What are the strength and direction of the electric field at the position indicated by the dot in the figure(Figure 1) ?

Question

Give your answer in component form. (Assume that xx-axis is horisontal and points to the right, and yy-axis points upward.)

Give your answer as a magnitude and angle measured cw from the positive 

x

x-axis.

Express your answer using two significant figures.

Answer 1

Step 1:

(a)

Observe the figure:

The three point charges are , and

The angle of the field at the dot from the bottom charge() is .

The angle of the field at the dot from the top charge() is .

The angle of the field at the dot from the top left 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 bottom charge and the dot is .

For the charged particle along bottom surface is .

The distance between the top charge and the dot is .

For the charged particle along bottom surface is .

The distance between the top left charge and the dot is .

For the charged particle along bottom surface is .

Step 3:

Find the net electric field.

is sum of horizontal and vertical components.

Find the sum of horizontal components.

Find the sum of vertical components.

Therefore .

Step 4:

Find the magnitude of electric field strength.

Strength of the electric field is

Find the direction of electric field.

Direction of electric field is above x -axis.

Solution:

.

Strength of the electric field is

Direction of electric field is above x -axis.