Physics

CBSE Class 12

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State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies.

Cyclotron works on the principle that an oscillating electric field can be used to accelerate a charge particle to high energy.

In a cyclotron, the charged particles across the gap between the two D-shaped magnetic field regions are accelerated by an electric field. The magnetic field is perpendicular to the paths of the charged particles that make them follow circular paths within the two Dee’s. An alternating voltage accelerates the charged particles each time they cross the Dee’s. The radius of each particle’s path increases with its speed. So, the accelerated particles spiral toward the outer wall of the cyclotron.

The accelerating electric field reverses just at the time the charge particle finishes its half circle so that it gets accelerated across the gap between the Dee’s. The particle gets accelerated again and again, and its velocity increases. Therefore, it attains high kinetic energy.

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12.

A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?

Given, convex lens placed in contact with a plane mirror.

Image of the object coincides with the object.

So, the rays refracted from the first lens and then reflected by the plane mirror will be retracing their path. This would happen when rays refracted by the convex lens fall normally on the mirror i.e., the refracted rays form a beam parallel to principal axis of the lens.

Hence, the object is at the focus of the convex lens.

Therefore, focal length, f = 20 cm

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13.

(a) Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.

(b) The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a.(a) Consider a parallel-plate capacitor of plate area *A*.

Let us say, charge Q is given to the capacitor. Now, in order to increase the separation between the plates, plate b is slowly pulled away from plate a.

Distance between the two capacitor plates = d

Force on plate b due to plate a is given by,

Work done inorder to displace the plate from its fixed position is, W=Fd

; where is the capacitance of the capacitor.

Work done is equal to increase in energy of the system.

Electric field is created in a volume which is given by, V = Ad

So, Energy stored per unit volume is given by,

where, E is the intensity of the electric field.

(b) Work done, W= F.d ;

where, F is the force exerted on electrical charge and d is the displacement.

Since, the charge is moved along a closed path, net displacement is zero.

Therefore, work done= 0

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14.

The figure given below shows the block diagram of a generalized communication system. Identify the element labelled 'X' and write its function.

The element labelled 'X' is called 'channel'.

Channel connects transmitter and receiver. The signal from the transmitter is carried to the receiver by the communication channel.

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15.

An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of 4 Nm. Calculate the potential energy of the dipole, if it has charge ±8 n C.

Given,

Length of the dipole, l = 4 cm

Torque, = 4 N m

Using the formula for torque, we have

Torque, τ = PEsinθ = (Ql) Esinθ ...(1)

Potential energy, U= −PEcosθ= −(Ql)Ecosθ ...(2)

Dividing equation (2) by (1),

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16.

(a) State Ampere's circuital law, expressing it in the integral form.

(b) Two long coaxial insulated solenoids, S_{1} and S_{2} of equal lengths are wound one over the other as shown in the figure. A steady current "I" flow thought the inner solenoid S_{1} to the other end B, which is connected to the outer solenoid S_{2} through which the same current "I" flows in the opposite direction so as to come out at end A. If n_{1} and n_{2} are the number of turns per unit length, find the magnitude and direction of the net magnetic field at a point

(a) Ampere’s circuital law states that the line integral of magnetic induction around a closed path in vacuum is equal to times the total current I threading the closed path.

In the above illustration, the Ampere’s Circuital Law can be written as follows:

(b) (i) The magnetic field due to a current carrying solenoid:

where, n = number of turns per unit length

i = current through the solenoid.

From the fig, we can say that, the direction of magnetic field due to solenoid S_{1} will be in the upward direction and the magnetic field due to S_{2} will be in the downward direction using right hand screw rule.

Therefore,

Net magnetic field is in the upward direction.

(ii) Since, there is no current which is flowing outside the solenoid, the magnetic field is zero.

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17.

For a single slit of width "a", the first minimum of the interference pattern of a monochromatic light of wavelength λ occurs at an angle of . At the same angle of , we get a maximum for two narrow slits separated by a distance "a". Explain.

Width of the slit = a

The path difference between two secondary wavelets is given by,

N λ = a sin *θ*.

Since, θ is very small sin θ = θ.

So, for the first order diffraction n = 1, the angle is λ/a.

Now we know that θ must be very small θ = 0 (nearly) because of which the diffraction pattern is minimum.

Now for interference case, for two interfering waves of intensity I_{1} and I_{2} we must have two slits separated by a distance.

We have the resultant intensity, I =

Since, *θ* = 0 (nearly) corresponding to angle λ/a so cos *θ* = 1 (nearly)

So,

We see the resultant intensity is sum of the two intensities, so there is a maxima corresponding to the angle λ/a.

This is why at the same angle of λ/a we get a maximum for two narrow slits separated by a distance "a".

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18.

Answer the following:

(a) Name the EM waves which are suitable for radar systems used in aircraft navigation. Write the range of frequency of these waves.

(b) If the earth did not have atmosphere, would its average surface temperature be higher or lower than what it is now? Explain.

(c) An EM wave exerts pressure on the surface on which it is incident. Justify.(a) Microwaves are suitable for radar systems used in aircraft navigation. The range of frequency for these waves is 10^{9} Hz to 10^{12} Hz.

(b) There would be no greenhouse effect on the surface of the Earth in the absence of atmosphere. As a result, the temperature of the Earth would decrease rapidly, making it difficult for human survival.

(c) When the wave is incident on the metal surface, it is completely absorbed. Energy U and hence momentum (p = is delivered to the surface of the earth. The momentum delivered becomes twice when, the wave is totally reflected because momentum is changed from p to –p. Thus, force and thereby pressure is exerted on the surface of the earth by EM waves.

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19.

Write the truth table for the combination of the gates shown. Name the gates used.

From the logic gates given above, we can say that

R is the OR GATE

S is the AND GATE

A |
B |
Y' = A+B |
Y = Y'.A |

0 |
0 |
0 |
0 |

0 |
1 |
1 |
0 |

1 |
0 |
1 |
1 |

1 |
1 |
1 |
1 |

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20.

A potentiometer wire of length 1 m has a resistance of 10 Ω. It is connected to a 6 V battery in series with a resistance of 5 Ω. Determine the emf of the primary cell which gives a balance point at 40 cm.

Given,

Total length of the potentiometer wire, *L* = 1m

Resistance of the wire, R = 10 Ω

Voltage of the battery = 6 V

Resistance of the battery = 5 Ω

Therefore, total resistance of the circuit, *R* = (*R*_{AB} + 5) Ω = 15 Ω

Using the figure given above, we have

Current in the circuit, I = V R = 6 x 15 A

Therefore,

Voltage across *AB*, *V _{AB}* =

Emf of the cell, e = ... (1)

Here, *Balance point is obtained at, l* = 40 cm

Total length, AB *= L* = 1 m = 100 cm

Putting the values in equation (1), we have

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