Question

Use Lenz's law to determine the direction of induced current in the situations described by Fig. (a) A wire of irregular shape turning into a circular shape; (b) A circular loop being deformed into a narrow straight wire.

Answer 1

Hint: This is a question of conceptual categories to address such kinds of questions that you should be consistent with all the theories and in this question try to use the law of the right thumb to find the direction of the induced current in both situations.

Complete Step-by-Step solution:
 For figure (a):
 

According to the given information an irregular shaped wire which is under the effect of magnetic field is turning its shape into a circular shape
So, we know that when the shape of wire will increase due to which the magnetic flux through wire will change which will generate a potential difference in wire this will cause an induced EMF which generates in a wire or a coil whenever the generation of potential difference occurs due to change in magnetic flux through a wire.
Induced EMF is represented as \[\varepsilon = - \dfrac{d}{{dt}}\left( {{\phi _B}} \right)\] here ${\phi _B}$ is the flux through a coil or a wire this repetition of induced EMF shows that the induced EMF occurs always in the opposite direction of magnetic flux
Since the direction of magnetic field is outward to wire therefore the induced EMF will occur opposite to magnetic flux to maintain the rate of flux through a wire or coil i.e. inward direction to the wire
We know that \[induced{\text{ }}current\left( i \right) = \left( {\dfrac{\varepsilon }{R}} \right)\]
So, the induced EMF is the direction of outward to the wire therefore with the help of right hand thumb rule we can say that the direction of induced current will be in clockwise direction.
For figure (b):

Here according to the given information the wire with circular loop shape is deforming into a narrow straight wire so since the shape of wire is changing its shape and its surface area in the magnetic field is decreasing, so the magnetic flux through it will decrease which will generate a potential difference in the wire due to which an induced EMF will generate in wire to maintain the flow of the flux through wire
Induced EMF is represented as \[\varepsilon = - \dfrac{d}{{dt}}\left( {{\phi _B}} \right)\] here ${\phi _B}$ is the flux through a coil or a wire this repetition of induced EMF shows that the induced EMF occurs always in the opposite direction of magnetic flux to maintain the rate of magnetic flux through a wire or a coil.

Since we know that the induced EMF always generates in the opposite to the direction of magnetic flux and the magnetic flux direction in the given condition is outward to the circular loop so the direction of magnetic flux will be outwards to the circular loop wire because the rate of the magnetic flux is decreasing through the wire therefore to maintain the rate of magnetic flux induced EMF generates inwards to wire.
So by the right hand thumb rule we can say that the direction of induced current in this condition will be anticlockwise.

Note: Let's figure out what is specified in Lenz's law; this law gives guidance to the electromagnetic induced force (EMF) and current resulting from electromagnetic induction. The law offers a physical description of Faraday’s induction law’s choice of symbol, suggesting that the mediated EMF and flux shifts have opposite signs.