A particle has charge -5.00 nC. (a) Find the magnitude and...

A particle has charge $-$5.00 nC. (a) Find the magnitude and direction of the electric field due to this particle at a point 0.250 m directly above it. (b) At what distance from this particle does its electric field have a magnitude of 12.0 N$/$C?

Key Concepts

Solving for Distance with a Given Field Magnitude

This concept involves rearranging the electric field formula E = k|q|/r² to solve for the distance r when the electric field's magnitude is known. It is an application of algebra in physics that connects the magnitude of the field to its distance from the charge.

Coulomb's Law and the Inverse Square Relationship

Coulomb's Law underpins the calculation of the electric field by establishing that the magnitude of interaction between charges decreases with the square of the distance between them. This inverse square law means that slight changes in distance can produce significant changes in the field's strength.

Electric Field of a Point Charge

This concept involves calculating the electric field created by a point charge using the formula E = k|q|/r², where E is the electric field magnitude, k is Coulomb's constant, q is the charge, and r is the distance from the charge. It is a fundamental idea in electromagnetism that allows us to determine how a charge influences the space around it.

Direction of the Electric Field

The electric field is defined as the force per unit positive charge. For a point charge, the field lines point radially outward if the charge is positive and radially inward if the charge is negative. This concept is crucial for determining the vector nature of the field, especially when considering the effects of the sign of the charge.

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