Charge density: Continuous charge Evenly distributed charges Body charge density

Question

Charge density: Continuous charge Evenly distributed charges Body charge density = Q/Volume = dq/dV = Q_total/total unit _____ Q_total = _____: dq = _____ surface charge density sigma = Q/area = dq/dA = Q_total/Area Q_total = _____: dq = _____ sigma unit _____ Linear charge density lambda = Q/length = dq/dL = Q_total/length total. Q_total = _____: dq = _____ For a cylinder with radius = r: length = L: total charge = Q. Area = Find its and lambda: Find the relation between and lambda. = Q/V = lambda = Q/ = lambda = Q = integral dq = integral = integral sigma = integral lambda sigma, and lambda can be non uniform, but in this course, we only consider uniform charge distribution, so that sigma, lambda are constants E = K_e Q/r^2 r is for A point charge. It is not for charges with various shapes and sizes. A ring bit of dq inside, can be considered as A point creates dE at P. dE = Total E at P is E = integral dE (Vectors!) E notequalto integral dE

Explanation / Answer

Fopr evenly distributed charges
Body charge density , rho = Q/Volume = dQ/dV = Qtotal/Vtotal
Qtotal = rho*VOlume
dQ = rho*dV
rho unit -> C/m^3

for surface charge density
sigma = Q/Area = dq/dA = Qtotal/Atotal
Qtotal = sigma*Area
dq = sigma*dA
sigma unit-> C/m^2

for linear charge distribution
lambda = Q/length = dq/dl = Qtotal/Ltotal
Qtotal = lambda*Ltotal
dQ = lambda*dl
unit of lambda = C/m

for a cylinder with radius r, length l, total charge Q

rho = Q/Volume = Q/pi*r^2*l
sigma = Q/surface area of cylinder = Q/(2*pi*r*l + pi*r^2)
lambda = Q/l

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