [ (9 x10^9 x 590 x 10^-9 x 98 x10^-9)/2sqrt(2)(0.072^2)]

= 0.0167 + 0.0355 = 0.0522 N

b) y components = summation of j terms

= - kq1q3 / a^2 + kq2q3/2sqrt(2)a^2

=-[ ( 9 x 10^9 x 98 x10^-9 x 590 x10^-9) / 0.072^2 ] + [ (9 x10^9 x 590 x 10^-9 x 98 x10^-9)/2sqrt(2)(0.072^2)]

= - 0.1 + 0.0355 =- 0.065 N