The figure below shows two current segments. The lower segment carries current i
ID: 1410469 • Letter: T
Question
The figure below shows two current segments. The lower segment carries current i_1 = 0.48 A and includes a circular are with radius 7.3 cm, angle 180 degree, and center point P. The upper segment carries current i_2 = 2i_1 and includes a circular are with radius 4.0 cm, angle 120 degree, and the same center point P. What are the magnitude and direction (into or otherwise of the page) of the net magnetic field B for the indicated current directions? What are the magnitude and direction (into or otherwise of the page) of B if i_1 is reversed?Explanation / Answer
magnetic field due to arc = k * theta * current / radius
180 degree = pi radian
120 degree = pi * 120 / 180 radian
120 degree = pi * 0.67 radian
magnetic field due to upper arc = 10^-7 * 2 * 0.48 * pi * 0.67 / 0.04
magnetic field due to upper arc = 5.05168 * 10^-6 T
magnetic field due to lower arc = 10^-7 * 0.48 * pi / 0.073
magnetic field due to lower arc = 2.0657 * 10^6 T
since the direction of the magnetic field will be opposite so,
net magnetic field = 2.0657 * 10^-6 - 5.05168 * 10^-6
net megnetic field = -2.98598 * 10^-6 T
magnitude = 2.98598 * 10^-6 T or 2.98598 uT
since the sign is negative direction will be into the page
if the direction of the i1 is reversed then
net magnetic field = -2.0657 * 10^-6 - 5.05168 * 10^-6
net magnetic field = -7.11738 * 10^-6 T
magnitude = 7.11738 * 10^-6 T or 7.11738 uT
direction will be into the page