Question

Suppose we have an infinitely long wire that is smoothed out into a quarter arc. In other words, the wire runs from y = +[infinity] to the point (0, b), then joined by a circular arc with radius b (centered at the point P(b, b)), continue on from (b, 0) to x = +[infinity], with b = 0.76 m. What is the magnitude of the magnetic field B (in T) at the point P(b, b) if the current is 2.9 A?

Answer 1

The magnetic field B is 1.34x10^-5 T

Step-by-step explanation:

The semi-infinite current along the y axis and in the magnetic field is equal to:

B1=((uo*I)/2)/(2*π*b)

the semi-infinite current along the x axis is equal to:

B2=((uo*I)/2)/(2*π*b)

the quart circle current is equal to:

B3=((uo*I)/4)/(2*π*b)

Btotal=B1+B2+B3

replacing:

Btotal=((uo*I)/2)/(2*π*b) + ((uo*I)/2)/(2*π*b) + ((uo*I)/4)/(2*π*b)

Btotal=((uo*I)/b)*((1/(4*π))+(1/(4*π))+(1/8))

Btotal=((4*π*10^-7*2.9)/0.76)*(0.28)=1.34x10^-5 T