wo charges lie in a line along the x axis. Charge 1 is q1 = 0.65 C and charge 2 is q2 = 2.45 C. They are each a distance of d = 0.021 m from the origin.

Question

Two charges lie in a line along the x axis. Charge 1 is q₁ = 0.65 C and charge 2 is q₂ = 2.45 C. They are each a distance of d = 0.021 m from the origin.

What is the distance on the x-axis from the origin at which the electric field will be zero. Give your answer in meters. 

x_o = ?

Answer 1

Let x₀ be the distance form the origin. Then q1 is at a distance of ..021-x and q2 is a t a distance of .021+ x. For the field to be zero then E₁ = E₂ . Hence q1 / (.021-x₀)² = q2/(.021+x₀)² where q1=.65C and q2=2.45C. So .65/(.021-x₀)²= 2.45/(.021+x₀)². This can be simplified as follows. .65/2.45= .265=(.021-x₀)²/(.021+x₀)². Hence .5148=(.021-x₀)/(.021+x₀). So .0108 +.5148x₀ =.021 - x₀. Solving for x₀ gives 1.5148x₀ = .0102 and x₀= .0067m.