Lenz Law - Find the direction of induced current

 In this problem, you are asked to find the direction of induced current in the loop (shown in Red). The situation is the loop is beside a long wire (shown in dark blue) in which current is increasing in (a) and current is decreasing in (b).

I will give you chance to guess so you need to scroll to see the answer.

Lenz law is one of the toughest part in high school/junior college physics. I still get a bit nervous when student ask me 😓. Some always ask me strange question where I feel not so sure. 😊

Below

is

the 

answer

The answer is both CCW (counter clockwise). Why so? Let's do stepwise analysis:

1. Let us try to find the direction of magnetic field from a long wire. We apply the right hand grip rule, where thumb is in the direction of current and fingers are in the direction of magnetic field. Hope you can figure that it is out of page above the long wire and into the page below the wire.
2. Let us now see the magnetic field inside the loop. 
1. For (a) magnetic field is into the page and increasing due to increase of current.
2. For (b) magnetic field is out of the page and decreasing due to decrease of current
3. Induction Response: According to the Lenz law, the induction is such that it resist the change. So to do that:
1.  For (a) the induced magnetic field (shown in Red) will be against the magnetic field from the wire so that it tries its best to decrease it. Once again. The magnetic field from wire increase, the induction is such that it will oppose it hence reverse direction
2. For (b) the induced magnetic field (shown in Red) will be in same direction of the magnetic field from the wire so that it tries its best to keep the magnetic field the same. Once again. The magnetic field from wire decrease, the induction is such that it will help keep the same so it will be in same direction.
4. Now only focus on the induced magnetic field (shown in Red). We will again apply the same right hand grip rule. But with thumb in direction of magnetic field and fingers in direction of current. (interestingly the right hand grip rule can be applied both ways, thumb in direction of current or thumb in direction of magnetic field). Now for the answer"
1. For (a): Applying the right hand grip rule, with thumb out of the page, the fingers are in CCW (counter clock wise), Hence the current is in counter clockwise direction
2. For (b): exactly the same argument. Hence CCW

THE END