A conducting loop with area 0.14 m2 and resistance 10 Ω lies in the x-y plane. A spatially uniform magnetic field points in the z direction. The field varies with time according to Bz=at2−b, where a = 3.0 T/s2 and b = 8.8 T . Find the loop current when Bz = 0.
The emf is given by:
EMF = V = -d(B*A)/dt
where, B = field strength and
A = area perpendicular to the field
Current = I = V/R
So you have a loop of wire with resistance R and radius r.
The B field is given by B = at^2 - b.
A = pi*r^2
BA = pi*r^2*(at^2 - b)
V = -d(BA)/dt = -pi*r^2*(2at)
I = -pi*r^2*(2at)/R
You need to find t such that B= 0
0 = at^2 - b
t = sqrt(8.8/3) = 1.71 s
Now substitute that value of t in the equation for I
I = - A*(2at)/R
= - 0.14*(2*3*1.71)/10
= - 0.14
A conducting loop with area 0.14 m2 and resistance 10 Ω lies in the x-y plane....
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