For what finite value of x is the electric field zero?

[Calcguy]

Homework Statement

A charge +q is at the origin. A charge -2q is at x = 1.60 m on the +x axis.
(a) For what finite value of x is the electric field zero?

Homework Equations

The Attempt at a Solution

I got -3.2m, but its wrong.

HELP!

 

[LowlyPion]

Homework Statement

A charge +q is at the origin. A charge -2q is at x = 1.60 m on the +x axis.
(a) For what finite value of x is the electric field zero?

Homework Equations

The Attempt at a Solution

I got -3.2m, but its wrong.

HELP!

Why don't you show the equation that gave that to you? I think there is just a simple mistake.

 

[baba89]

The electric field at a point is given by the equation E = kq/r^2, where k is the Coulomb's constant, q is the charge, and r is the distance between the two charges. In this scenario, we have a positive charge q at the origin and a negative charge -2q at x = 1.60 m.

To find the point where the electric field is zero, we can set E = 0 in the equation and solve for x.

0 = kq/(x^2) - k(-2q)/(1.60 - x)^2

Simplifying this equation, we get 0 = kq[(1.60 - x)^2 - 4x^2]

Expanding the squared terms and rearranging, we get 0 = -3.2x^2 + 8.32x - 3.2

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac))/2a

Where a = -3.2, b = 8.32, and c = -3.2

Plugging in these values, we get x = 1.6 m or x = -0.5 m

Since a negative distance does not make sense in this scenario, the only valid solution is x = 1.6 m.

Therefore, at a distance of 1.6 m from the origin, the electric field will be zero.