When a test charge of +5.00 nC is placed at a certain point, the force that acts on it has a mag

step 1 This problem covers the concept of the electric force exerted by electric field on a charge. So

When a test charge of +5.00 nC is placed at a certain point,...

When a test charge of $+5.00 \mathrm{nC}$ is placed at a certain point, the force that acts on it has a magnitude of $0.0800 \mathrm{~N}$ and is directed northeast. (a) If the test charge were $-2.00 \mathrm{nC}$ instead, what force would act on it? (b) What is the electric field at the point in question? Example $16-5$

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Key Concepts

Electric Force and Its Proportionality to Charge

This concept is based on the relationship F = qE, which states that the force experienced by a charge in an electric field is directly proportional to the magnitude of the charge and the strength of the electric field. The direction of the force depends on the sign of the charge relative to the field direction. Hence, if the charge is positive, the force is in the direction of the electric field, and if the charge is negative, the force reverses its direction.

Electric Field

The electric field represents the force per unit charge at any given point in space. It is a vector quantity that exists around any charged object or distribution of charges and determines the force that any test charge would experience if placed in that field, independent of the test charge’s size or sign.

Test Charge Concept

A test charge is a hypothetical small charge used to probe the electric field without disturbing it. Its interactions help determine the characteristics of the field, since the induced force (F = qE) on the test charge is used to measure the field's magnitude and direction. Using different test charges illustrates how force scales with charge and how sign influences the force’s direction.

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