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Three point charges are positioned as follows: a positive charge +q is located on the x-axis at the point (b, 0), a negative charge -2q is located on the x-axis at the point (-2b, 0), and the third, a positive point charge +q/3 is located at the point (-2/3b, -1/3b). What is the symbolic expression for the electric field at the origin due to this system of point charges, in terms of k e, q and b and what is the magnitude of the electric field at the origin? To answer this question, please go through the following steps: To begin, carefully draw the three electric field vectors originating from the origin: the contribution to the net electric field from each of the three source charges. Consider: what information do you need to find the x and y-components of each of these three vectors?

Respuesta :

Answer:

 Ex = k q / b2 [- ¾] ,   Ey = k q / b2 3

Explanation:

For this exercise we calculate the electric field created by each load on a test charge located at the origin

Field created by load q = + q

        E₁ = k q / r²

        r = b-0

        E₁ = k q / b²

in the negative direction of the x axis

Field created by load q = -2q

         E₂ = k (2q) / (2b-0)₂

         E₂ = K q / 2b₂

The field is in the negative direction of the x-axis

Field created by charge q = + q / 3

this charge creates a field that has components on the x and y axes

X axis

        E3x = K (q / 3) / (2b / 3) 2

         E3x = K q 3 / 4b²

as the charge is on the negative side of the x axis. The field goes to the bright side

Axis y

            E3y = k (q / 3) / (b / 3) 2

            E3y = k q / b²

directed up

therefore the electric field is the sum of the field created by each charge

X axis

          Ex = -E1 + E2 + E3x

          Ex = -k q / b2 - k q / 2b2 + k q 3 / 4b2

          Ex = k q / b2 [-1 -1/2 + ¾]

          Ex = k q / b2 [- ¾]

Axis y

          Ey = k q / b2 3