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ISC Class 12 Physics Solved Question Paper 2005

Short Answer Type

21. An electric dipole is placed in a uniform external electric field E. Show that the torque acting on the dipole is given by

, where p is the dipole moment.

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22.

A potential difference of V volt is applied across a copper wire of length I and diameter d. How will the drift velocity be affected if

(i) V is double (ii) I is doubled.

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23. State Biot-Savart law. Derive an expression for magnetic field at the centre of a circular current carrying coil of radius r.

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24. Distinguish between diamagnetic and paramagnetic substance in terms of its relative permeability (μ_r) and magnetic susceptibility (x).

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25. A current of 4A flows in a coil when connected to a 12 V dc source. If the same coil is connected to a 12 V, 8 Hz ac source, a current of 2.4 A flows in the coil. Calculate the inductance of the coil.

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26. In the diagram given below (figure), find the current drawn from the battery:

(i) just when the switch S is closed.

(ii) when sufficient time has elapsed after closing the switch.

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27.

Microwaves, X-rays, U.V. rays, infrared rays.

Which of the above electromagnetic waves has—

(i) the shortest wavelength.

(ii) the lowest frequency.

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28. Derive Snell’s law of refraction using Huygen’s principle.

Snell’s law of refraction using Huygen’s Principle :

Consider a plane wavefront AB incident on a surface PQ separating two media 1 and 2.

The medium 1 is a rarer medium of refractive index n₁ in which light travels with a velocity C₁ The medium 2 is a denser medium of refractive index n₂ in which light travels with a velocity C_2.

The angle between the incident ray FA and the normal NA at the point of incidence A is equal to i.

The angle is also equal to the angle between the incident plane wavefront BA and the surface of separation PQ.

So ∠BAD is the angle of incidence of the incident plane wavefront AB.

Similarly, the angle between the refracted wavefront and the surface of separation PQ is equal to the angle of refraction r.

i.e.. ∠ADC = r.

Consider the triangles BAD and ACD figure above.

sin i = $sin space angle B A D space equals space fraction numerator B D over denominator A D end fraction space equals space fraction numerator C subscript 1 t over denominator A D end fraction$
$sin space r space equals space s i n space angle space A D C space equals space fraction numerator A C over denominator A D end fraction space equals space fraction numerator C subscript 2 t over denominator A D end fraction fraction numerator s i n space i over denominator s i n space r end fraction space equals space fraction numerator C subscript 1 t over denominator C subscript 2 t end fraction space equals space C subscript 1 over C subscript 2 space equals space a space c o n s t a n t$

This constant is called the refractive index of the second medium (2) with respect to the first medium (1).

$straight C subscript 1 over straight C subscript 2 space equals space n subscript 2 over n subscript 1 space equals space n presubscript 1 subscript 2$

This equation proves the Snell's law.

Let the first medium be vacuum or free space of n₁ = 1 and velocity of light C₁ - C.

Let the refractive index of the second medium n₂ be n and C₂ = v.

Then,

$straight C over straight v space equals space n n space equals space fraction numerator S p e e d space o f space l i g h t space i n space v a c u u m over denominator S p e e d space o f space l i g h t space i n space t h e space m e d i u m end fraction$

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29. In a Youngs double slit experiment with monochromatic light, fringes are obtained on a screen placed at a distance D from the slits. If the screen is moved by 5 x 10^-2 m towards the slits, the change in the fringe width is 3 x 10^-5 m If the distance between the slits is 10^-3m, calculate the wavelength of the light used.

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