Question

Two point charges sit along the x-axis. Charge A is qA =-100 nC and sits at the origin. Charge B is qB =-50 nC and is positioned at +0.25 m on the x-axis. At what point on the x-axis is the electric field zero? x 0.146 At what point on the x-axis is the electric potential zero? X-0167

Answer 1

a )

using equation

E = k Q / x²

so now

k Q₁ / x₁² = k Q₂ / x₂²

k Q₁ / x² = k Q₂ / ( x - 0.25 )²

Q₁ / x² = Q₂ / ( x - 0.25 )²

100 x 10^-9 / x² = 50 x 10^-9 / ( x - 0.25 )²

2 / x² = 1 / ( x - 0.25 )²

( x - 0.25 ) / x = 0.5^1/2

0.25/x = 1 - 0.5^1/2

= 0.2928

x = 0.25 / 0.2928

x = 0.8538 m

b )

V₁ + V₂ = 0

Q₁ / x + Q₂ / ( x - 0.25 ) = 0

- 100 x 10^-9 / x = 50 x 10^-9 / ( x - 0.25 )

- 2 / x = 1 / ( x - 0.25 )

x = - 2 x + 0.5

3 x = 0.5

x = 0.16666667

x = 0.167 m