In the figure below, two circular arcs have radii a = 10.0 cm and b = 5.0 cm, su
ID: 1646657 • Letter: I
Question
In the figure below, two circular arcs have radii a = 10.0 cm and b = 5.0 cm, subtend angle theta = 80.0 degree, carry current I = 3.50 A, and share the same center of curvature P. (a) Show me how you would set up the integral to solve for the magnetic fields due to current along these wires. You must show me the equation you are using, and label the important factors on a diagram for full credit.(I know there is a formula on the sheet where this is worked out for you, but I want to see you do it) (b) What is the magnitude and direction of the net magnetic field at P? (Take out of the page to be positive, and here you can just use the formula on the formula sheet if you like)Explanation / Answer
from biot savarts law we kjnow that
dB = k*Idl/r^2 [ I is current through the element of the wire of length dl at ditance r from the point, k being the constant mu/4*pi]
the direction can be found using the right hand corckscrew rule
so, magnetic field due to a loop subtending angle theta at a point is
B = integrate(k*Idl)/r^2
dl = rd(theta)
B = integrate(k*I*rd(theta))/r^2 = kI(theta)/r =
b) In the given question
i = 3.5 A
theta = 80 deg = pi*80/180
a = 10 cm
b = 5 cm
so, B = kI*Theta/b - kI*theta/a = 10^-7*3.5*pi*80(100/5 - 100/10)/180 = 48.88*10^-7 T ( out of the poage)