All the Impotant Fomulae that a student should know fom. XII Physics Unit : CHAPTER - ELECTRIC CHARGES AND FIELD CHAPTER ELECTROSTATIC POTENTIAL AND CAPACITANCE S. Fomula No.. Quantization of chage Q = ± ne, Desciption Q = total chage (coulomb) e = chage on one electon (coulomb) n = numbe of electons. The foce between two chages q and q at a distance fom each othe qq F = ˆ. Supeposition pinciple - F = F + F + F +... 4. Electic field stength E at a point distance away fom a point chage q q E = ˆ 5. Electostatic foce F on a chage q inside the electic field E F = q E F = foce (newton) q and q = chages (coulomb) = distance between chages F = net foce on the system (newton) F,F and F. = diffeent foces woking on the system (newton) E = Electic field stength (volt / mete) = distance fom a point chage q = point chage (coulomb) E = Electic field stength (volt / mete) F = Electostatic foce (newton) q = point chage (coulomb) 6. Dipole moment p = q a q = one of the chages (coulomb) a = sepaation between two chages
7. Dipole field intensity on axial line of dipole p E = 4 πε ( a ) E = Electic field stength (volt / mete) a = sepaation between two chages of the dipole 8. Dipole field intensity on equatoial line of dipole p E = 4 πε ( + a ) / E = Electic field stength (volt / mete) a = sepaation between two chages of the dipole 9. Dipole field intensity at any point due to a shot dipole p E = cos α +, 4πε and tanβ = tan α E = Electic field stength (volt / mete) of the dipole α= angle which the line joining the point to cente of dipole makes with the axis of dipole. Toque on dipole inside electic field is τ = p E. Potential enegy of dipole U = pe(cos θ cos θ ) β = the angle at which E is inclined to the line joining the point the cente of dipole. E = Electic field stength (volt / mete) τ = toque (newton mete) E= Electic field stength (volt / mete) θ = initial angle betweenp and E
θ = final angle between p and E. Flux φ = E. S U = potential enegy E = Electic field stength (volt / mete) S = S ˆn = aea element (mete ) φ = flux (webe). Gauss s law: q φ = ε 4. Application of Gauss s law: Electic field due to thin infinitely long staight wie of unifom linea chage density λ E = nˆ πε 5. Electic field due to infinite thin plane sheet of unifom suface chage density σ E = ε nˆ 6. Electic field due to thin spheical shell unifom suface chage density q E = ˆ ( R ) E = ( < R ) 7. Potential at a point due to single chage φ = Electic flux though a closed suface (webe) S = aea of closed suface (mete ) q = total chage enclosed by S (coulomb) λ= linea chage density (coulomb / mete) = pependicula distance of the point fom the wie E = Electic field intensity (volt / mete) ˆn = adial unit vecto σ = suface chage density (coulomb / mete ) E = Electic field intensity (volt / mete) ˆn = unit vecto nomal to the plane σ = suface chage density (coulomb / mete ) E = Electic field intensity (volt / mete) = the distance of the point fom the cente of the shell R = adius of the shell q =total chage on shell V = Potential (volt) q = Point chage (coulomb)
q = distance V = 4πε 8. Potential at a point due to goup of N chages = = πε i N qi V 4 i= i 9. Relation between potential gadient and electic field E = dv d. Electic potential enegy of a system of two point chages qq U = 4πε. Electic potential enegy of a system of n point chages qq U = πε i j 4 i,j,i j ij V = Potential (volt) q i = Point chages (coulomb) i = Distances E = Electic field (volt / mete) dv d = Potential gadient (volt / mete) U = Electic potential enegy (joule) q and q = Chages (coulomb) = Distance between chages U = Electic potential enegy (joule) q i and q j = Chages (coulomb) ij = Distance between chages. Capacity C = Q / V Q = Chage (coulomb). Capacity of a spheical conducto C = 4πε 4. Capacity of a paallel plate capacito with ai as dielectic ε C = A d 5. Capacity of a paallel plate capacito with insulating medium as dielectic kεa C = d V = Potential diffeence (volt) = adius A = Aea of plate (mete ) A = Aea of plate (mete ) k = dielectic constant 6. Capacitos in seies C s = Resultant capacitance
= + +... Cs C C C C, C, C = Independent capacitances 7. Capacitos in paallel C p = Resultant capacitance Cp = C + C + C +... 8. Enegy stoed in capacito Q E = QV = = CV C C, C, C = Independent capacitances E = Enegy stoed (joule) Q = Chage (coulomb) C = Capacitance 9. Common potential q + q C V + C V V = = C + C C + C. Loss of enegy on shaing chages CC (V V ) E = (C + C ). Capacity of a paallel plate capacito with a conducting slab of thickness t in between the plates C ε = A d t. Capacity of a paallel plate capacito with a dielectic slab of thickness t in between the plates ε C = A d t( ) k V = Potential diffeence (volt) V = Common potential (volt) V, V = Independent voltages (volt) C, C = Independent capacitances E= Enegy loss (joule) V, V = Independent voltages (volt) C, C = Independent capacitances t = Thickness of slab A = Aea of plate (mete ) t = Thickness of slab A = Aea of plate (mete ) k = dielectic constant