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.

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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
*
.

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*

Because of this, magnitude of the force on charge is

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