Question

..In a rectangular coordinate system a positive point charge is placed at the point and an identical point charge is placed at. Find the x- and y-components, the magnitude, and the direction of the electric field at the following points: (a) the origin; (b) (c) (d) .

Short answer

(a)AT Origin the electric field at the origin is zero

(b)AT the electric field is

(c) AT the electric field is = = and and the angle is

(d)AT the electric field is

Step-by-step solution

Step 1:About Electric field magnitude and direction  

Electric field can be considered as an electric property associated with each point in the space where a charge is present in any form. An electric field is also described as the electric force per unit charge.

Direction of the electric field is given by

Plot the Graph

Step 3:Determine the  x- and y-components, the magnitude, and the direction of the electric field

(a) AT Origin

The electric field at the origin is zero because the magnitude of each field is equal but in opposite direction

(b)

Therefore the AT the electric field is

Electric field for the first charge is given by

For the second charge

Now the magnitude is

The fieldcomponentis given by

The total field is

The magnitude is

The angle is

(c) Therefore AT the electric field is = = and and the angle is

(d)

The Electric field component in the horizontal direction will cancel each other but the vertical component are equal in magnitude and same in direction

The magnitude and the direction is given by

Therefore (d)AT the electric field is