A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8 cm `s^(-1)` in the positive x-direction in an environment containing a magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of `10^(-3) T cm^(-1)` along the negative x-direction (that is it increases by `10^(-3) T cm^(-1 )`as one moves in the negative x-direction), and it is decreasing in time at the rate of `10^(-3) T s^(-1)`. Determine the direction and magnitude of the induced current in the loop if its resistance is 4.50 `mOmega`.

Explanation

To solve the problem step by step, we will analyze the situation involving the square loop, the magnetic field, and the induced current.

### Step 1: Understand the given parameters
- **Side of the square loop (s)**: 12 cm = 0.12 m
- **Velocity of the loop (v)**: 8 cm/s = 0.08 m/s
- **Gradient of the magnetic field (dB/dx)**: \(10^{-3} \, \text{T/cm} = 10^{-1} \, \text{T/m}\)
- **Rate of change of magnetic field with time (dB/dt)**: \(10^{-3} \, \text{T/s}\)
- **Resistance of the loop (R)**: 4.5 mΩ = \(4.5 \times 10^{-3} \, \Omega\)
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