Question

Two circular arcs have radii a = 11.5 cm and b = 7.7 cm, subtend an angle = 74^o, carry a current I = 0.411 A, and share the same center of curvature P. What is the magnitude of the net magnetic field (in microTesla) at point P?

Answer 1

The magnetic field at the center of the circular coil is given by

that means the circualr arc subtended at angle or radian , the magnetic field =

where R = radius of the circle

Hence, magnetic field at the center of circular arc with radius a and subtended at angle 74 degree is given by

Similarly, the magnetic field at the center of circular arc with radius b and subtended at angle 74 degree is given by

a = 11.5 cm = 11.5/100 m

b = 7.7 cm = 7.7/100 m

Since both the magnetic fields are in the opposite direction (because the direction of current flowing in one arc is opposite in other)

the net magnetic field is given by

(since )   

= 107 * 100* 0.0429* 1.291 = 0.055*109 = 5.5*107 Tesla (Ans)