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Homework Statement
A circular loop of wire with radius 0.0300m and resistance 0.380Ω is in a region of spatially uniform magnetic field, as shown in the following figure(Figure 1). The magnetic field is directed into the plane of the figure. At t = 0, B = 0. The magnetic field then begins increasing, with B(t)=( 0.350T/s3)t3.
Homework Equations
ε = -N*(dΦB / dt)
The Attempt at a Solution
Area = pi*r^2 = pi(.03^2) = .0028 m^2
Magnetic field is perpendicular to plane of loop.
ΦB = (B→)⋅dA→ = BA cos(Θ)
B(t) is given at an instant where it equals 1.42 T, so solving 1.42 = .35 t^3 for t: (1.42/.35)^(1/3) = 1.59 seconds
I then reason that since t and be started at 0, at this given instant dB = 1.42 Tesla and dt = 1.59 seconds.
Since only the magnetic field changes, I can say dΦB/dt = (dB/dt)Acos(Θ)
Since Θ = 0 due to magnetic field being perpendicular to plane of loop, it simplifies to dΦB/dt = (dB/dt)A
So ε = 1*(dB/dt)A = (1.42/1.59)*.0028 = .0025 volts
However the question asks for current I in the loop, so I said ε = IR: thus ε/R = I by ohm's law
.0025 volts / .380 ohms = .0065 Amps.
This is incorrect, the correct answer was .0199 Amps and I'm not sure what I did wrong. Was I supposed to differentiate B(t) or something? I got the direction of the current in the loop correct, I understand Lemz law and recall the common right hand rule conventions. Any and all help is appreciated.