Show a conduction loop placed near a long, straight wire carrying current i as shown. If the current increases continuously, find the direction of the induced current in the loop.

Explanation

Let us put an arrow on the loop as shows in the figure
The right- hand thumb rule shows that the positive normal to the loop is going into the plane of the diagram
Also, the same rule shows that the magnetic field at the site of the loop due ot the current is also going into the plane of hte diagram
Thus, `vec(B)` and `d vacS` are along the same direction everywhere so that the flux `Phi =intvecB
dvecS` is positive
If i increases, the magnitude of `Phi` increases
Since `Phi` is positive and its magnitude increases, `(dPhi)/(dt)` is positive
Thus `varepsilon` is nagative and hence, the current is negative
The ` varepsilon` is negative and hence, the current is negative
the current is, therefore, induced in the direction opposite to the arrow.