GRE Question of the Day (January 11th)

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Without a doubt, one of the pinnacle achievements of modern physics is the development of Maxwell’s equations. Their beauty lies in their elegant simplicity, while the breadth and depth of Maxwell’s equations speak for themselves. These four simple equations, coupled with the Lorenz Force Equation, form a full basis for modeling the behavior of an entire branch of physics: classical electrodynamics and optics. Further, despite their deceptive simplicity, Maxwell’s equations have withstood the test of time. While equations modeling most other fields of physics have been modified to accommodate new experimental results and theories, Maxwell’s equations have not been altered since their original conception in 1861.Take, for instance, Einstein’s theory of general relativity, first published in 1916. Although the equation governing general relativity was also elegant and powerful and laid the framework for most modern astrophysics, Einstein himself did not realize and correct an error within his equation until nearly fifteen years later. Newtonian mechanics has given way to more powerful theoretical frameworks and analytical mechanics has bent under the weight of quantum theory, but Maxwell’s equations stand as originally written, tried and true.

Maxwell’s four equations, the majority of which are less than twenty characters, are the mathematical formulation of four very simple ideas. First, any free electric charge will result in an electric field. Second, magnets do not have free charges, but are always paired together with a positive and negative end, yielding a magnetic field that has a looped structure. Third, a magnetic field that changes in time will result in an electric field and, fourth, an electric current or changing electric field will produce a magnetic field. It is truly amazing that these four simple rules, unmodified, have been used to model all electric, magnetic, and optics studies for more than 150 years.

Which of the following best expresses the author’s intent in writing the passage?

(A) To argue that Maxwell’s equations are the most important equations in all of physics
(B) To explain the significance and meaning of Maxwell’s equations
(C) To argue that Maxwell is a more important name in physics than Einstein
(D) To describe the implications of each of Maxwell’s four equations
(E) To advocate further studies in the field of electromagnetism and optics

Correct Answer -- (click and drag your mouse to see the answer)

The author references Einstein’s theory of general relativity for which of the following reasons?

(A) To argue that the equations of electricity and magnetism are more important than the equations of relativity
(B) To provide an example of an equation that has been unwavering in time
(C) To advocate that Maxwell was a more important historical figure than Einstein
(D) To show that the implications of Maxwell’s equations are far more powerful than general relativity
(E) To provide an example of an important equation that has been modified over time

Correct Answer -- (click and drag your mouse to see the answer)

Which of the following is not mentioned as a rule in any of Maxwell’s four equations?

(A) The looped structure of a magnetic field results from coupled charges.
(B) A magnetic field that changes in time results in an electric field.
(C) Any free electric charge results in an electric field.
(D) Magnetic fields are generated by unpaired magnetic charges.
(E) An electric current will produce a magnetic field.

Correct Answer - D - (click and drag your mouse to see the answer)

Consider each of the answer choices separately and indicate all that apply.

Which of the following can be correctly inferred from the passage?

❑ Maxwell’s four equations form a full basis for modeling the behavior of classical electrodynamics and optics.
❑ Einstein’s equations of general relativity were incorrect as originally written in 1916.
❑ Newtonian mechanics has been modified by quantum theory.

Correct Answer -- (click and drag your mouse to see the answer)

Question Discussion & Explanation

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