Electromagnetism- Potential Energy

Potential Energy

It is the amount of work done to bring a charge q from infinity to that point against the electric fields of a given charge without changing its kinetic energy.

PE = qQ/4πε₀r = qV

Work doneW = ?PE = PE_final- PE_initial

= q₁q₂/4πε₀[(1/r_f) - (1/r₁]

Force on a surface charge:- the repulsive force acting on an element of a charged surface due to rest of the charged surface is called electric force on a charged conducting surface.

E = E_!+ E₂= σ/ε₀whereE₁is the electric field due to small element andE₂is due to rest of the charge.

E₁= E₂

Therefore electric field intensity near a charged surface =σ/ 2ε₀and forcedF = σ²/ 2ε₀ds

ThereforeF = ?σ²/ 2ε₀ds

和压力p_埃尔ect.= dF / ds = σ²/ 2ε₀= ε₀E₂/ 2

In case of a soap bubble

P_in- p_out= P_excess= P_ST= P_埃尔ect.= 4T / r = σ²/ 2ε₀

= 4T / r - q²/ 2 A²ε²₀= 4T / r - q²/ 32 π²r₄ε₀

If air pressure inside and outside the bubble are equal then

P_in= P_outor 4T / r = q²/ 32 π²r₄ε₀

Energy density = energy per unit volume

U = ε₀E²/ 2 = σ²/ 2ε₀

总能量U_tot= ∫ε₀E2 / 2 dV

Charged liquid drop if a identical drops each of radius r and charge q are joined to form a big drop of radius R and charge Q

ThenR = n₁/3 r Q big = nqsmall

E_大= n₁/3 E_small; V_大= n₂/3 V_small; σ_大= n1/3 σ_small


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