Consider a conductor XY carrying current I. There we choose an infinitesimal element dl of the conductor. The magnetic field dB due to this element is to be determined at a point P which is at a distance ‘r’ from it. Let θ be the angle between dl and the position vector ‘r’. According to Biot-Savart’s law, the magnitude of the magnetic field dB at a point p is proportional to the current I, the element length |dl|, and inversely proportional to the square of the distance r and dB is directed perpendicular to the plane containing dl and r. 

here μ₀ = 4π x 10^-7 Hm^-1 is a constant called permeability of vacuum. 

The energy or potential applied in the electron-beam tube or system to increase the energy of the electrons and accelerate their speed is known as accelerating potential.

The negative potential of the collector plate at which the photoelectric current becomes zero is called stopping potential or cut-off potential. Stopping potential is that value of retarding potential difference between two plates which is just sufficient to halt the most energetic photoelectrons emitted.

Considera dipole with charges +q and -q placed in a uniform eletric field as shown in figure.

In unifor electric field, dipole experiences a torque τ, which is given by

τ = p×E

where p is electric dipole moment. Torque τ will tend to rotate the dipole if p is not parallel to E.

Suppose an external torque τ_ext is applied to neutalize this torque and rotates the dipole from an angle θo to θ₁

at an infinitesimal angular speed and without angular acceleration. The amount of workdon by the external torque will be given by

W = 

This work is stored as the potential energy of the system.

We can then assosciate potential energy U(θ) with an inclination θ of the dipole. Inorder to choose the

reference angular position where potential Energy is considered as zero, we select θ_o as π/2 as the reference angular position.

We can then write U(θ) = pE( cos(π/2) - cosθ) = -pE cosθ = -p·E

when θ = 0 , i.e., p is aligned in the direction of E, potential energy is minimum.

when θ = π , i.e., p is aligned in the oposite direction of E, potential energy is maximum

Einstein’s photoelectric equation,

 K_max​=hν−ϕ0​ where

Kmax​ is the max kinetic energy of emitted electrons and ϕ0​ is the work function.

According to Planck’s quantum theory, light radiations consist of small packets of energy. Einstein postulated that a photon of energy hv is absorbed by the electron of the metal surface, then the energy is used to liberate electron from the surface and rest of the energy becomes the kinetic energy of the electron.

Energy of photon is,

E=hv

Where,  h = Planck’s constant

v = frequency of light

The minimum energy required by the electron of a material to escape out of it, is work function.

The additional energy acquired by the electron appears as the maximum kinetic energy ‘K_max’ of the electron.

Einstein's photoelectric equation

K_max​=eVo​

Salient features observed in photoelectric effect: —

The stopping potential and hence the maximum kinetic energy of emitted electrons varies linearly with the frequency of incident radiation.

There exists a minimum cut - off frequency , for which the stopping potential is zero.

Photoelectric emission is instantaneous.

Einstein's photoelectric equation is E_k = hv -W for a single photon ejecting a single electron. 

(i) Explanation of frequency law: When frequency of incident photon (v), increases, the kinetic energy of emitted electron increases. Intensity has no effect on kinetic energy of photoelectrons.

(ii) Explanation of intensity law: When intensity of incident light increases, the number of incident photons increases, as one photon ejects one electron; the increase in intensity will increase the number of ejected electrons. In other words, photocurrent will increase with increase of intensity. Frequency has no effect on photocurrent. 

(iii) Explanation of no time lag law: When the energy of incident photon is greater than work function, the photoelectron is immediately ejected. Thus there is no time lag between incidence of light and emission of photoelectrons.c

Law of Refraction using Huygens' Principle:
Similarly, we can use a Huygens construction to illustrate the law of refraction.
Here we must take into account a different speed of light in the upper and lower media. If the speed of light in a vacuum is c, we express the speed in the upper medium by the ratio ni​c​, where ni​ is the refractive index. Similarly, the speed of light in the lower medium is nt​c​. The points D, E and F on the incident wavefront arrive at points D, J and I of the plane interface XY at different times. In the absence of the refracting surface, the wavefront GI is formed at the instant ray DF reaches I. During the progress of ray CF from F to I in time t, however , the ray AD has entered the lower medium, where the speed in different. Thus if the distance DG is vi​t, a wavelet of radius vt​t is constructed with center at D. The radius DM can also be expressed as  
DM=v_i​t 
=v_i​(​DG/v_i​)

=(​n₁/n_t​​)DG 

Similarly, a wavelet of radius n₁/n_t​​n₁/n_t​​ JH is drawn centered at J. The new wavefront KI includes a point I on the interface and is tangent to the two wavelets at points M and N. The geometric relationship between the angles i and t, formed by the representative incident ray AD and refracted ray DL, is Snell's law , which may be expressed as ni​sinθi​=ni​sinθi​.

Reflection of a plane wavefront of light at a plane surface

Where MN: Plane mirror,
RA and QC: Incident rays, 
AP: Normal to MN,
AB: Incident wavefront,
i: Angle of incident,
CE: Reflected wavefront,
 r: Angle of reflection

When wavefront AB is incident on the mirror, at first, point A becomes a secondary source and emits secondary waves in the same medium. If T is the time taken by the incident wavefront to travel from B to C, then BC = vT. During this time, the secondary wave originating at A covers the same distance, so that the secondary spherical wavelet has a radius vT at time T.

To construct the reflected wavefront, a hemisphere of radius vT is drawn from point A. Draw a tangent EC to the secondary wavelet.

The arrow AE shows the direction of propagation of the reflected wave.

AP is the normal to MN at A,

∠RAP = i = angle of incidence and

∠PAE = r = angle of reflection

In Δ ABC and Δ AEC,

AE = BC and ∠ABC = ∠AEC = 90°

∴ Δ ABC and Δ AEC are congruent.

∴ ∠ACE = ∠BAC = i        .....(1)

 Also, as AE is perpendicular to CE and AP is perpendicular to AC,

∠ACE = ∠PAE = r       .....(2)

∴ From Eqs (1) and (2),

i = r

Thus, the angle of incidence is equal to the angle of reflection. This is the first law of reflection. Also, it can be seen from the figure that the incident ray and reflected ray lie on the opposite sides of the normal to the reflecting surface at the point of incidence and all of them lie in the same plane. This is the second law of reflection. Thus, the laws of reflection of light can be deduced by Huygens' construction of a plane wavefront.

The symbol of the NAND gate is represented as a combination of AND gate and NOT gate. The Boolean expression is given as Y=A.B¯.

The truth table of a NAND gate is given below

Let

X,  be the initial length, and r

Y be the cross-sectional area

R be the resistance of wire.

Let X', Y' and R' be the new length, cross- sectional area and resistance of wire after the length of wire is increased.

Length is increased by 0.1%, therefore,

L' = L+(0.1/100)L

L' = 1.001 L

Since the volume of wire remains same, thus,

V' = V

A'*L' = A*L

A' * 1.001 L = A*L

A' = A/1.001

New Resistance,

R' = ρL'/A'

= ρ*1.001 L/(A/1.001)

= (1.001)²(ρL/A)

R' = 1.002*R

% change in resistance = (Final resistance - Initial resistance)/Initial resistance * 100%

= (R' - R)/R*100%

= (1.002R - R)/R*100%

= 0.002 * 100%

= 0.2%

Thus, resistance of wire is increased by 0.2%.

Physiology is the study of the characteristics and mechanisms of the human body.

Cells are the basic unit of life and approximately 100 trillion cells make up the typical human, each specially adapted to perform one or a few particular functions. Nearly 25 trillion red blood cells function by transporting oxygen from the lungs to all tissues in the body. All cells have some basic commonalities. Oxygen reacts with carbohydrates, fat, and protein to release energy, nutrient consumption, and energy production mechanisms. Almost all cells have the ability to reproduce further similar cells.

Physiology is the study of the characteristics and mechanisms of the human body.

Cells are the basic unit of life and approximately 100 trillion cells make up the typical human, each specially adapted to perform one or a few particular functions. Nearly 25 trillion red blood cells function by transporting oxygen from the lungs to all tissues in the body. All cells have some basic commonalities. Oxygen reacts with carbohydrates, fat, and protein to release energy, nutrient consumption, and energy production mechanisms. Almost all cells have the ability to reproduce further similar cells.

A mean colour is that colour whose wavelength lies in between that of violet and red. For white light, yellow colour is, generally, taken to be the mean colour.

If the refractive indices corresponding to the mean colour, violet and red are μ, μ_v and μ_r respectively. The deviation corresponding to yellow colour is taken as the mean deviation.

On July 7, HRD Minister Ramesh Pokhriyal announced a major CBSE syllabus reduction with 30% of the syllabus slashed for the year 2020-21 for classes 9 to 12 because of the reduction in classroom teaching time due to the Covid-19 pandemic and lockdown.

CBSE has rationalized the syllabus with the help of suggestions from NCERT and the same has been notified by a new CBSE notification as well.

Deleted syllabus of CBSE Class 12 Physics

Continuous method of endurance development: In this training method exercise is done for long duration without giving any break or pause in between the exercises. In these types of exercises or activities duration of work is more and intensity is less. For example, cross country runs. The continuous method is divided into: 

(a) Slow continuous method: In slow continuous method the athlete exercises at a slow pace without any break or pause for very long duration. Marathon and cross country runs are typical examples of continuous method. The heart rate ranges between 140 and 160 beats per minute. The duration of exercise should not be less than 30 minutes and may last upto 2 hours or even more. The activities involved are running, walking, cycling, etc. This type of training aids the runner in preparing himself/herself for actual competition. 

(b) Fast continuous method: In fast continuous method, the work is done at faster speed without changing the pace for long without any pause or break in-between the exercise. The duration of work should not be less than 20 minutes for well trained athletes. Heart rate ranges from 160 to 180 beats per minute. As the nature of activity is fast, intensity is high so anaerobic is more strenuous and exhaustive. Fast pace method is very effective for improving the VO₂ maximum. 

(c) Varied pace method: This method involves change of pace. In this method sportsmen start with fast continuous method then switch on to slow continuous method. Tire heart beat is maintained between 140 and 180 beats per minute. It is also beneficial for improving both aerobic and anaerobic capacity. The total duration ranges from 15 minutes to 1 hour.

The electric field exists if and only if there is a electric potential difference. If the charge is uniform at all points, however high the electric potential is, there will not be any electric field. Thus, the relation between electric field and electric potential can be generally expressed as – “Electric field is the negative space derivative of electric potential.”

The relation between Electric field and electric potential is mathematically given by-

{tex}E=-\frac{dV}{dx}{/tex}

Where,

E is the Electric field.

V is the electric potential.

dx is the path length.

The relation between Electric field and electric potential is mathematically given by-

Where,

E is the Electric field.

V is the electric potential.

dx is the path length.

– Sign is the electric gradient

Direction of Electric Field

• If the field is directed from lower potential to higher then the direction is taken to be positive.
• If the field is directed from higher potential to lower potential then the direction is taken as negative.

• The process of emission of electrons from the metal surface when a certain amount of energy is absorbed by the metal, is called electron emission
• There are free electrons on the metal surface, present in the outermost (valence) shell that are loosely bound to the nucleus
• These electrons are emitted when a certain minimum amount of external energy is provided to the metal surface. This least value of energy is called work function of metal (denoted by Φ₀)
• The unit of Φ₀ is electron volt(eV). 1eV is defined as the energy needed to accelerate an electron through the potential difference of 1volt(V).
• Work function of a material depends mainly on the nature of metal, and electronic configuration of metal (meaning the number of valence shell electrons, lesser the number, lesser the work function)

The Rayleigh Criterion
The Rayleigh criterion is the generally accepted criterion for the minimum resolvable detail - the imaging process is said to be diffraction-limited when the first diffraction minimum of the image of one source point coincides with the maximum of another.

• Mass defect:-
  • Mass defect is the difference in the mass of nucleus and its constituents(neutrons and protons).
  • It is denoted by ΔM.
  • Mathematically :- ΔM = [Z m_p+ (A-Z) m_n]- M
    • Where m_p=mass of 1 proton, Z=number of protons,(A-Z)= mass of neutrons, m_N = mass of 1 neutronand M =nuclearmass of the atom.
  • For example: -(¹⁶₈O)àOxygen atom has 8 protons and 8 neutrons.
  • Mass of 8 protons à (8x1.00866) u and Mass of 8 neutrons à(8x1.00727) u.
  • Therefore Oxygen nucleus à(8p+8n) à8(1.00866 + 1.00727) = 16.12744u.
  • From spectroscopy ->Atomic mass of (¹⁶₈O) =15.9949u.
  • Mass of 8 electrons =(8x0.00055) u.
  • Therefore Nuclear mass of (¹⁶₈O) = (15.9949 – (8x0.00055)) =15.99053u.
  • Nuclear mass is less than sum of the masses of its constituents.
  • This difference in mass is known as mass defect.
  • It is also known as excess mass.

Lateral inversion is the effect produced by a plane mirror in reversing images from left to right. This is the reason why ambulance is written laterally inverted so that its image is aligned properly.