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PY106 Notes - Electric field
Excellent tutorial covering the electric field derived from Dr. Duffy''s second semester lecture notes for a physics course geared to premedical students at Boston University.

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Special points of emphasis



Are you comfortable with the field concept? The concept of the field is crucial for understanding the context for both electrical or gravitational problem solving. What is it you are describing when you draw field lines?

When you speak of the electrical or gravitational field of an object, you are describing the capability of that object to exert force. Think of it as a capability permeating the space around the the mass or charge producing the gravitational or electric field respectively.

The stronger the field at a given position in space near the object, the stronger the interaction which would occur if another mass (gravity) or charge (electricity) were introduced at that position relative to the field producing object. For a single spherical mass (gravity) or point charge (electricity), field lines can be drawn spreading out in space (diverging) to show that the field is decreasing in intensity with increasing distance from the object.

Newton's Laws


The strength of the electric field existing at a position in space near a charged particle can be expressed in terms of how many Newtons of force would exert per Coulomb of hypothetical test-charge placed at that position.

Similarly, the gravitational field strength at that position can be represented in terms of how many Newtons per kilogram per hypothetical test-mass introduced at that position.

In both cases, the field permeates the space around the object (initial charge or mass under discussion) even if there is no second charge or mass necessary for force interaction.

In contrast to the electric field, however, the Newtons per kilogram units of gravitational field reduce to the units of acceleration (remember that a Newton is a kilogram meter per second squared, so kilogram appears in both the numerator and denominator) while the Newtons per Coulomb units of electric field do not reduce. The larger the gravitational force leading to acceleration, the larger the inertia resisting that acceleration, (because both rise with the mass of the test object) and so larger and smaller masses all have the same acceleration at given position in the gravitational field of another.

With the electrical field, the analysis is different. While force depends on the magnitude of charge present on the test object, the inertia of the test object depends on its mass. The resulting acceleration will be different for larger and smaller masses of identical charge because their inertia will be different. This is why the gravitational field can be represented by acceleration vectors or Newtons per Kilogram while the electric field must be represented by vectors with units Newtons per Coulomb. This is an important difference embodying some important insights about gravitational and electric fields.

One of the consequences is that while masses launched into a uniform gravitational field (projectiles) will follow the same trajectory if the initial velocity is the same (and there is no air friction), charges launched into the uniform electric field between two capacitor plates may have a different trajectory if the charge to mass ratio is different.

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