Suppose there is a double loop of wire (making 2 turns) is in the x-y plane centered at the origin. There is also uniform magnetic field is increasing at a constant rate in the positive z-direction.Viewed from the positive z-axis, in which direction is the induced magnetic field in the loop?
Consider Lenz's law: the current induced will generate a magnetic field that opposes the +z axis. My right hand then tells me it will generate a current that is clockwise.
so the induced magnetic field in the loop will be in the negative z direction?
To determine the direction of the induced magnetic field in the loop, we can apply a variation of Faraday's law of electromagnetic induction, known as Lenz's law.
According to Lenz's law, the direction of the induced magnetic field opposes the change in the magnetic field that is causing it. In this case, the uniform magnetic field is increasing in the positive z-direction.
To apply Lenz's law, we can consider the loop as two individual loops, each with a single turn. Let's label the loops as Loop 1 and Loop 2, where Loop 1 is the inner loop and Loop 2 is the outer loop.
Now, consider the magnetic field lines passing through Loop 1. Since the magnetic field is increasing in the positive z-direction, Lenz's law tells us that the induced magnetic field in Loop 1 will loop in the opposite direction to the magnetic field lines passing through it. This means that the induced magnetic field in Loop 1 will circulate in the clockwise direction when viewed from the positive z-axis.
Next, consider the magnetic field lines passing through Loop 2. Similarly, the induced magnetic field in Loop 2 will also circulate in the opposite direction to the magnetic field lines passing through it. Therefore, the induced magnetic field in Loop 2 will also circulate in the clockwise direction when viewed from the positive z-axis.
To summarize, when viewed from the positive z-axis, the induced magnetic field in both loops will circulate in the clockwise direction.