A particle has a charge of -3.00 nC. (a) Find the magnitude and direction of the electric field

step 1 The electric field due to a point charge at a given point is given by equal to k k u .m r square

A particle has a charge of -3.00 nC. (a) Find the magnitude...

A particle has a charge of $-3.00 \mathrm{nC}$. (a) Find the magnitude and direction of the electric field due to this particle at a point $0.250 \mathrm{~m}$ directly above it. (b) At what distance from the particle does its electric field have a magnitude of $12.0 \mathrm{~N} / \mathrm{C}$ ?

Key Concepts

Electric Field

The electric field is defined as the force per unit charge experienced by a test charge placed in the vicinity of other charges. It describes how a charged object affects the space around it, with the field vector indicating both the magnitude and the direction of the force exerted on a positive test charge.

Coulomb's Law

Coulomb's Law quantifies the electrostatic force between two point charges. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law forms the basis for calculating the electric field produced by a point charge.

Inverse-Square Law

The inverse-square law is a characteristic of forces that spread out uniformly in three-dimensional space, such as gravitational and electrostatic forces. In the context of electric fields, it implies that the strength of the field decreases as the square of the distance from the point charge, meaning that doubling the distance reduces the field's magnitude by a factor of four.

Electric Field Direction

The direction of the electric field is determined by the sign of the source charge. For a positive charge, the electric field vectors point radially outward, whereas for a negative charge, they point radially inward. This directional property is crucial for understanding how electric charges interact with each other and how the field influences other charges in its vicinity.

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