Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 T. (b) Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

Question

Illustration of a shrinking circular loop in a magnetic field, depicting induced current direction.

Accepted Answer

Hi everyone today, we are going to determine the direction of the induced current of a spring that is stretched into a square loop of perimeter 200 centimeter using four rods and is placed in a uniform magnetic field of 0.8 Tesla oriented parallel to the axis of the loop. Its perimeter actually decreases over time, with a rate of 18 centimeters per second. Asteroids are actually moving closer to one another and the magnetic field itself is oriented parallel to the axis of the square loop. A. K. A. The magnetic field is kind of going into this plane right here and we need to determine the direction of the induced current relative to an observer fueling in the direction of the magnetic field itself. Okay, so the way we want to tackle this is to actually by using lenses law, and Lance is largely will give us the direction of the induced E. M. F. Where the flow of the current opposes the change in the magnetic flux. So the lenses law is given by here, the epsilon is to induce E M F minus and D uh D five B. Which is the change in the magnetic flux over time, D. T. So the direction of the induced E M F actually will correlate to the change in the magnetic flux itself. So, because we know that the loop is shrinking A. K. A. The area actually decreases as the spring itself compresses in the magnetic field, then we will know that induced E M F. Induced E will actually be in the clockwise direction because the pathetic flux is decreasing. So we know that positive flux is flux as decreasing because the loop that we have here is getting smaller and smaller. So because of that we need are induced E. M. F two B in the clockwise direction. To actually create so clockwise direction to create a field be in the opposite direction to oppose this change just like so, so we can actually also use the right hand rule by pointing the thumb our thumb in the direction of the induced field and curling the rest four of our fingers in the direction of the induced current. By using that, we can determine that are induced current needs to actually be going clockwise just like so just like so while our induced um field will actually be Yeah, just like so to make sure that we create a field B in the opposite direction, opposing the change that is happening, which is the group that's shrinking. So because of this we can determine that I induce will be going clockwise and that will correspond to option A. In our answer choice and that will be it for this particular problem. So if you guys still have any sort of confusion, please make sure to check out our other lesson videos on this topic and that will be all for this video. Thank you

Verified Solution

Key Concepts

Faraday's Law of Electromagnetic Induction

Lenz's Law

Magnetic Field Orientation