The magnetic flux passing through a metal ring varies with time `t` as: `phi_(B)=3(at^3-bt^2)T-m^2` with `a=2.00s^-3` and `b=6.00s^-2`. The resistance of the ring is `3.0Omega`. Determine the maximum current induced in the ring during te interval from `t=0` to `t=2.0s`.

Explanation

To determine the maximum current induced in the metal ring, we will follow these steps:

### Step 1: Write down the expression for magnetic flux
The magnetic flux through the metal ring is given by:
\[ \Phi_B = 3(at^3 - bt^2) \text{ T-m}^2 \]
where \( a = 2.00 \, \text{s}^{-3} \) and \( b = 6.00 \, \text{s}^{-2} \).
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