# Physics

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Physics

## 2. Electric

### 2.1. Electrostatic

2.1.1. Columb law. F=kqq'/r^2

2.1.2. Field. E=F/q

2.1.2.1. Due to ring. E=KQx/(R^2+x^2)^3/2

2.1.3. Potential energy. U=kqq'/r

2.1.4. Potential. V=kq/r or v=w/q

2.1.4.1. dv=E.dr

2.1.5. Dipole moment, p=q*2a

2.1.5.1. Axis =2kp/r^3

2.1.5.2. Equator =-kp/r^3

2.1.6. Gauss law.

2.1.6.1. Φ=E. A=EAcosα

2.1.6.2. Φ=§E.dA=q in. /€•

2.1.6.3. Net flux =0 for close surface

2.1.7. Capacitor

2.1.7.1. Capacitance. C=Q/V

2.1.7.1.1. For parallel plate. =A€o/d

2.1.7.1.2. Spherical. =4π€oRr/r-R

2.1.7.2. Combination

2.1.7.2.1. Series. 1/C=1/c1+.....+1/cn

2.1.7.2.2. Parallel. C=c1+....+cn

2.1.7.3. Field between capacitor =Q/2A€o

2.1.7.4. Dielectric. C=C€o

### 2.2. Current electricity

2.2.1. Density. i=§ j. dA

2.2.1.1. j=nev(d)

2.2.2. Drift v. =eΕτ/2m

2.2.3. Ohm'slaw

2.2.3.1. j=σE

2.2.3.2. ९=1/σ

2.2.4. Charging of capacitor

2.2.4.1. q=£C(1-e^-t/cR)

2.2.5. Discharging capacitor

2.2.5.1. q=Qe^-t/RC

2.2.6. Thermal energy produce in resistor U=i^2Rt

## 3. Magnetic

### 3.1. Force

3.1.1. On point F=qvBsinα

3.1.2. On current carrying wire F'=il' X B'

3.1.3. Torque. τ=iA' x B' (iA= magnetic dipole moment)

3.1.4. Pitch of helical. P=T v(parallel)

### 3.2. Field due to current

3.2.1. Biotsivert law . Β=μi dl sinθ /4πr^2

3.2.2. Amperes law. §B. dl=μο i(net)

3.2.3. Large sheet of current. B=μοk/2

## 4. Electro magnetic

### 4.2. motional emf.f=-e(v x b)

4.2.1. Motion of electron stop when. F(electric)=F(magnetic)

4.2.2. Emf of moving conductor.ε=Blv

4.2.3. With angle Θ . ε=Bvl sinθ

4.2.4. Due to rotation. ε=Bωl^2/2

4.2.5. General form. §(v x B). dl

### 4.3. Induced electric field.

4.3.1. §E. dl=-dΦ(B) /dt

### 4.4. Mutual induction. (M)

4.4.1. Φ2=-M i1

4.4.1.1. ε=-M di/dt

### 4.5. Self induction. (L)

4.5.1. Φ=-Li

4.5.1.1. ε=-Ldi/dt

### 4.6. Induced emf. ε(ind.)=-dΦ/dt

4.6.1. Emf produced only when ф varies. ф = BA cosፀ

### 4.7. Energy stored in inductor. E=L i^2/2

4.7.1. Energy density in magnetic field. U=B^2V/2μο.(V=volume)

## 5. Modern physics

### 5.1. Photoelectric effect. (ejection of electron)

5.1.1. Energy of photons. E=hc/λ=hν (h= plank's constant=6.62 x 10^-34

5.1.1.1. Kinetic energy. K(max)=hν-Φ

5.1.2. Momentum of photons. P=h/λ=E/c.

5.1.3. Frequency. ν=Φ/h

5.1.4. Stopping potential. Vο=K. E. /e=hν/e - φ/e

### 5.2. Dual nature of light.

5.2.1. Equivalent mass of photon

5.2.1.1. M=hν/c^2

5.2.2. No. of photon per unit time from source.

5.2.2.1. n=p/E (p=power of source)

5.2.3. Intensity

5.2.3.1. I=p/A

5.2.4. Photon flux

5.2.4.1. Φ=I/E

5.2.5. Force on surface

5.2.5.1. For black body.

5.2.5.1.1. F=p/c

5.2.5.2. Reflecting body

5.2.5.2.1. F=2p/c

5.2.6. De broglie.

5.2.6.1. λ=h/p=h/mv=h/√2mk=h/√2mqV(volt)

5.2.6.2. For electron. λ=12.27/√V(volt)

### 5.3. Atomic physics

5.3.1. ΔΕ=hν, mvr=nh/2π

5.3.2.1. Velocity. v=cz/137 n

5.3.3. K. E. =ze^2/8πεοr P. E. U=-2 K. E.

5.3.3.1. Total = K. E + U = -K. E. =13.6z^2/n^2

5.3.3.1.1. E=-k. E=1/2 U

5.3.3.2. Exitation potential. V=E(ext) /e

5.3.4. Wave length of photons. 1/λ=R[1/n^2 - 1/m^2]

5.3.4.1. Lyman, Balmer, paschen, Brackett, pfund

### 5.4. Nuclear physics

5.4.1. Radius of nucleus. R=R'A^1/3 (R'=1.1 x 10^-15)

5.4.1.1. Mass defect =mass expected - mass observed

5.4.1.1.1. Mass expected=atomic mass Mass observed=atom mass - mass of electron

5.4.2. Stability is depending on B. E. / nucleon

5.4.2.1. B. E. /nucleon=B.E./mass no.

5.4.2.1.1. B. E. =Mass defect x c^2

5.4.3. Packing fraction (f) α 1/stability

5.4.3.1. (f) = mass defect/ mass no.

5.4.4. Q value. Is define energy release during decay process

5.4.4.1. Q=Σ(B. E.) product -Σ(B. E.) reactant

5.5.1. Law of decay. N=Nο(e-λt)

5.5.2. Average life of nucleus. T(avg)=1/λ.

5.5.3. Activity. Rate of disintegration

5.5.3.1. A=Aο (e^-λt). (Aο =Nο (-λ))

5.5.4. Probability of surviving nuclei

5.5.4.1. P(survival)=e^-λt

## 6. Optics

### 6.1. Reflection

6.1.1. Mirror formula. 1/v+1/u=1/f

6.1.1.1. Magnification. M=h(obj)/h(img)=-v/u

6.1.1.1.1. Power. P=-1/f

6.1.2. Velocity. v(i)=-m^2v(obj)

### 6.2. Refraction

6.2.1. Snells law. sin(i)/sin(r)=v1/v2=μ2/μ1

6.2.2. Image due to refraction at plan surface

6.2.2.1. For denser to rare Apparent depth =μ2/μ1(actual depth)

6.2.2.2. For rare to denser Apparent depth /actual depth =1/μ

6.2.2.3. Multiple medium

6.2.2.3.1. d(ape)=d(act)/μ1+d(act)μ2....

6.2.3. At curved surface. μ2/v -μ1/u= μ2-μ1/R

6.2.3.1. Magnification. M=h(i)/h(o)=vμ1/uμ2

6.2.4. TIR critical angle. Θ(c)

6.2.5. Glass slab

6.2.5.1. Normal shift. d=(μ-1)t/μ

6.2.5.2. Lateral shift. Δ=t sin(i-r) /cosr

6.2.6. Prism.

6.2.6.1. Deviation. δ=i+e-(r1+r2) (A=r1+r2= angle of prism)

6.2.6.1.1. Minimum deviation. i=e ,r1=r2

6.2.6.1.2. Max. deviation. i=π/2

6.2.6.2. Grazing angle. A<or= 2 θc.

6.2.6.3. Dispersion.

6.2.6.3.1. Deviation ray. δ=A(μ-1).

6.2.7. Lens

6.2.7.1. Lens maker formula. 1/v-1/u=(μ2/μ1-1)[1/R1-1/R2]

6.2.7.1.1. Lens formula. 1/v-1/u=1/f

### 6.3. Wave

6.3.1. Δφ/2π=ΔΧ/λ

6.3.2. Amplitude. A^2=A1^2+A2^2+A1A2cosφ

6.3.3. Intensity. I α A^2

6.3.3.1. I(max)= (√I1 + √I2)^2

6.3.3.2. I(min)=(√I1 - √I2)^2