Electric Fields and Forces

Question

A charge of -6.4 μC is fixed on the x axis at the x=-4.0 m, while a charge of +1.6 μC is fixed at the origin

 

Which points on the x axis at which the net electric field is zero?

Answer 1

At the point x where the field is zero, the fields from the 2 source charges must be equal and opposite, so their magnitudes must the same.

 

(E1):    k|q₁|/(x - x₁)² = k|q₂|/(x - x₂)²

 

|q₁| = 6.4 μC

|q₂| = 1.6 μC

x₁ = -4.0

x₂ = 0

 

Plug into equation (E1) and simplify.

 

6.4/(x + 4)² = 1.6/x²

 

x² + 8x + 16 = 4x²

 

-3x² + 8x + 16 = 0

 

x = 4m

or

x ≅ -1.33 m

 

Note that a solution of -1.33 m is not physically possible, since that would place the test charge in between 2 source charges of opposite signs, which will always result in a net electric force on the test charge.  Therefore, the only solution must be

 

x = 4m.