NTA NEET PHYSICS

Formula Chart- Motion in plane

🔥🔥Electric Dipole 🔥🔥 🔻The energy of electric dipole is given by U = – p.E. 🔻The energy of a magnetic dipole is U = – μ .B C. 🔻Electric Charge : Q = ± ne (e = 1.60218 × 10-29 C) 🔻SI unit of Electric Charge is Coulomb (C) 🔻Coulomb’s Law : Electrostatic Force (F) = k[q1q2/r2] and, In Vector Form : →F=k(q1q2)×→r/r3 Where, q1 and q2 = Charges on the Particle, r = Separation between them, →r = Position Vector, k = Constant = 14πϵ0=8.98755×109Nm2C2 🔻Electric Current : The current at Time t : i=limΔt→0 ΔQ/Δt= dQ/dT Where Δ Q and Δ T = Charges crosses an Area in time Δ T SI unit of Current is Ampere (A) and 1A = 1 C/s 🔻Average current density: →j=Δi/Δs j=limΔs→0 Δi/Δs=di/dS , j=Δi/ΔScosθ Where, Δ S = Small Area, Δ i = Current through the Area Δ S, P = Perpendicular to the flow of Charges, θ = Angle Between the normal to the Area and the direction of the current. 🔻Kirchhoff’s Law: Law of Conservation of Charge: I3 = I1 + I2 Resistance 🔻Resistivity : ρ(T)=ρ(T0)[1+α(T−T0)] R (T) =R (T0) [1+α (T−T0)] Where, ρ (T) and ρ (T0) = Resistivity at Temperature T and T0 respectively, α = Constant for given material. 🔻Lorentz Force : →F=q[→E+(→v×→B)] Where, E = Electric Field, B = Magnetic Field, q = Charge of Particle, v = Velocity of Particle. 🔻Magnetic Flux: Magnetic Flux through Area dS = ϕ=→B⋅d → S= B⋅dS Cos θ Where, d→S = Perpendicular vector to the surface and has a magnitude equal to are Ds, →B = Magnetic Field at an element, θ = Angle Between →B and d→S, SI unit of Magnetic Flux is Weber (Wb).

Formulas related to distance, displacement, velocity and accelration 📝d = vt 📝d = at² 📝d = (vf + vi/2) ×t 📝d = 5t² (for distance in 'n' seconds) 📝d = 5(2tn - 1) (for distance in 'nth' second) 📝d = 1/2 mv²/F 📝d = vit + 5t² 📝d = v × underroot 2H/g 📝d = vt = x°wt = x°2pi/T × t = x°2pift 📝x = x° Sin wt 📝x = x° Sin (underroot k/m) t vf = vi + at 📝2as = vf² - vi² 📝2as = (vi + at)² - vi² 📝2as = vf² - (vf - at) ² 📝v = underroot Vfx² + Vfy² 📝v = Power/Force 📝v = 2×K.E/momentum (k.e = 1/2 Pv) 📝v² = 2×Power×time/mass (P = mv²/2t) v = underroot 2as v = underroot gr (speed at highest point in a verticle circle) v = underroot 5gr (speed at lowest point in a verticle circle) 📝v² = 2FS/m 📝v² = 2E/m 📝v² = 2Ve/m 📝v = eBr/m (velocity of particle under action of magnetic force along circular path) 📝v² = Force/Area.Density 📝v = w underroot x°² - x² 📝v = underroot k/m × underroot x°² - x² 📝v = x°w (at mean position where x=0) 📝v = x° underoot k/m 📝v = v° underroot 1 - x²/x°² (for determining ratio b/w inst. Velocity and maxi. Velocity) 📝v= x°2pif = x°2pi/T 📝a = x°w² = x°w.w = vw = v.2pif Common velocity = m1v1/m1+m2 📝vi² = Rg/Sin2theta 📝v = underoot Tension×length/mass 📝V = 2pi ke²/nh (speed of e- in nth orbit) 📝Vn = V/n 📝v = nh/2pimr (lambda = 2pir and lambda=h/p) 📝ma = kx 📝a = kx/m (SHM) 📝a = - gx/l (Simple pendulum) 📝ac = v²/r

📚Notes on Trigonometric Equations and Identities📚 A function f(x) is said to be periodic if there exists some T > 0 such that f(x+T) = f(x) for all x in the domain of f(x). In case, the T in the definition of period of f(x) is the smallest positive real number then this ‘T’ is called the period of f(x). Periods of various trigonometric functions are listed below: 1) sin x has period 2π 2) cos x has period 2π 3) tan x has period π 4) sin(ax+b), cos (ax+b), sec(ax+b), cosec (ax+b) all are of period 2π/a 5) tan (ax+b) and cot (ax+b) have π/a as their period 6) |sin (ax+b)|, |cos (ax+b)|, |sec(ax+b)|, |cosec (ax+b)| all are of period π/a 7) |tan (ax+b)| and |cot (ax+b)| have π/2a as their period ➖Sum and Difference Formulae of Trigonometric Ratios 1) sin(a + ß) = sin(a)cos(ß) + cos(a)sin(ß) 2) sin(a – ß) = sin(a)cos(ß) – cos(a)sin(ß) 3) cos(a + ß) = cos(a)cos(ß) – sin(a)sin(ß) 4) cos(a – ß) = cos(a)cos(ß) + sin(a)sin(ß) 5) tan(a + ß) = [tan(a) + tan (ß)]/ [1 - tan(a)tan (ß)] 6)tan(a - ß) = [tan(a) - tan (ß)]/ [1 + tan (a) tan (ß)] 7) tan (π/4 + θ) = (1 + tan θ)/(1 - tan θ) 8) tan (π/4 - θ) = (1 - tan θ)/(1 + tan θ) 9) cot (a + ß) = [cot(a) . cot (ß) - 1]/ [cot (a) +cot (ß)] 10) cot (a - ß) = [cot(a) . cot (ß) + 1]/ [cot (ß) - cot (a)] ➖Double or Triple -Angle Identities 1) sin 2x = 2sin x cos x 2) cos2x = cos2x – sin2x = 1 – 2sin2x = 2cos2x – 1 3) tan 2x = 2 tan x / (1-tan 2x) 4) sin 3x = 3 sin x – 4 sin3x 5) cos3x = 4 cos3x – 3 cosx 6) tan 3x = (3 tan x - tan3x) / (1- 3tan 2x) ➖For angles A, B and C, we have 1) sin (A + B +C) = sinAcosBcosC + cosAsinBcosC + cosAcosBsinC - sinAsinBsinC 2) cos (A + B +C) = cosAcosBcosC- cosAsinBsinC - sinAcosBsinC - sinAsinBcosC 3) tan (A + B +C) = [tan A + tan B + tan C –tan A tan B tan C]/ [1- tan Atan B - tan B tan C –tan A tan C 4) cot (A + B +C) = [cot A cot B cot C – cotA - cot B - cot C]/ [cot A cot B + cot Bcot C +  cot A cotC–1] ➖List of some other trigonometric formulas: 1) 2sinAcosB = sin(A + B) + sin (A - B) 2) 2cosAsinB = sin(A + B) - sin (A - B) 3) 2cosAcosB = cos(A + B) + cos(A - B) 4) 2sinAsinB = cos(A - B) - cos (A + B) 5) sin A + sin  B = 2 sin [(A+B)/2] cos [(A-B)/2] 6) sin A - sin  B = 2 sin [(A-B)/2] cos [(A+B)/2] 7) cosA + cos  B = 2 cos [(A+B)/2] cos [(A-B)/2] 8) cosA - cos  B = 2 sin [(A+B)/2] sin [(B-A)/2] 9) tanA ± tanB = sin (A ± B)/ cos A cos B 10)cot A ± cot B = sin (B ± A)/ sin A sin B ➖Method of solving a trigonometric equation: 1) If possible, reduce the equation in terms of any one variable, preferably x. Then solve the equation as you used to in case of a single variable. 2) Try to derive the linear/algebraic simultaneous equations from the given trigonometric equations and solve them as algebraic simultaneous equations. 3) At times, you might be required to make certain substitutions. It would be beneficial when the system has only two trigonometric functions. ➖Some results which are useful for solving trigonometric equations: 1) sin θ = sina and cosθ = cosa ⇒ θ = 2nπ + a 2) sin θ = 0 ⇒ θ = nπ 3) cosθ = 0 ⇒ θ = (2n + 1)π/2 4) tan θ = 0 ⇒ θ = nπ 5) sinθ = sina⇒ θ = nπ + (-1)na where a ∈ [–π/2, π/2] 6) cosθ= cos a ⇒ θ = 2nπ ± a, where a ∈[0,π] 7) tanθ = tana⇒ θ = nπ+ a, where a ∈[–π/2, π/2] 8) sinθ = 1 ⇒ θ= (4n + 1)π/2 9) sin θ = -1 ⇒ θ = (4n - 1) π /2 10) sin θ = -1 ⇒ θ = (2n +1) π /2 11) |sinθ| = 1⇒ θ =2nπ 12) cosθ = 1 ⇒ θ =(2n + 1) 13) |cosθ| = 1⇒ θ =nπ

Modern physics

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🔰Thermal properties of matter 🔰

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