Bizkit
Oct31-09, 10:56 PM
1. The problem statement, all variables and given/known data
Given that the electric field in a certain region is E = (z+1)*sin(Φ)aρ + (z+1)*ρ*cos(Φ)aΦ + ρ*sin(Φ)az V/m, determine the work done in moving a 4 nC charge from (4,0,0) to (4,30°,0).
2. Relevant equations
W = -Q*int(E·dl)
3. The attempt at a solution
Here is what I get:
W = -4*int((z+1)*ρ*cos(Φ)*ρ*dΦ from 0 to 30°) nJ
W = -4*(z+1)*ρ²*int(cos(Φ) from 0 to 30°) nJ
W = -4*(0+1)*4²*(sin(Φ) from 0 to 30°) nJ
W = -64*(sin(30°) - sin(0)) nJ
W = -64*(.5 - 0) nJ
W = -32 nJ
The book, however, says the answer is -8 nJ. I get this answer when I leave off the ρ from the dl. This is how I think the answer in the book is found:
W = -4*int((z+1)*ρ*cos(Φ)*dΦ from 0 to 30°) nJ
W = -4*(z+1)*ρ*int(cos(Φ) from 0 to 30°) nJ
W = -4*(0+1)*4*(sin(Φ) from 0 to 30°) nJ
W = -16*(sin(30°) - sin(0)) nJ
W = -16*(.5 - 0) nJ
W = -8 nJ
My question is: Is my answer the correct answer?
Given that the electric field in a certain region is E = (z+1)*sin(Φ)aρ + (z+1)*ρ*cos(Φ)aΦ + ρ*sin(Φ)az V/m, determine the work done in moving a 4 nC charge from (4,0,0) to (4,30°,0).
2. Relevant equations
W = -Q*int(E·dl)
3. The attempt at a solution
Here is what I get:
W = -4*int((z+1)*ρ*cos(Φ)*ρ*dΦ from 0 to 30°) nJ
W = -4*(z+1)*ρ²*int(cos(Φ) from 0 to 30°) nJ
W = -4*(0+1)*4²*(sin(Φ) from 0 to 30°) nJ
W = -64*(sin(30°) - sin(0)) nJ
W = -64*(.5 - 0) nJ
W = -32 nJ
The book, however, says the answer is -8 nJ. I get this answer when I leave off the ρ from the dl. This is how I think the answer in the book is found:
W = -4*int((z+1)*ρ*cos(Φ)*dΦ from 0 to 30°) nJ
W = -4*(z+1)*ρ*int(cos(Φ) from 0 to 30°) nJ
W = -4*(0+1)*4*(sin(Φ) from 0 to 30°) nJ
W = -16*(sin(30°) - sin(0)) nJ
W = -16*(.5 - 0) nJ
W = -8 nJ
My question is: Is my answer the correct answer?