In figure ( a ), two circular loops with different currents but the same radius
ID: 1597935 • Letter: I
Question
In figure (a), two circular loops with different currents but the same radius of 4.0 cm, are centered on a y axis. They are initially separated by distance L = 3.0 cm, with loop 2 positioned at the origin of the axis. The currents in the two loops produce a net magnetic field at the origin, with y component By. That component is to be measured as loop 2 is gradually moved in the positive direction of the y axis. Figure (b) gives By as a function of the position y of loop 2. The horizontal axis is marked in increments of 2 cm, the vertical axis is marked in increments of 5 T, and the curve approaches an asymptote of By = 1.9 T as y .
(a) What is the current i1 in loop 1?
A
(b) What is the current i2 in loop 2?
A
Explanation / Answer
a )
r = radius of 4.0 cm
L = 3.0 cm
4 X 3.14 X 10-7 X 0.042 X i1 / 2 X ( 0.032 + 0.042 )3/2 = 1.9 X 10-6
i1 = 1.9 X 10-6 X ( 2 X ( 0.032 + 0.042 )3/2 / 4 X 3.14 X 10-7 X 0.042
i1 = 0.3342 A
b )
By = 0 , y = 3 cm
B1 = B2
i1 / ( 0.032 + 0.042 )3/2 = i2 / ( 0.032 + 0.042 )3/2
i2 = 1.37 A