# What are the strength and direction of the electric field at the position indicated by the dot in the figure?

#1

What are the strength and direction of the electric field at the position indicated by the dot in the figure ?

1. Specify the strength of the electric field.
2. Specify the angle of the direction.

Concept and reason
The concepts used to solve this problem are electric field due to a point charge, superposition of vectors, and formula for the angle made by the vector.
Need to use the concept of electric field at the given location due to a point charge to find the electric field due to each charge.
And then, the superposition of vectors is to be used to calculate the total strength of the electric field at the given location due to the given system of charges.
The electric field at the given location due to each charge can be expressed as rectangular components
(in x and y-axis directions). These components further used to calculate the x and y-components of the net electric field.

Fundamentals
The magnitude of the electric field E at the given location due to the point charge q is,

Here, k is the constant and r is the distance from the point charge q to the point where the strength of the field is to be found.

(a)
Need to express the electric field due to each charge in vector form.

The following figure shows the location of the charges, the location of the point where the net electric field is to be found, and the direction of the individual electric fields.

From the figure provided in the question, the distance of the position of the point where the electric field is to be found is same for both the charges. Let the distance be r. Thus,

And, the magnitude of the point charge of both the charges is also given same.

The direction of the electric field due to positive point charge is always acts away from the point charge and electric field due to the negative charge acts towards the negative charge.
The electric field is a vector quantity. They cannot be added directly, but can be added vectorially.