Calculate the magnitude and direction of the electric field...

Calculate the magnitude and direction of the electric field at a point $25.0 \mathrm{~cm}$ to the left of a tiny sphere carrying a uniform charge of $-500 \mathrm{nC}$. The entire space is filled with methanol at $20{ }^{\circ} \mathrm{C}$. [Hint:
Use Table 24-1.]

Key Concepts

Sign of the Charge and Field Direction

The sign of the charge determines the direction of the electric field relative to the charge. A negative charge, for example, produces an electric field that points toward it, while a positive charge produces a field that points away from it. This concept is essential for understanding not only the magnitude but also the directional characteristics of the electric field.

Electric Field

The electric field is a vector quantity that represents the force per unit positive charge at a point in space. It defines how a charge influences the space around it, and its magnitude and direction determine the force experienced by another charge in that field.

Coulomb's Law

Coulomb's Law quantifies the 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. When calculating electric fields, Coulomb's Law is used in its form that relates the field to a point charge, giving a formula that involves the charge magnitude divided by the square of the distance.

Permittivity and the Influence of a Medium

The electric field generated by a charge is affected by the medium surrounding it. In a medium other than vacuum, the permittivity of the medium (which is the product of the relative permittivity and the permittivity of free space) replaces the permittivity of free space in Coulomb's Law. This adjustment accounts for how the medium, such as methanol, influences the strength of the electric field by reducing it compared to the field in a vacuum.

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