Find the magnitude of the magnetic force on a wire, which has semicircular secti

Question

Find the magnitude of the magnetic force on a wire, which has semicircular section of radius R followed by a straight section of length R as shown in the figure, carrying a current (I1)= 10 A, due to the magnetic field created by a second wire, which is perpendicular to the page, carrying a current (I2) = 10 A. (I2) flows out of the page and R = 10 cm.

Find the magnitude of the magnetic force on a wire, which has semicircular section of radius R followed by a straight section of length R as shown in the figure, carrying a current (I1)= 10 A, due to the magnetic field created by a second wire, which is perpendicular to the page, carrying a current (I2) = 10 A. (I2) flows out of the page and R = 10 cm.

Explanation / Answer

force on the circular portion will be zero as magneetic field due to i2 is tangential on the periphery force on straight portion=(muo*i1*i2/2*pi)*integral from R to 2R (dx/x) F=muo*i1*i2*ln(2)/2*pi=1.38*10^-5 N

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