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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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The balls in the figure are charged to 5.8 nCnC . What are the strength and direction of the electric field at the position indicated by the dot in the figure? (Figure 1)

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Specify the strength of the electric field

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Specify the direction as an angle above horizontal

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$\"\"$

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Step 1:

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Observe the figure:

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The two point charges are positive, hence $\"\"$

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$\"\"$

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

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The angle of the field at the dot from the botton charge is $\"\"$ .

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Electric field due to charged particle is $\"\"$ , where

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$\"image\"$ is the permittivity of free space $\"image\"$ .

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$\"\"$ is the charge of the electron.

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$\"\"$ is the distance between the two point charges.

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Step 2:

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The distance between the top charge and the dot is $\"\"$ .

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For the charged particle along top surface is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The distance between the bottom charge and the dot is $\"\"$ .

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For the charged particle along top surface is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Step 3:

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Find the net electric field.

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$\"\"$ is sum of horizontal and vertical components.

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Find the sum of horizontal components.

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$\"\"$

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Find the sum of vertical components.

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$\"\"$

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Therefore $\"\"$ .

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Find the magnitude of electric field strength.

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$\"\"$

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Strength of the electric field is $\"\"$

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Find the direction of electric field.

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$\"\"$

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$\"\"$

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Direction of electric field is $\"\"$ above the $\"\"$ -axis.

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Solution:

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Strength of the electric field is $\"\"$

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Direction of electric field is $\"\"$ above the $\"\"$ -axis.