The magnetic flux threading a metal ring....?

Question

...varies with time t according to Flux = 3at^3 - bt^2, with a = 1.5s^-3 m^2T, and b = 6.1 s^-2m^2T. The resistance of the ring is 2.7 ohms. Determine the maximum current induced in the ring during the interval from t1 = -3.6 s to t2 = 1.6 s.

I began this problem by doing the derivative of the equation given for flux. The new derived equation I obtained was t(13.5t - 12.2). I know that Emf = dFlux/dt. I just don't know what the t in my derived flux equation represents, t1 or t2, or if I have to use both and subtract. In any case, I know to find current you just divide the induced emf by the resistance. Any help would be appreciated.

Answer 1

F=3at^3 - bt^2
emf=dF/dt=9at^2-2bt
the maximum emf will either be at a end point of interval or when d(emf)/dt=18at-2b=0 or t=b/(9a)=6.1/(9*1.5) =.45 sec which is in the interval if I have done the math right.

after thought:
for t=-3.6 sec the emf=(1.5*3.6^2+6.1*3.6)T which will be the max in the interval. the value above is the minimum emf

Answer 2

In physics, a magnetic field is that element of the electromagnetic field that exists at the same time as there's a replacing electric powered field. A replacing electric powered field will be led to by using the move of an electrically charged merchandise, as in an electric powered modern-day; or a blend of the orbit of an electron round an atom and the spin of electrons themselves, as in an enduring magnet. Magnetic flux, represented by using the greek letter phi, is a level of volume of magnetism, taking account of the flexibility and the quantity of a magnetic field. The SI unit of magnetic flux is the weber (in derived gadgets: volt-seconds), and the unit of magnetic flux density is the weber in step with sq. meter, or tesla. Description: The flux with the help of a element of section perpendicular to the course of magnetic field is given by using the manufactured from the magnetic field density and the area element. better in many circumstances, magnetic flux is defined by using a scalar manufactured from the magnetic field density and the area element vector. Gauss's regulation for magnetism, it really is between the 4 Maxwell's equations, states that the completed magnetic flux with the help of a closed floor is 0. This regulation is a outcome of the empirical remark that magnetic monopoles do no longer exist or are not to any extent further measureable.