. Point charges q1 = q2 = 4.0 × 10−6 C are fixed on the x-axis at x = −3.0 m and x = 3.0 m. What charge q must be placed at the origin so that the electric field vanishes at x = 0, y = 3.0 m?

Explanation:

Electric Field

The total electric field is the sum of all the individual electric fields produced by each charge. Please refer to the image below. The charges q1 and q2 produce the electric fields shown in the point (0,3). Since both charges are equal in magnitude and sign and are at the same distance from the point, the horizontal component of their electric fields cancel each other, only the vertical component remains and it's directed upwards.

The third charge q3 must be negative, so the total electric field is zero. Let's first compute the value of the angle by analyzing the distances in the right triangle formed by the charges q1, q2, and the point (0,3)

It follows that

The distance from q1 (or q2) to the point (0,3) is computed by

Let's compute the magnitude of the electric of q1 or q2:

The vertical component of both fields is given by

The total field produced by q1 and q2 is twice that quantity

That should be the value of E3 to make the total field vanish (equal to 0)

Solving for q3

We had already established the sign of q3 must be negative

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force