Four allude charges are at the corners of a square of side a as displayed in Figure P15.8. Determine the magnitude and direction of the resultant electric pressure on q, via ke, q, and a left in symbolic create.

You are watching: Four point charges are at the corners of a square of side a

The electrical field as a result of a suggest charge at a distance

is,

Here

is the Coulomb’s continuous,
is the charge of the allude charge, and
is the distance from the allude charge to the area point.

The arrangement of charges is presented in the listed below figure.

The electrical area at allude

as a result of the charge
along the horizontal axis is,

Here,

is the distance of allude
from the charge
.

The electric field at point

as a result of charge
alengthy the horizontal direction is,

Here,

is equal to the size of the diagonal of the square. That is,
is the distance of the point
from the charge
.

The electric area at suggest

due to charge
alengthy the vertical direction is,

Because of this, the complete electric area at

due to the charge
is,

Here,

and
are the unit vectors alengthy the horizontal and also vertical axes respectively.

The electrical area at

because of the charge
alengthy the vertical direction is,

Here,

is the distance of the point
from the charge
.

The net electric field at allude

is the amount of the electrical fields because of the charges 3 charges in the corners of the square.

Hence, the magnitude of the net field at allude

is,

The direction of the net electric area is

The direction is counter-clockwise with the positive x axis.

The magnitude of the net electrostatic force is,

Substitute

for
.

See more: Find Cheap Flights To Copenhagen From London (Lhr), (Lhr) To Copenhagen (Cph)

Because of this, magnitude of the force on charge is

and the direction of the net force via the horizontal is
.