In Figure ( a ), a circular loop of wire is concentric with a solenoid and lies
ID: 2298553 • Letter: I
Question
In Figure (a), a circular loop of wire is concentric with a solenoid and lies in a plane perpendicular to the solenoid's central axis.The loop has radius 6.27 cm. The solenoid has radius 2.00 cm, consists of 8240 turns/m, and has a current isol varying with time t as given in Figure (b), where the vertical axis scale is set by is = 1.20 A and the horizontal axis scale is set by ts = 4.2 s. Figure (c) shows, as a function of time, the energy Eth that is transferred to thermal energy of the loop; the vertical axis scale is set by Es = 100.3 nJ. What is the loop's resistance?
Explanation / Answer
Area
A=pi*r2 =pi*0.02^2
A=1.2566*10-3 m^2
From Graph B rate of change of current is
dIs/dt =1.2/4.2 =0.2857 A/s
From graph C ,power is given by rate of change of electric field is
P=dEs/dt =(100.3-20.06)/4.2 =19.1 nJ/s
Induced emf in the loop is
E=uo*n*A*(dI/dt)
E=(4pi*10-7)*(8240)*(1.2566*10-3)*0.2857
E=3.72*10-6 Volts
so resistance of the loop is
R=E2/P =(3.72*10-6)2/(19.1*10-9)
R=7.24*10-4 ohms or 0.724 mohms