Question

A point charge q1 = 4.00 nC is placed at the origin, and a second point charge q2 = -2.90 nC is placed on the x -axis at x=+ 21.0 cm . A third point charge q3 = 2.00 nC is to be placed on the x -axis between q1 and q2 . (Take as zero the potential energy of the three charges when they are infinitely far apart.)

Where should q3 be placed between q1 and q2 to make the potential energy of the system equal to zero?

Answer 1

A point charge q1 = 4.00 nC is placed at the origin,

and

a second point charge q2 = -2.90 nC is placed on the x -axis at x=+ 21.0 cm

A third point charge q3 = 2.00 nC

the potential energy is

V = Kq₁q₂ / r₁₂ + Kq₃q₂ / r₃₂ + Kq₁q₃ / r₁₃ = 0

V = 9 X 10⁹ ( 4 X 10^-9 X (-2.9) X 10^-9 / 21 X 10^-2 + 2 X 10^-9 X (-2.9) X 10^-9 / ( 21 - x ) X 10^-2 + 4 X 10^-9 X 2 X 10^-9 / x X 10^-2 ) = 0

V = [ ( - 11.6 / 21 ) + ( - 5.8 / 21 - x ) + 8 / x ] = 0

0.55 + 5.8 / (21-x) -8/x = 0

0.55 ( 21 - x ) x + 5.8 x - 8 X ( 21 - x ) = 0

11.55 x - 0.55x² + 5.8 x - 168 + 8x = 0

0.55x² - 25.35 x +168 = 0

x = 51.96 and -5.87 cm

x = - 5.87 cm will be equal to zero