The electric field strength 1.7 cmcm from the surface of a 10-cmcm-diameter metal ball is 8.0×10⁴ N/C

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The electric field

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F

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Step 1:

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The electric field strength is $\"\"$ .

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The distance between surface to metal ball is $\"\"$ .

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The diameter of the metal ball is $\"\"$ .

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The radius of the metal ball is $\"\"$ .

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The total distance from surface to center of the ball is $\"\"$ .

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Find the charge of the metal ball.

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

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

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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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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The charge on the metal ball is $\"\"$ .

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Solution:

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The charge on the metal ball is $\"\"$ .

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Your problem is unit conversion.

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Consider electric field strength $\"\"$ .

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Write units of $\"image\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The units of electric field strength is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The units of electric field strength is $\"\"$ .

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Dimensions of electric charge:

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Consider electric field strength $\"image\"$ .

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Write units of $\"image\"$ , $\"\"$ and $\"\"$ .

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$\"image\"$

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$\"image\"$

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$\"image\"$ .

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The units of electric field strength is $\"image\"$ .