Without a doubt, one of the pinnacle achievements of modern physics is

Question

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.

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.    1 
 1. 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

2 
 2. 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

3 
 3. 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.

4 
 4. Which of the following can be correctly inferred from the passage?

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

A. I Only
B. II Only
C. III Only
D. I and II Only
E. II and III Only

Manhattan GRE 5lb.

_ankitchawla_ · Answer

hi  Sajjad1994

I have a doubt regarding #4:

"Newtonian mechanics has given way to more powerful theoretical frameworks and analytical mechanics has bent under the weight of quantum theory"

Dosen't this statement clearly mean that

Newtonian mechanics has been modified by quantum theory.  ??

YogeshBardia · Answer

Hey  _ankitchawla_ , let me try to help you with that.
The difference can be understood like this.

Quantum Theory might've proved some cases where the Newtonian Mechanics were proved wrong. But it doesn't mean that it was corrected by quantum theory, it just proved it wrong and hence we can't say that "Newtonian Mechanics were modified  by  quantum theory" but rather that would imply that "Newtonian Mechanics were modified  because  of Quantum theory".

I hope you understood what I was trying to tell you. Have a great day and All the best!!

Rebaz · Answer

"Newtonian mechanics has given way to more powerful theoretical frameworks  and  analytical mechanics has bent under the weight of quantum theory"

If you read the sentence carefully, you see that the sentence consists of 2 sentences connected by  AND , meaning the sentence after the end is independent of the sentence before the  AND . Thus you cannot assume that Newtonian mechanics equals to analytical mechanics.

Analytical mechanics has bent under the weight of quantum theory  NOT  Newtonian mechanics.

So, what this choice does is mixing up Newtonian mechanics with Analytical mechanics to confuse you.

I hope you understand what I mean.

rishu00 · Answer

Can anybody explain why in question-1 a) option can't be correct

rishu00 · Answer

can anybody explain me the 4th question why option a is not included and option b is included

guddo · Answer

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

The passage praises Maxwell’s equations, explains why they are important, and briefly describes what the four equations mean. The author’s main purpose is not just to list the equations, but to show their  significance  and explain their basic content in  simple terms .

(A) To argue that Maxwell’s equations are the most important equations in all of physics

Wrong. The passage strongly praises Maxwell’s equations, but it does not clearly argue that they are the most important equations in all of physics.

(B) To explain the significance and meaning of Maxwell’s equations

Correct. The first paragraph explains their importance, durability, and role in physics. The second paragraph explains the basic ideas behind the four equations.

(C) To argue that Maxwell is a more important name in physics than Einstein

Wrong. Einstein is mentioned only as a comparison to show how unusually stable Maxwell’s equations have been.

(D) To describe the implications of each of Maxwell’s four equations

Too narrow. The passage does describe the four equations briefly, but its broader purpose is to explain both their importance and meaning.

(E) To advocate further studies in the field of electromagnetism and optics

Wrong. The passage does not call for more research.

Answer: (B)

guddo · Answer

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

A. I Only
B. II Only
C. III Only
D. I and II Only
E. II and III Only

The passage’s main point is that Maxwell’s equations are unusually simple, powerful, and stable over time. For this inference question, the key is to avoid overstating what the passage says.

I. Maxwell’s four equations form a full basis for modeling the behavior of classical electrodynamics and optics.

Not supported as written. The passage says Maxwell’s equations,  coupled with the Lorenz Force Equation , form a full basis. So Maxwell’s four equations alone are not stated to form the full basis.

II. Einstein’s original equations of general relativity were incorrect as originally written in 1916.

Supported. The passage says Einstein did not realize and correct an error in his equation until nearly fifteen years later. That means the original version contained an error.

III. Newtonian mechanics has been modified by quantum theory.

Not supported. The passage says Newtonian mechanics “has given way to” more powerful frameworks, and that analytical mechanics has bent under quantum theory. It does not say  Newtonian mechanics itself  was modified by quantum theory.

Answer: (B)

Without a doubt, one of the pinnacle achievements of modern physics is

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Without a doubt, one of the pinnacle achievements of modern physics is

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