In Figure ( a ), two circular loops with different currents but the same radius
ID: 2239282 • Letter: I
Question
In Figure (a), two circular loops with different currents but the same radius of2.0cm, are centered on ayaxis. They are initially separated by distanceL=1.5cm, with loop 2 positioned at the origin of the axis. The currents in the two loops produce a net magnetic field at the origin, withycomponentBy. That component is to be measured as loop 2 is gradually moved in the positive direction of theyaxis. Figure (b) givesByas a function of the positionyof loop 2. The horizontal axis is marked in increments of1cm, the vertical axis is marked in increments of25
Explanation / Answer
(a) L = 1.5 cm
uo*R^2*I1/(2*(L^2+R^2)^(3/2)) = 9 uT
4pi*10^-7*0.02^2*I1/(2*(0.015^ + 0.02^2)^(3/2)) = 9*10^-6
I1 =(2*(0.015^ + 0.02^2)^(3/2))9*10^-6/(4pi*10^-7*0.02^2)
I1 =0.55953 A
(b)
By = 0 at y = 3 cm
B1 = B2
I1/(1.5^2 + 2^2)^(3/2) = I2^2/(3^2+2^2)^(3/2)
I2 = I1*(13/6.25)^(3/2)
I2 = 0.55953*(13/6.25)^(3/2)
I2 =1.678 A