Consider a spiral of 20 turns with inner radius R and outer radius 2R. If the current is i, find magnetic field at the center of spiral
From Biot-Savart law-dB=mu(idl)/4pi*x^2
The Attempt at a Solution
Integration seems like a good option. x is continuously increasing from R to 2R, dl=xdθ. Now I'm confused as how to combine integrating dl and x...I've been thinking the whole day and turned up nothing. An interesting side question I got during the process was how to find the length of a wire used to make a spiral such as this- I feel this is somehow key to solving this problem but I'm not sure. If there is an easier method than a full blown integration, please let me know. Note- I know all the standard results such as the formula for magnetic field due to a loop, wire, arc etc. and they can be used directly if needed but I don't see anyway this can be done.
Any ideas on how to proceed with the integration or otherwise?
Also, I apologize in case I'm not able to return soon and thank you for helping me since I am buried under a huge pile of coursework- I hope you know I'm deeply grateful for the help. Thank you very much.