Using Lenz's law, determine the direction of the current in re...

Question

Using Lenz's law, determine the direction of the current in resistor ab of Fig. E29.19 when (a) switch S is opened after having been closed for several minutes; (b) coil B is brought closer to coil A with the switch closed; (c) the resistance of R is decreased while the switch remains closed.

Accepted Answer

Hello, fellow physicist today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Explain the effect of the following actions on the current through the resistor PQ I. The switch S is initially in a on state and is suddenly turned off I I with the switch in the on position, coil Q is moved away from coil pii I with switch S in the on state, the resistance of R is increased. OK. So for this particular problem, it appears that we're asked to solve for three separate answers. So we're first asked to figure out what the effect on the following actions on the current through resistor PQ will be if I, the switch S is in the on position and is suddenly turned off. And for I, I, we're considering with the switch in the on position, coil Q is moved away from coil P. And for II I, we're asked to consider with the switch S in the on position, the resistance of R is increased. Awesome. So let's look at our figure that's provided to us in the problem itself. So as we can see, we have Q or the coil Q and it's wrapped around a rod shape. And we can see from going from the far left of our figure going down, we have P and then our jagged line which represents the resistor going to P sorry. So for P to Q, so it goes P resistor to queue and then looking at the right side of our figure, we have coil P, which is a similar situation to Q. We have it wrapped around a rod shape and then we have our capital R resistor represented by a jagged line going down to the bottom of our figure to the negative end of our battery. And then going to the right, we have our positive end of our battery leading up to the switch indicated by an S. And then, as you could see in this particular picture in our figure, the switch is open and going up towards coil pee and it goes around as such. OK. And now that we have an idea of what's going on in our figure, let's look over our multiple choice answers for parts II I and II I to see what our final answer set might be. So A is P to Q and P to Q and Q to P B is Q to P Q to PQ to PC is P to QQ to P and P to Q and finally, D is Q to PP to Q and P to Q. OK. So first off, we need to recall and apply Lenz's law which states that the flux of the induced current tends to oppose the change in the flux. Now, we need to also recall and apply and use the right hand rule for a solenoid. We need to curl our fingers on our right hand in the direction of the current and our thumb will point in the direction of the magnetic field. So with this in mind, we can start solving for part I. So let us note that the magnetic field of coil P will point to the left in the direction towards Q. Let's also note that our thumb will point to the left and the current flows from higher to lower potential. So from the positive end of our battery to the negative end of our battery, so the magnetic field points to the left when the switch is closed. So the magnetic field of coil P will decrease when the switch is opened. Therefore, if we use lens's law, in order to oppose the decrease in the flux, the current that is induced within coil Q must produce a magnetic field that is directed from the left direction in order to strengthen the magnetic flux that is decreasing in order to produce a magnetic field from the left direction and the current in the circuit with coil Q must follow through the resistor in the direction from drum roll, Q to P Woo Woo, we solve for part I. So once again, it's Q two P. So moving right along to solve for part I I, we must note that the magnetic field from the current through coil P will point towards the direction of coil Q. In the left direction, the magnetic field will be stronger at points near coil P and will weaken for points located far from coil P. And the flux flowing through coil Q will decrease. Therefore, if we use lens's law by opposing the decreasing flux, the current from the magnetic field from the left and the current in the circuit with coil Q must flow through the resistor in the direction from drum roll Q to P. Oh we're moving right along here. So to solve for part II I OK. So we must note that the magnetic field of coil P will point from the left towards coil Q. When the switch is closed, the current in coil P will decrease when R is increased, which just to remember that R is the resistor. So when this is increased, which will lead to a decrease in the magnetic field from coil P. Therefore, by using Lenz's law, the direction of the magnetic field of the induced current in coil Q is to the left in order to oppose the decrease in the flux to the left. So this in return will produce a magnetic field that is directed from the left to the direction of the current in the circuit with coil Q which must then flow through the resistor R in the direction Q two P. Well, once we did it, we solved for all of our answers. So ultimately, in order to solve for a practice problem like this, we must have a strong understanding of the conceptual physics that are involved with circuits and solenoids. So if circuits and soil like solenoids that this like conceptual physics was ex like difficult to you to understand, I would suggest going back to your textbook and reading the chapter again, maybe watch a few other videos about circuits and solenoids. They get a really strong understanding of the conceptual physics. And once you have a really good understanding of what's going on then solving a problem like this will be a breeze. So with that said, looking at our multiple choice answers, the correct answer has to be the letter B. So I is Q to pi, I is Q to P and II, I is Q to P and that's it we've solved for this practice problem. Hooray. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Using Lenz's law, determine the direction of the current in resistor ab of Fig. E29.19 when (a) switch S is opened after having been closed for several minutes; (b) coil B is brought closer to coil A with the switch closed; (c) the resistance of R is decreased while the switch remains closed.

Key Concepts

Lenz's Law

Electromagnetic Induction

Magnetic Flux

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