Shahjahan notes:Electrostatics formula-1
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1. This document lists formulas related to electrostatics including: 2. Quantization of electric charge, Coulomb's law, electric field due to point charges, dipoles, and conductors. 3. It also includes formulas for electric potential, capacitance, work and energy related to electrostatic systems, and forces between charged plates.
Shahjahan notes:Electrostatics formula-1
- 1. Shahjahan-electrostatics-formula… Shahjahan-electrostatics-formula SL. NO. quantities FORMULA (RELATIONS ) Electrostatics 1 Quantisationof Elect.Charges(Q) on a body Q = n.e n isIntegral Number,e ischarge on electron 1.6 X 10-19 C 2 Electrostaticforce constant 1/(4πϵ₀) value : 9 x 109 Nm2 C-2 3 Permittivity ϵ₀ 8.85 x 10-12 C2 N-1 m-2 4 Coulumb'sLaw F = q1q2/4πε₀r² q1 and q2 are two chargesplacedat distance r. 5 Forceson twocharges F12 = - F21 Directionof F isalongr. 6 DielectricConstant K = ε/ε₀ = εr ε is absolute permittivityof medium, ε₀ is permittivity of free space, εr is relative permittivity. 7 ElectricFieldata point E = F/q F isforce experiencedbythe testcharge q at a point.E is called fieldintensityatthat point Force withrespectto field F = q.E 8 Electricfielddue tosource charge Q at distance r E = Q/(4πε₀r²) Directionof E is alongr. 9 ElectricFielddue todipole ona pointon axial line E = 2P/(4πε₀r³) P isdipole moment,risdistance from centre of dipole onaxial line. 10 ElectricFielddue todipole ona pointon equitorialline E = P/(4πε₀r³) P isdipole moment,risdistance from centre of dipole onequitorial line. 11 Electric Field due to dipoleatany general point, atdistancer making angleθ with P ⃗ E = P√I(3cos²θ+1)/4πε₀r³ r is distanceof pointfrom midpointof dipole, θ is anglebetween direction of r and dipolemoment P E makesangle α withr then tan α = 1 2 tanθ α isangle betweenresultantfieldand directionof r, θ isangle betweenrandP 12 E atany pointon the axis of a uniformly charged ringat distancer qr/4πε₀(r²+a²)³⁄² 13 Torque on a dipole keptin ElectricField τ = PESinθ or τ = Px E P is dipolemoment, E is electric field,Direction of Torque is normal to plain containingP and E 14 Work done forrotatingdipole by angle θ W = PE(1- Cosθ) P isdipole moment.Eiselectricfield 15 Potential Energy of dipolein equilibriumcondition when P is alongE. U = - PE P isdipole moment.Eiselectricfield 16 Potential energyof dipole at90 degree toE Zero 17 Potential energy of dipoleat 180 0 U = + PE P isdipole moment.Eiselectricfield 18 ElectricFlux φE φE= E.S = ∫E.ds 19 gausstheorem φE= ∮〖E.ds〗 = q/ε₀ Flux linkedtoaclosedsurface isq/ε₀times the charge enclosedinit. 20 Fielddue toinfinite longstraight chargedconductor λ/2πϵ₀r λ is linearcharge densityinthe conductor,ris the perpendiculardistance. 21 Electricfielddue toinfinite plane sheetof charge σ /2ϵ₀ σ is areal charge density.Independentof distance 22 Withintwoparallal sheetsof σ /ϵ₀ Outside,fieldiszero
- 2. Shahjahan-electrostatics-formula… opposite charges 23 Withintwoparallal sheetsof similarcharges zero Outside,fieldisσ/ϵ₀ 24 Electricfielddue tospherical shell, outside shell E = q/(4πε₀r²) q ischarge on shell,rdistance fromcentre. 25 Electricfieldonthe surface of spherical shell. E = q/(4πε₀R²) R is radiusof shell 26 Electric field inside spherical shell. Zero 27 Electric field insidethe sphere of charge distributed uniformly all over the volume . E = rρ/3Є r is radiusof sphere, ρ is volumetric charge density, is permittivity of medium 28 Potential due tocharge Q at distance r V = Q/(4πε₀r) Potential ischaracteristicof thatlocation 29 Potential Energywithcharge q keptat a pointwithpotentialV U = qV = Qq/(4πε₀r) Potential Energyisthatof the system containingQand q. 30 Work done for in moving a chargeq through a potential difference of V W = q(V2-V1) V = (v2 -v1) Energyof systemof twocharges U = q1q2/(4πε₀r) 31 Relationof E andV E = - dv/dr dv is potential difference between two points at distancer where r and E are in the same direction. 32 Relationof E andV and θ E Cosθ = - dv/dr where θis angle betweendrandE 33 Potential atinfinity /inearth Zero 34 Electric Potential due to dipoleon a point on axial line V = P/(4πε₀r²) P isdipole momentum,risdistance from centre of dipole 35 Electric Potential due to dipoleon a point on equitorial line Zero 36 ElectricPotential due todipole at any general point, V = P cosθ / 4πε₀ (r2- a2 cos²θ) P isdipole momentum,risdistance from centre of dipole,aishalf lengthof dipole, is angle betweenrandP 37 Work done in moving a charge between two points of an equipotential surface Zero 38 Capacitance of a spherical conductor 4πε₀R R is radiusof the sphere 39 Capacitance of a parallal plate capacitor ε₀kA/d A is area of each plate, d is distancebetween them, k is dilectric constantof the medium between plates. 40 DielectricConstant k = C / C₀ Cis capacitancewith medium within plates,and C₀ is capacitancein free space. 41 Capacitance of a spherical capacitor. C = 4πε₀rarb/(ra-rb) ra and rb are radius of internal and external spherical shells 42 Equivalentcapacitance for Capacitorsinparallal C = c1 + c2 +c3…. Cisequivalentcapacitance,c1,c2 are capacitnce of the capacitorsjointtogether. 43 Equivalentcapacitance for Capacitorsin series 1/C = 1/c1 + 1/c2 + 1/c3 . . . 44 Charge,capacitance,Potential Difference C = q/V q ischarge onthe plate of capacitor andV is Potential Difference betweenthe plates. 45 Energystoredincapacitor ½cv2 , ½qv, ½q2 /c q ischarge, c is capacitance,vis Pot. Difference
- 3. Shahjahan-electrostatics-formula… 46 CommonPotential V=C1V1+C2V2)/C1+C2 47 Energylossinconnecting 1 2 C₁C₂ C1+C₂ (V1-V2)2 c1 at v1 is connectedtoc2 at v2 48 C withdielectricslab inserted ε₀kA/d-t(1-1/k) t is thicknessof dielectricslabof constantk, 49 C withmetal plate inserted ε₀kA/(d-t) t is thicknessof metal plate inserted, 50 Force of attraction between plates ½q2 /ε₀A, ½ε₀E2 A q ischarge on plate,A isarea, E Elect.Field.