Mo0o
Lifer
Ok guys ive been mulling over the physics question for awhile now. I've actually already solved it once except when i come back and look at it again i can't figure out how I did it.
Picture
A half-ring with a radius 8 cm has a total charge 3 µC uniformly distributed along its length. A half-ring with a radius 8 cm has a total charge 3 µC uniformly distributed along its length.
I found the charge density on the ring to be .0000119 (1.19 e -15 C/M). Now I'm trying to set up my integral to figure out the total Ex since that will be Enet since Ey's cancel. I know that for a small charge dQ on the ring, the E field produced is kdQ/r^2 and the Ex component would be k(dQ)/r^2cos(theta). So now I'm trying to define dQ and to figure out an appropriate integral to find the total E field.
I tried dQ=Lamda * dx (which in hindsight didn't make a lot of sense). So i set the integral to int( (k*lambda/r^2) * cos(theta) dx ). I then converted cos(theta) to x/r and moved all the non variables out front so I just have (k*lambda/r^3)*int(xdx). I then set the limits of the integral to 0, .08 since the minimum x distance is 0 when looking at the top of the ring and X=R when directly to the left. I then multiplied the whole thing by 2 to account for the bottom half.
When I get the answer it's half of what I should be getting. Where am I going wrong? What should be the appropriate definition of dQ in this case?
Picture
A half-ring with a radius 8 cm has a total charge 3 µC uniformly distributed along its length. A half-ring with a radius 8 cm has a total charge 3 µC uniformly distributed along its length.
I found the charge density on the ring to be .0000119 (1.19 e -15 C/M). Now I'm trying to set up my integral to figure out the total Ex since that will be Enet since Ey's cancel. I know that for a small charge dQ on the ring, the E field produced is kdQ/r^2 and the Ex component would be k(dQ)/r^2cos(theta). So now I'm trying to define dQ and to figure out an appropriate integral to find the total E field.
I tried dQ=Lamda * dx (which in hindsight didn't make a lot of sense). So i set the integral to int( (k*lambda/r^2) * cos(theta) dx ). I then converted cos(theta) to x/r and moved all the non variables out front so I just have (k*lambda/r^3)*int(xdx). I then set the limits of the integral to 0, .08 since the minimum x distance is 0 when looking at the top of the ring and X=R when directly to the left. I then multiplied the whole thing by 2 to account for the bottom half.
When I get the answer it's half of what I should be getting. Where am I going wrong? What should be the appropriate definition of dQ in this case?
