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What are the strength and direction of the electric field at the position indicated by the dot in the figure

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Let r = 8.0 cm .

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Express your answer to two significant figures and include the appropriate units

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Step 1:

Observe the figure:

The two point charges are positive, hence

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

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

For the charged particle along top surface is .

The distance between the bottom charge and the dot is .

For the charged particle along top 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 .

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 the -axis.

Solution:

Strength of the electric field is

Direction of electric field is above the -axis.