Current Induced in Loops by Resistance Change

[Hypercubes]

Homework Statement

a). If the resistance of the resistor in Fig. 21-46 is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop? b). What would it be if the small loop were placed outside the larger one, to the left?

Homework Equations

The Attempt at a Solution

a) Since the current in the outer loop induces a magnetic field, which in turn induces a current in the inner loop, and Lenz's Law states that this must flow in the opposite direction, shouldn't it flow clockwise? According to the answer key this is incorrect.

Any help would be much appreciated.

 

[PeterO]

Homework Statement

a). If the resistance of the resistor in Fig. 21-46 is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop? b). What would it be if the small loop were placed outside the larger one, to the left?

Homework Equations

The Attempt at a Solution

a) Since the current in the outer loop induces a magnetic field, which in turn induces a current in the inner loop, and Lenz's Law states that this must flow in the opposite direction, shouldn't it flow clockwise? According to the answer key this is incorrect.

Any help would be much appreciated.

Lenz's law says the induced current is in a direction to opposite the change in field, not necessarily the field itself.

If the field created by the outer loop is getting stronger, the induced current will be in the opposite direction as the current in the outer loop
If the field created by the outer loop is getting weaker, the induced current will be in the same direction as the current in the outer loop.

So what is happening in this example?

 

[Hypercubes]

Thanks, that makes sense.

So in essence, this stems from the negative sign in Faraday's Law, doesn't it?

[itex]\varepsilon=-N\frac{\Delta(BA)}{\Delta t}[/itex]

Since the magnetic field B is weakening, the delta B is negative, thus cancelling out the negative sign.

 

[PeterO]

Thanks, that makes sense.

So in essence, this stems from the negative sign in Faraday's Law, doesn't it?

[itex]\varepsilon=-N\frac{\Delta(BA)}{\Delta t}[/itex]

Since the magnetic field B is weakening, the delta is negative, thus cancelling out the negative sign.

Now you thinking! Those minus signs are always there for a reason.

 

[rwisz]

Your reasoning is correct. According to Lenz's Law, the induced current in the inner loop will flow in the opposite direction to the change in the magnetic field. In this case, as the resistance of the resistor increases, the magnetic field will decrease, and therefore the induced current in the inner loop will flow clockwise. The answer key may have a typo or a mistake. It is important to always use your own reasoning and understanding to arrive at the correct solution.