Why is there no induced current in a stationary loop?

There is no induced current in a stationary loop because there is no change in magnetic flux through the loop.

According to Faraday's law of electromagnetic induction, an electromotive force (EMF) is induced in a loop of wire when the magnetic flux through the loop changes. This induced EMF can cause a current to flow, creating what we call an induced current. However, if the loop is stationary and the magnetic field it is in is also constant, there is no change in magnetic flux through the loop. Therefore, no EMF is induced and no current is generated.

The magnetic flux through a loop is given by the product of the magnetic field strength, the area of the loop, and the cosine of the angle between the magnetic field lines and the normal to the loop. If the loop is stationary, the area of the loop and the angle between the field lines and the normal to the loop are constant. If the magnetic field is also constant, then the magnetic field strength is constant. Therefore, the magnetic flux through the loop is constant.

In order for an EMF to be induced, and hence a current to be generated, there needs to be a change in magnetic flux. This can occur if the magnetic field changes, if the area of the loop changes, or if the angle between the field lines and the normal to the loop changes. However, if the loop is stationary and the magnetic field is constant, none of these changes occur. Therefore, there is no change in magnetic flux, no EMF is induced, and no current is generated.

In summary, a stationary loop in a constant magnetic field experiences no change in magnetic flux. According to Faraday's law of electromagnetic induction, this means that no EMF is induced and no current is generated. This is why there is no induced current in a stationary loop.