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The magnitude of an electric field is 100 newtons per coulomb at a distance of 0.50 meters from a point particle that has a charge of π.
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What is the value of π?
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Weβre told the electric field magnitude is 100 newtons per coulomb, which weβll call capital πΈ, and that that is the value of the electric field a distance of 0.50 meters from a point particle π.
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Weβll call that distance π.
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We want to solve for the value of π.
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As a start, we can recall the relationship for an electric field caused by a point particle.
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The electric field that created by a point particle with charge π is equal to that charge times Coulombβs constant, π, divided by the distance squared between the charge, π, and where the electric field, πΈ, is being experienced or measured.
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In this exercise, weβll treat π as exactly 8.99 times 10 to the ninth newton meter squared per coulomb squared.
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When we write the equation for electric field in terms of the variables in our situation, we see we can rearrange this equation to solve for π.
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π equals the electric field times the distance squared divided by π, the constant.
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When we plug in for πΈ, π, and π and enter these values on our calculator, we find that π, the charge creating this electric field, has a value of 2.8 times 10 to the negative ninth coulombs.
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That is the value of the point charge π.