Find the direction of induced current in the coil for the given cases.
(a) If current ‘I’ is increasing with respect to time.

 (b) If the coil is moving with velocity ‘v’ as shown.

Hint: A changing magnetic flux through the coil induces current in it. The direction of induced current can be given by Lenz law which states that direction of electric current induced in a conductor by changing magnetic field is such that the magnetic field created by induced current opposes the initial changing magnetic field.

Complete step-by-step answer:
When a magnetic field is changing through a coil, a current is generated in the coil which is known as induced current. The direction of this induced current is given by Lenz law.
Lenz law states that, “The direction of induced current due to changing magnetic field is such that it creates a magnetic field which opposes the initial changing magnetic field.”
Here, the current flowing through the wire produces a magnetic field. Direction of the magnetic field produced is given by the right hand thumb rule according to which, when we point the thumb of our right hand in the direction of current, the curled fingers indicate the direction of the magnetic field. Therefore, on the right hand side of the conductor, the magnetic field is into the screen as shown in figure below.

(a) Magnetic field due to a straight wire is linearly proportional to electric current through it. Since current is increasing, the magnetic field also increases which results in induction of current in the coil. Applying Lenz law, the direction of induced current through the coil is anti-clockwise.

(b) Magnetic field due to a straight wire at any point is inversely proportional to its separation from the wire. Since, the coil is moving away from the wire, the magnetic field through it is decreasing. Therefore, a clockwise current is induced in the coil according to Lenz law.


Note: Electric current is induced in the coil only if the magnetic field through it changes. If the magnetic field does not change through the coil, no current is induced in it.
Also if the surface of the coil is placed parallel to the direction of magnetic field, no current is induced in the coil.