Two small beads having positive charges q1 28q and q2 q ar

Two small beads having positive charges q_1 = 28q and q_2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.50 m. The bead with charge q_1 is at the origin. As shown in the figure below, a third small, charged bead is free to slide on the rod. At what position x is the third bead in equilibrium?

Solution

Distance from q1 to Q = x

Force on Q due to q₁ = k * 28 q * Q/ x²

Distance from q₂ to Q = 1.5 - x

Force on Q due to q₂ = k q Q / (1.5 - x )²

k * 28 q * Q/ x² = k q Q / (1.5 - x )²

28 / x² = 1 / (1.5 - x )²

Square root both sides , 5.29 / x = 1 / (1.5 - x )

5.29 ( 1.5 - x ) = x

7.94 - 5.29 x = x

6.29 x = 7.94

x = 1.26 m