# Optionals IAS Mains Physics: Questions 280 - 285 of 307

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## Question 280

Appeared in Year: *2006*

### Describe in Detail

Essay▾Starting from Maxwell՚s equation , where is the electric displacement density and is the charge density, derive Poisson՚s equation. Deduce Laplace equation for charge free region from Poisson՚s equation. (Marks: 20)

### Explanation

Poisson՚s and Laplace՚s equations are easily derived from Gauss՚s law (for a linear, isotropic material medium)

And (Procedure for determining the electric field when the potential is known throughout the region) .

Substituting equation (2) into equation (1) gives

For an inhomogeneous medium: for a homogeneous medium, equation (3) becomes

This is…

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## Question 281

Appeared in Year: *2003*

### Describe in Detail

Essay▾Obtain an expression for the intensity of light in the fraunhofer diffraction pattern due to circular aperture. What is Airy pattern? Explain with a neat diagram. (Marks: 20)

### Explanation

In Fig (1) , is a circular aperture of diameter . Is the centre of the aperture and is a point on the screen. is perpendicular to the screen. The screen is perpendicular to the plane of the paper. A plane wave front is incident on the circular aperture. The secondary wave travelling in the direction comes to the focus at . Therefore , correspo…

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## Question 282

Appeared in Year: *2003*

### Describe in Detail

Essay▾Explain the principle of feedback in an amplifier. What are the advantages of negative feedback? (Marks: 8)

### Explanation

Feedback is the process of taking a part of output signal and feeding it back to the input circuit. Fig (1) shows a block diagram of a basic simplifier. Here, is the input signal and the output. If A is the voltage gain of the simplifier, the output is related to the input by

In this simplifier, the input does not know what is happening at the …

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## Question 283

Appeared in Year: *2015*

### Describe in Detail

Essay▾What is Zeeman effect? How it can be understood on the basis of quantum mechanics?

(Marks: 25)

### Explanation

Zeeman, in 1896, observed that when a light-source giving line spectrum is placed in an external magnetic field, the spectral lines emitted by the atoms of the source are split into a number of polarised components. For fields less than several lengths of 1Tesla, the splitting is proportional to the strength of the field. This effect of magnetic fi…

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## Question 284

Appeared in Year: *2003*

### Describe in Detail

Essay▾Write the Lagrange՚s equation for a system of particles which is acted upon by conservative forces. What is a cyclic coordinate? Show that the generalized momentum conjugate to a cyclic coordinate is conserved. (Marks: 20)

### Explanation

Lagrange՚s equation in general is given by

As range from , there will be such second order equations.

Kinetic energy &

We consider a conservative system and use above set of equation (1) to obtain Lagrange՚s equation of motion. For a conservative system, forces are derivable from potential function v, which is the function of coordinates only. Th…

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## Question 285

Appeared in Year: *2003*

### Describe in Detail

Essay▾Calculate the Larmor frequency of Spin particle in a magnetic field B. (Marks: 10)

### Explanation

An electron moving around the nucleus of an atom is equivalent to a magnetic dipole. Hence, when the atom is placed in an external magnetic field, the electron orbit processes about the field direction as axis. This precession is called ‘Larmor Precession’ and the frequency of this precession is called ‘Larmor Frequency’ .

In Fig (1) is shown an ele…

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