A long straight wire carrying a 3.0 A current enters a room through a window 1.5 m high and 1.0 m wide.The path integral around the window frame has the value:

Question

A long straight wire carrying a 3.0 A current enters a room through a window 1.5 m high and 1.0 m wide.The path integral  around the window frame has the value:

Quizplus · Accepted Answer

The path integral around the window frame can be found by summing the magnetic field contributions at each point along the frame. At the top and bottom of the frame, the magnetic field is perpendicular to the frame and has magnitude:
B = μ0I/2πr
Where μ0 is the permeability of free space (4π×10^-7 Tm/A), I is the current, and r is the distance from the wire to the frame. At the left and right sides of the frame, the magnetic field is parallel to the frame and has magnitude:
B = μ0I/2πd
Where d is the width of the frame. Using these equations and the dimensions given in the problem, we can calculate the path integral:
11eab079_9794_47df_a51f_79ea4778578d_TB6585_12 = 2(Btop + Bbottom)×h + 2(Bleft + Bright)×d
= 2(μ0I/2π(1.5 m) + μ0I/2π(1.5 m))×1.0 m + 2(μ0I/2π(1.0 m))×1.5 m
= 3.8×10^-6 Tm (or 3.8 mTm) = 3.8 mTm
Therefore, the best choice is (D), 3.8 mTm.

A Long Straight Wire Carrying a 3