Electric fields around point charges

Electric fields around point charges.

Let us further discuss the similarities and differences of gravitational and electrostatic force to improve our conceptual understanding of both.

Gravitational force arises from mass-mass interaction, while electric force arises from charge-charge interaction.

The amount of gravitational or electric force produced on a certain object will be directly proportional to the mass or charge, respectively. In other words, the gravitational force experience by an mass within a given gravitational field will be proportional to its mass. Likewise, larger charges feel greater force at a certain position in a given electric field.

Now the comparison becomes interesting when we move from force prediction to actually predicting the result on the object's motion. We know from Newton's Second Law that the force, whether gravitational or electric, will cause an acceleration inversely proportional to the mass of the object upon which the force is acting. For gravity this has interesting consequences, because the combination of Newton's Second Law and the Law of Universal Gravitation predicts that a gravitational field will cause the same acceleration due to gravity on any mass at a certain position in the field. The larger the variable test mass, by Universal Gravitation, the larger the force on it, but by Newton's Second Law, the larger the test mass the smaller the acceleration. Stop and think about it. The two effects cancel out. The inertia of the larger mass resists the greater gravitational force, so the acceleration is the same for any object placed at that position in the field.

In fact, you can use the acceleration vector to represent the gravitational field at that position. Just looking at the units, we see that the strength of the gravitational field, Newtons per kilogram, reduces to meters per second per second, the units of acceleration. In other words, because of the classical equivalence of gravitational mass and inertial mass, the gravitational field reduces to acceleration.

In the case of the electric field, however, the same reasoning cannot be applied. 'Newtons per Coulomb' does not reduce any further. In other words, the electric force an a charged particle depends on the surrounding electric field and the particle's charge, but the inertial resistance to that force depends on mass, by Newton's Second Law.

In summary, while the gravitational field can be expressed as an acceleration (Newtons per kilogram is the same as m/s2), the electric field cannot (only Newtons/Coulomb). For electricity, this has the consequence that equivalent charges may be accelerated differently at the same position if they have different masses.