Help with this problem would be appreciated, steyp by step much better. I would

Question

Help with this problem would be appreciated, steyp by step much better. I would like to understand it since ive been trying it for a while already. Relevant equations: Bx=(µIa2)/2(x2+a2)3/2 A circular loop of radius 10 cm and three long straight wires carry currents of I1=60A, I2=20A, I3=10A, and I4=10A, respectively, as shown. Each straight wire is 30cm from the center of the loop. In the figure shown, the y-component of the resultant magnetic field at the center of the loop is closest to:

A)+20uT
B)-25uT
C)+25uT
D)-20uT
E)Other (show answer)

Explanation / Answer

r = 10 cm, I1 = 60 A, I2 = 20 A, I3 = 10 A, I4 = 10 A, d = 30 cm the magnetic field at the center of the loop due to I1 is -z direction the magnetic field at the center of the loop due to I2 is +z direction the magnetic field at the center of the loop due to I3 is µ_0*I3/(2*pi*d) which has y component = -µ_0*I3/(2*pi*d) * cos(45) the magnetic field at the center of the loop due to I4 is µ_0*I4/(2*pi*d) which has y component = -µ_0*I4/(2*pi*d) so y-component of the resultant magnetic field is -µ_0*I3/(2*pi*d) * cos(45) - µ_0*I4/(2*pi*d) = -µ_0*[I3*cos(45) + I4]/(2*pi*d) = -1.14*10^-5 T = -11.4 uT

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