Linear/Surface/Volume Charge Density

In summary, the linear charge density along the arc is -1.9309*10^-15 C/m, the surface charge density over the face of the disk is -4.8733*10^-14 C/m^2, the surface charge density over the surface of the sphere is -1.2183*10^-14 C/m^2, and the volume charge density in the sphere is -1.9236*10^-12 C/m^3.
  • #1
wbluem88
4
0

Homework Statement



(a) A charge of -345e is uniformly distributed along a circular arc of radius 4.00 cm, which subtends an angle of 41°. What is the linear charge density along the arc?

(b) A charge of -345e is uniformly distributed over one face of a circular disk of radius 1.90 cm. What is the surface charge density over that face?

(c) A charge of -345e is uniformly distributed over the surface of a sphere of radius 1.90 cm. What is the surface charge density over that surface?

(d) A charge of -345e is uniformly spread through the volume of a sphere of radius 1.90 cm. What is the volume charge density in that sphere?

Homework Equations





The Attempt at a Solution



OK so this should be really simple right??

Part a)

CHARGE / DISTANCE
(-345 * 1.602 * 10^-19)/((41/360)*2*pi*.04) = -1.9309*10^-15 C/m


Part b)

CHARGE / AREA
(-345 * 1.602 * 10^-19)/(pi*.019^2) = -4.8733*10^-14 C/m^2


part c)

CHARGE / AREA
(-345 * 1.602 * 10^-19)/(4*pi*.019^2) = -1.2183*10^-14 C/m^2


part d)

CHARGE / VOLUME
(-345 * 1.602 * 10^-19)/((4/3)*pi*.019^3) = -1.9236*10^-12 C/m^3



According to my WebAssign homework, all these are wrong. What am I doing?
 
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  • #2
Nothing that I can see. I get a different exponent for the first one, but that's probably just a typo. Wrong number of significant figures? Something nit-picky like that?
 

FAQ: Linear/Surface/Volume Charge Density

What is linear charge density?

Linear charge density, also known as linear charge distribution, is a measure of the amount of electric charge per unit length along a line. It is denoted by the symbol λ (lambda) and is expressed in units of coulombs per meter (C/m).

How is surface charge density defined?

Surface charge density is a measure of the amount of electric charge per unit area on a charged surface. It is denoted by the symbol σ (sigma) and is expressed in units of coulombs per square meter (C/m²).

What is volume charge density?

Volume charge density, also known as volumetric charge density, is a measure of the amount of electric charge per unit volume in a three-dimensional space. It is denoted by the symbol ρ (rho) and is expressed in units of coulombs per cubic meter (C/m³).

How is linear charge density calculated?

Linear charge density can be calculated by dividing the total charge on a line by its length. The formula for linear charge density is λ = Q/L, where λ is the linear charge density, Q is the total charge, and L is the length of the line.

What is the relationship between surface and volume charge density?

The relationship between surface and volume charge density is that they are both measures of electric charge per unit area or volume, respectively. Surface charge density is used for two-dimensional surfaces, while volume charge density is used for three-dimensional spaces. They are related by the formula ρ = σ/d, where ρ is the volume charge density, σ is the surface charge density, and d is the thickness of the charged surface.

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