91Ó°ÊÓ

Faraday's law states that the electromotive force (EMF) induced in the loop is equal to the rate of change of the magnetic flux through the loop. It can be calculated as \[ \varepsilon = - \frac{\Delta \Phi}{\Delta t} \] where \(\varepsilon\) is the EMF, \(\Delta \Phi\) is the change in the magnetic flux, and \(\Delta t\) is the time interval. Remember that the negative sign indicates the opposition to the change in the magnetic flux according to Lenz's law.

The magnetic flux (\(\Phi\)) is given by the product of the magnetic field (B), the area through which the field lines pass (A), and the cosine of the angle between the magnetic field and the area vector (cos(θ)). As magnetic field in this case is perpendicular to the plane of the loop, cos(θ) = 1. Thus, the magnetic flux is \[ \Phi = B \times A \] The area of the square loop is \(L^2\), so when the loop enters the magnetic field, the area inside the magnetic field is equal to the base, which is x meters (say x as variable as the loop moves with v), multiplied by side length L: \[ A = xL \] So the change in magnetic flux during the interval of time \( \Delta t \) is calculated as: \[ \Delta \Phi = B(xL) - B((x - v\Delta t)L) = BvL\Delta t \]

Next, we will apply Faraday's law to calculate the induced EMF: \[ \varepsilon = -\frac{\Delta \Phi}{\Delta t} = -\frac{BvL\Delta t}{\Delta t} = -BvL \] Here, the negative sign indicates that the induced EMF will oppose the change in magnetic flux.

Ohm's law can be used to find the induced current in the loop: \[ I = \frac{\varepsilon}{R} \] Substituting the calculated induced EMF, we get: \[ I = \frac{-BvL}{R} \] As the induced current is negative, it means that the direction of current will be anti-clockwise. So, the induced current is given by the option (B) \(B L v / R\) anti-clockwise.