Write the electric field at point P in component form.

Question

 

Assume that x-axis is horizontal and points to the right, and y-axis points upward.

Answer 1

Step 1:

Draw the related diagram:

The angle of the field at the dot from the upper left charge is .

The angle of the field at the dot from the lower left charge is .

The angle of the field at the dot from the lower right charge is .

Electric field due to charged particle is , where .

is the permittivity of free space .

is the charge of the electron.

is the distance between the two point charges.

Step 2:

The distance between the upper left charge and the point is .

For the charged particle along upper left surface : .

The distance between the lower left charge and the point is .

For the charged particle along lower left surface : .

The distance between the lower right charge and the point is .

For the charged particle along lower right surface : .

Step 3:

Find the net electric field.

is sum of horizontal and vertical components.

Find the sum of horizontal components.

.

Substitute and .

.

The horizontal component is .

Find the sum of vertical components.

.

Substitute and .

.

The vertical component is .

.

.

The electric field at point in component form is .

Solution:

The electric field at point in component form is .