Current i1 flows through the circular loop of wire in the...

Current i1 flows through the circular loop of wire in the center, as shown in the figure. The direction of the current is counterclockwise when viewed from above. (The grey bars, which indicate the central axes of the loops, have been added to help you visualize the geometry of the problem.) If this current increases with time, what are the directions of the currents i2, i3, and i4 induced in the three adjacent circular loops of wire? Loop 3, whose current is i3, is located above loop 1, whose current is i1. In the answers, "cw" stands for clockwise, and "ccw" stands for counterclockwise, both when viewed from above, and "0" means no induced current.

Transcript

00:01 So this is going to be a little difficult because we're going to have to use right -hand rule and using right -hand rule when you're not next to someone in person, or at least explaining it can be a bit difficult, but we'll get through it.

00:12 So we have this configuration of circular loops of wires.

00:19 And so there's these bars that represent the central axes of the wires.

00:25 So we have one right here.

00:30 And we have this loop.

00:31 We will call this i1 and then we have this central axis up here another loop of wires so this is directly above i1 and we will call this current i3 and then we have two loops of wires to either side of i1 so we have one right here and one right and the one to the left is i2 and the one to the one to the left is i2 and the one to the the right is i4.

01:10 So we're told that the direction of current in loop i1 is counterclockwise.

01:20 And so i3 is directly above it and i2 and i4 are directly to the sides.

01:28 And so those bars don't represent anything other than a hypothetical axis to help us imagine something to wrap our fingers around for right -hand rule.

01:37 And so we are saying that current i1 is increasing, right? and so we want to know what induced currents i3, i2, and i4 produce due to i1 increasing.

01:58 But first, we have to realize what's happening when i1 increases.

02:03 So we know that current in a loop produces a magnetic field.

02:08 And the magnetic field produced by current i1, wrap your fingers around the loop in the direction of the current and around that imaginary axis.

02:17 Your thumb should point upwards because this loop is producing a b field upwards.

02:23 So we have something like this, right? it's producing some loop like this.

02:32 Same thing on the other side.

02:38 Sorry for the horrible circles, but they should get the point across.

02:41 So the b field is producing something like this because it is going, up and then back around through the loop.

02:52 And so that current is increasing, which means that this b field, b1, is also increasing.

03:05 And so if that b field is increasing, we know that currents will be induced in loops 3, 2, and 4...

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