A metallic coil of N turns of radius r, resistance R, and inductance L is held fixed with its axis along a spatial uniform magnetic field `bar(B)` whose magnitude is given by `B_(0) sin(omegat)`.
Write the equation for the current i in the coil.
given that `B_(0)=1.00"tesla", N=10, r=10cm, omega=1000.0 rad s^(-1), R=10.0Omega, L-100,0mH`.

Explanation

To solve the problem, we need to find the equation for the current \( i \) in the coil subjected to a time-varying magnetic field. We'll follow these steps:

### Step 1: Understand the Magnetic Flux
The magnetic flux \( \Phi \) through the coil can be expressed as:
\[ \Phi = N \cdot A \cdot B \]
where:
...